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Science & Engineering Calculators

Mechanics, energy, circuits and solutions — with the idealisation each formula rests on stated rather than hidden. All 295 are free and run in your browser. Each one shows the formula behind the result.

Speed Distance Time Calculator

Any one of the three from the other two, in four units.

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Velocity Calculator

Final velocity under constant acceleration, with the distance.

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Acceleration Calculator

Acceleration in m/s² and in g, which is the legible one.

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Free Fall Calculator

Fall speed and time, with the air resistance caveat stated.

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Projectile Motion Calculator

Range, height and flight time, and why 45° is optimal.

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Force Calculator

F = ma, in newtons, kilograms-force and pounds-force.

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Kinetic Energy Calculator

½mv², and why doubling speed quadruples the damage.

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Potential Energy Calculator

mgh, and how little food energy lifting actually costs.

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Work Calculator

W = Fd cos θ, including the case that comes out zero.

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Power Calculator

Watts, kilowatts and horsepower, with a running cost.

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Momentum Calculator

Momentum, impulse, and the principle behind crumple zones.

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Torque Calculator

Turning force, in newton-metres and pound-feet.

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Density Calculator

Density, mass or volume, and whether it floats.

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Pressure Calculator

From a force on an area, or from a depth of fluid.

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Resistor Calculator

Series and parallel totals for up to four resistors.

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Capacitor Calculator

Series and parallel, which are the reverse of resistors.

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Voltage Divider Calculator

Output voltage, current and the power each resistor dissipates.

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LED Resistor Calculator

The series resistor, rounded up to a standard value.

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Battery Life Calculator

Runtime with a derating factor, because the ideal figure never happens.

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Transformer Calculator

Turns ratio, secondary voltage and current, with power conserved.

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RC Time Constant Calculator

τ = RC, with the charging percentages and the filter cutoff.

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Inductance Calculator

Reactance at frequency, and where L and C cancel.

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Power Factor Calculator

Real against apparent power, and the current it costs.

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Molarity Calculator

Moles per litre of solution — not of solvent.

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Dilution Calculator

M₁V₁ = M₂V₂, with the diluent volume you actually need.

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Ideal Gas Law Calculator

PV = nRT, solving for whichever term is missing.

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pH Calculator

pH, pOH and both ion concentrations, on a log scale.

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Half-Life Calculator

Exponential decay, and why it never reaches zero.

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Percent Yield Calculator

Actual over theoretical, and what a figure above 100 means.

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Boiling Point Calculator

Water's boiling point at altitude, from the pressure.

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Molar Mass Calculator

Any formula, with brackets, hydrates and percent composition.

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Moles to Grams Calculator

Mass, moles and particle count, in either direction.

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Percent Composition Calculator

Mass share of each element, totalling exactly 100.

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Empirical Formula Calculator

From percentages to formula, without rounding 1.5 to 2.

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Limiting Reagent Calculator

Fewest equivalents, not fewest moles.

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Atom Economy Calculator

How much reactant mass can reach the product at all.

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Molality Calculator

Per kilogram of solvent — not per litre of solution.

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Normality Calculator

Equivalents per litre, and why the factor depends on the reaction.

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PPM Calculator

Parts per million, with the mg/L approximation named.

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Mole Fraction Calculator

Dimensionless ratios that always sum to one.

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Serial Dilution Calculator

Every step in the series, with the compounding shown.

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Boiling Point Elevation Calculator

ΔT = i·Kb·b, with the van 't Hoff factor made explicit.

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Freezing Point Depression Calculator

Why road salt works, quantified.

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Osmotic Pressure Calculator

Π = iMRT, and the figures are larger than you expect.

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Raoult's Law Calculator

Vapour pressure lowering, in proportion to mole fraction.

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Combined Gas Law Calculator

P₁V₁/T₁ = P₂V₂/T₂, with kelvin handled for you.

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Boyle's Law Calculator

PV constant: halve the volume, double the pressure.

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Charles's Law Calculator

V/T constant, and only in kelvin.

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Dalton's Law Calculator

Partial pressures from mole fractions.

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Graham's Law Calculator

Effusion rates, as the inverse square root of molar mass.

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pOH Calculator

pOH, pH and both ion concentrations, with the 14 explained.

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Henderson-Hasselbalch Calculator

Buffer pH, and where the buffer stops buffering.

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Weak Acid pH Calculator

Solved exactly, without the x ≪ C approximation.

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Titration Calculator

Equivalence by equivalents, not by moles.

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Specific Heat Calculator

q = mcΔT, in joules and calories.

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Gibbs Free Energy Calculator

ΔG = ΔH − TΔS, with the unit mismatch handled.

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Arrhenius Equation Calculator

Rate constants, and where the 'doubles per 10 degrees' rule comes from.

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Equilibrium Constant Calculator

Kp from Kc, with Δn counting gases only.

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Nernst Equation Calculator

Cell potential away from standard conditions, plus ΔG and K.

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Electrolysis Calculator

Faraday's law: mass deposited from charge passed.

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Beer-Lambert Law Calculator

A = εlc, with the linearity limit flagged.

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Carbon Dating Calculator

Radiocarbon age from the fraction of carbon-14 left.

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Nuclear Binding Energy Calculator

Mass defect and binding energy per nucleon, from atomic mass.

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Photon Energy Calculator

Energy, wavelength and frequency, from whichever you know.

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Rydberg Equation Calculator

Hydrogen spectral lines from any pair of energy levels.

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de Broglie Wavelength Calculator

Matter wavelength for an electron, proton or anything else.

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Effective Nuclear Charge Calculator

Zeff by Slater's rules, with the screening broken down.

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Solubility Product (Ksp) Calculator

Molar solubility from Ksp, for any salt stoichiometry.

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Common Ion Effect Calculator

How far a shared ion suppresses solubility.

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Reaction Quotient Calculator

Compare Q to K and see which way a reaction runs.

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Integrated Rate Law Calculator

Zero, first and second order, with half-life and the linear plot.

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Relative Standard Deviation Calculator

RSD and coefficient of variation for replicate measurements.

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Retention Factor (Rf) Calculator

Rf from a TLC plate, with what the value implies.

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Calibration Curve Calculator

Least-squares standard curve, then read an unknown off it.

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Degrees of Unsaturation Calculator

Rings plus π bonds, straight from a molecular formula.

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Gas Density Calculator

Density from molar mass, pressure and temperature.

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Clausius-Clapeyron Calculator

Vapour pressure at a second temperature.

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Bond Energy Calculator

Estimate ΔH from bonds broken and bonds formed.

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Chemical Equation Balancer

Any equation, including the redox ones that take a page by hand.

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Stoichiometry Calculator

Grams to moles to moles to grams, through the mole ratio.

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Electron Configuration Calculator

Aufbau order, with the elements that break it built in.

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Molecular Geometry Calculator

VSEPR shape, hybridisation and bond angle from two counts.

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Ionic Strength Calculator

I = ½Σcz², where charge counts squared.

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Activity Coefficient Calculator

Debye-Hückel γ, and where it stops being reliable.

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Molarity from Percent Calculator

Turn a reagent bottle label into a usable molarity.

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Solution Mixing Calculator

Final concentration when two solutions are combined.

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Molar Conductivity Calculator

Λm = κ/c, plus the degree of dissociation.

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Water Hardness Calculator

Calcium and magnesium as CaCO₃, in every unit used.

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Mean Free Path Calculator

How far a molecule gets between collisions.

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Nuclear Decay Product Calculator

What a nuclide becomes, for every decay mode.

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Radiation Dose Calculator

Gray to sievert, with the radiation weighting factor.

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Lattice Energy Calculator

Born-Haber cycle, for the one term nobody can measure.

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Enthalpy of Solution Calculator

Two huge numbers nearly cancelling, which is the point.

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Michaelis-Menten Calculator

Velocity, saturation and catalytic efficiency.

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Lineweaver-Burk Calculator

Vmax and Km from a double-reciprocal fit.

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Buffer Recipe Calculator

How much acid and base to weigh out for a target pH.

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Redox Half-Reaction Balancer

Water, protons and electrons, in the right order.

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DNA Concentration Calculator

A₂₆₀ to µg/mL, with purity ratio and melting temperature.

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Protein Concentration Calculator

A₂₈₀ to mg/mL, and when that stops working.

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NMR Chemical Shift Calculator

ppm to hertz, and why only one of them is portable.

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Titration Curve Calculator

pH at any point, including the equivalence point that is not 7.

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Crystal Field Splitting Calculator

High spin or low spin, and the colour that follows.

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Centripetal Force Calculator

F = mv²/r, with the g-force it works out to.

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Angular Velocity Calculator

RPM, rad/s, degrees and period, all at once.

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Moment of Inertia Calculator

Seven standard shapes, with rotational energy.

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Simple Harmonic Motion Calculator

Period, frequency and energy for a mass on a spring.

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Pendulum Calculator

Period from length — and how wrong the formula goes.

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Hooke's Law Calculator

F = kx, and the energy that goes with it.

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Friction Calculator

Friction on the flat or a slope, with the angle of repose.

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Gravitational Force Calculator

Newton's law of gravitation, with field strength.

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Escape Velocity Calculator

Escape and orbital speed for any body, plus its black-hole radius.

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Wave Speed Calculator

v = fλ, solved for whichever you are missing.

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Doppler Effect Calculator

The shift you actually hear, source and observer separately.

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Decibel Calculator

Intensity to dB, and what that actually sounds like.

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Standing Wave Calculator

Harmonics on a string or in a pipe, open or stopped.

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Snell's Law Calculator

Refraction angle, with the critical angle and TIR.

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Lens and Mirror Calculator

1/f = 1/dₒ + 1/dᵢ, with what the image actually looks like.

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Thermal Expansion Calculator

Linear, area and volume — with the right multiple of α.

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Heat Conduction Calculator

Q/t = kAΔT/d, with the R-value.

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Carnot Efficiency Calculator

The ceiling no engine gets past, and the heat-pump COP.

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Coulomb's Law Calculator

Electrostatic force, and how far it beats gravity.

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Electric Field Calculator

Point charge or parallel plates, in N/C and V/m.

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Magnetic Force Calculator

F = qvB·sinθ, with the radius of the curl.

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Time Dilation Calculator

Lorentz factor, dilated time and contracted length.

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Photoelectric Effect Calculator

KEmax = hf − φ, and the threshold that broke classical physics.

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Bernoulli Equation Calculator

Pressure along a streamline, and why faster means lower.

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Reynolds Number Calculator

Laminar, transitional or turbulent.

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Terminal Velocity Calculator

Where drag balances weight and falling stops accelerating.

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Hydrostatic Pressure Calculator

P = ρgh, in gauge and absolute.

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Buoyancy Calculator

Floats, sinks, or hangs exactly where you put it.

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Flow Rate Calculator

Continuity — narrow the pipe, speed up the fluid.

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Poiseuille's Law Calculator

The fourth power on radius that dominates everything.

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Specific Gravity Calculator

Density as a ratio, plus the API petroleum scale.

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Drag Force Calculator

Force goes as v², power goes as v³.

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Impulse Calculator

Why airbags work — same impulse, longer time, smaller force.

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Elastic Collision Calculator

Both limiting cases, with the energy lost in each.

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Inclined Plane Calculator

a = g(sin θ − μ cos θ), with the forces broken out.

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Banked Curve Calculator

The angle that needs no friction at all.

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Tension Calculator

T = m(g + a) — why lifts feel heavy then light.

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Beat Frequency Calculator

The throbbing two close notes make.

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Diffraction Grating Calculator

d sin θ = mλ, with the orders that actually fit.

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Stefan-Boltzmann Calculator

Radiated power as T⁴, with Wien's peak wavelength.

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Solenoid Calculator

B = μ₀nI — turns per metre, not total turns.

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RLC Impedance Calculator

Impedance, phase and the resonance a tuner exploits.

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Mass-Energy Equivalence Calculator

E = mc², in joules, kWh and tonnes of TNT.

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Compton Scattering Calculator

The wavelength shift that proved photons carry momentum.

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Depth of Field Calculator

Near limit, far limit and the sensor that changes both.

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Hyperfocal Distance Calculator

Focus here and everything to infinity stays sharp.

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Field of View Calculator

How wide a lens really sees, in degrees and in metres.

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Crop Factor Calculator

Equivalent focal length and the aperture rule everyone gets wrong.

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Exposure Triangle Calculator

Change one setting, find the shutter speed that keeps it even.

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Video File Size Calculator

Bitrate times duration. Resolution does not enter into it.

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Video Bitrate Calculator

The bitrate that fits, and whether it is enough.

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Frame Rate & Slow Motion Calculator

Shoot at 120, play at 24, get five times the runtime.

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BPM to Delay Time Calculator

Every note value in milliseconds, from one tempo.

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Note Frequency Calculator

Frequency to note, note to frequency, with cents.

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Decibel Distance Calculator

6 dB quieter every time the distance doubles.

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Speaker Impedance Calculator

Series adds, parallel divides, and parallel is how amps die.

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Audio File Size Calculator

Sample rate, bit depth, channels, duration. That is all of it.

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Tyre Size Calculator

The middle number is a percentage, not a measurement.

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Gear Ratio Calculator

Engine speed at road speed, through the gearbox and the tyres.

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Towing Capacity Calculator

Nose weight comes off the car's payload, not the trailer's.

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EV Range Calculator

Cold and speed, which the WLTP figure does not include.

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Resistor Series & Parallel Calculator

Parallel is always below the smallest. That is the check.

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Inductor Calculator

Reactance, energy and the L/R time constant.

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LC Resonance Calculator

Where the reactances cancel, and how sharply.

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Impedance Calculator

Magnitude and phase — they do not simply add.

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Three-Phase Power Calculator

The √3 is geometry, not a safety margin.

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Circuit Breaker Size Calculator

The breaker protects the wire, not the appliance.

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Conduit Fill Calculator

Two cables have the tightest limit. Not a typo.

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Motor Amperage Calculator

Sized to the surge, not the running current.

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Heat Loss Calculator

Fabric plus ventilation, with the assumption stated.

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Heat Pump Calculator

COP, running cost, and the Carnot ceiling above it.

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Radiator Size Calculator

At heat pump temperatures, output more than halves.

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Duct Size Calculator

Velocity is what makes ductwork audible.

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Water Heating Calculator

Water's heat capacity is why this costs so much.

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Battery Bank Calculator

Usable capacity, not nameplate. The gap is enormous.

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Inverter Size Calculator

Sized by the surge, and the DC current will surprise you.

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Electricity Cost Calculator

The things left on beat the things used briefly.

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Heat Transfer Calculator

R-value and U-value are the same physics, inverted.

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Wall U-Value Calculator

R-values add. U-values never do.

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Latent Heat Calculator

Boiling costs five times more than heating to boiling.

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Wavelength & Frequency Calculator

With the photon energy that makes the spectrum mean something.

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Diffraction Calculator

Including which fringes cannot exist at all.

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Thin Lens Calculator

A negative image distance is a magnifying glass, not an error.

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Mirror Equation Calculator

Focal length is half the radius. Sign does the rest.

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Critical Angle Calculator

Only exists going from dense to less dense.

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Radioactive Decay Calculator

Mean lifetime is 1.44 half-lives, not one.

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Nuclear Binding Energy Calculator

Why fusion works below iron and fission above it.

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Length Contraction & Time Dilation Calculator

One factor, γ, does all of it.

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Relativistic Momentum Calculator

γmv, and the ratio to classical is exactly γ.

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Orbital Period Calculator

In solar masses and AU, the constant disappears.

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Kepler's Third Law Calculator

Run backwards: how far out, from how long it takes.

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Schwarzschild Radius Calculator

Bigger black holes are less dense, not more.

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Stellar Luminosity Calculator

Temperature to the fourth power dominates everything.

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Stellar Parallax Calculator

Distance in parsecs is one over the parallax. No constant.

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Redshift Calculator

Above z = 0.1, v = cz stops being true.

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Mortar Calculator

Dry volume is a third more than wet. That is the whole thing.

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Block Wall Calculator

With the three tonnes of blockwork nobody weighs.

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Insulation R-Value Calculator

What is already there decides what the next 100mm is worth.

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Rebar Calculator

Counts the bars. Does not design the slab.

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Joist Span Calculator

Depth cubed. Width barely matters.

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Pipe Volume Calculator

Watch the velocity, not just the volume.

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Excavation Calculator

A 10 m³ hole makes 13.5 m³ of clay.

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Cutting Speed Calculator

Spindle speed is not cutting speed.

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Feed Rate Calculator

Too small a chip load burns more cutters than too large.

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Tap Drill Calculator

75% engagement is optimal, not a compromise.

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Thread Pitch Calculator

Pitch and lead differ the moment you add a start.

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Sheet Metal Bend Calculator

The flat blank is always shorter than the legs.

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Fillet Weld Calculator

The throat carries the load, not the leg.

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Bolt Torque & Preload Calculator

Ninety percent of your torque is fighting friction.

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IP Subnet Calculator

Handles /31 and /32 properly, which most do not.

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CIDR Calculator

Shows the addresses you waste rounding up.

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Bandwidth Calculator

Nobody sizes a link at 100% utilisation.

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Download Time Calculator

Bits and bytes differ by eight. That is the whole trap.

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Data Transfer Cost Calculator

Egress is where cloud bills go wrong.

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Storage Unit Converter

Why your 1 TB drive says 931 GB.

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Colour Converter

With the WCAG contrast that decides readability.

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ASCII & UTF-8 Converter

Characters and bytes are not the same count.

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Password Entropy Calculator

No 'strong' verdict — a verdict needs a threat model.

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Hash Rate Calculator

Expected wait is a mean, not a schedule.

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R-Value Calculator

R adds in series, U does not.

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Heat Loss Calculator

Floor area alone cannot tell you the answer.

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ABV Calculator

Two formulas that diverge above about 7%.

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Pool Chlorine Calculator

A 65% product is not 100% — dose the active, not the tub.

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Hot Tub Chemical Calculator

Small volume means the margin for error is tiny.

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Pipe Flow Rate Calculator

Flow goes with the square of the bore.

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Pump Head Calculator

Choosing on static lift alone is why pumps stall.

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Protons Neutrons Electrons Calculator

A positive charge means electrons were lost, not gained.

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Theoretical Yield Calculator

A yield over 100% means wet product, not a good day.

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Molecular Formula Calculator

A ratio that is not near a whole number means bad data.

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Combustion Analysis Calculator

Oxygen is found by difference, so every error lands on it.

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ICE Table Calculator

Solved properly, with no assumption that x is small.

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Percent Ionization Calculator

Shows the 5% rule failing instead of describing it.

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Molar Volume Calculator

STP is ambiguous — 22.414 and 22.711 are both correct.

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Isoelectric Point Calculator

Average two pKa values, never all three.

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Primer Melting Temperature Calculator

The Wallace rule stops working above about 14 bases.

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Chromatography Resolution Calculator

Doubling column length buys only 41% more resolution.

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Bond Order Calculator

Explains why O₂ is paramagnetic and He₂ does not exist.

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Osmolarity Calculator

Counts particles, so 0.154 M saline is 308 mOsm/L.

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Electronegativity Difference Calculator

1.7 is a teaching convention, not a physical boundary.

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Specific Rotation Calculator

Path length in decimetres, concentration in g/mL.

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Vapor Pressure Calculator

Antoine constants are inputs, because ranges matter.

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Neutralization Calculator

Equivalents, so polyprotic acids need no extra step.

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Gas Stoichiometry Calculator

Both volumes shown, because the room is not at STP.

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Wood Shrinkage Calculator

Tangential is twice radial. That is why boards cup.

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Shelf Sag Calculator

A front lip beats a thicker board. Depth is cubed.

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3D Print Time Calculator

Tall and thin is layer-limited. Bulky is flow-limited.

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Layer Height Calculator

Not a whole number of Z steps means visible banding.

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Resin Print Calculator

Forty parts take the same time as one.

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Seed Rate Calculator

Kilograms mean nothing without a thousand-grain weight.

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Fertiliser Rate Calculator

The bag says P₂O₅. Your soil test may not.

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Stocking Rate Calculator

Compares your growth against your demand. Nothing more.

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Hay Bale Calculator

A lighter hay bale can carry more feed than a heavy silage one.

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Growing Degree Days Calculator

Crops count heat, not days.

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Carbon Footprint Calculator

Every emission factor here is an input, not a claim.

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Rainwater Harvesting Calculator

Use the plan area. A steep roof collects no more.

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Composting Calculator

Equal weights of grass and straw is not a balanced pile.

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Tree Carbon Calculator

Double the diameter, nearly six times the carbon.

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Water Footprint Calculator

Shorter showers are the smallest term in the sum.

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Wind Turbine Calculator

20% more wind is 73% more energy.

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Frost Date Calculator

The published date is usually a coin flip.

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Snow Load Calculator

A metre of powder can weigh less than 20 cm of slush.

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Lightning Distance Calculator

Tells you where the last strike was. Not the next one.

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Cloud Base Calculator

The 400 ft rule, derived rather than memorised.

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Evapotranspiration Calculator

Hot and still, or cool and windy — same total, different fix.

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Density Altitude Calculator

The aircraft flies the air it is in, not the altimeter.

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True Airspeed Calculator

The 2% rule is a linearisation, and it drifts.

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Aircraft Fuel Calculator

Reserve fuel is not fuel you have.

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Glide Ratio Calculator

Airborne for the same time. Only the ground moves.

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Hull Speed Calculator

Widely quoted as a limit. It is not one.

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Sunrise Sunset Calculator

Solar noon is almost never at twelve.

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Percent Error Calculator

Percent error and percent difference, which are not the same.

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Average Atomic Mass Calculator

Weighted mass from isotope abundances, with a normalisation check.

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Oxidation Number Calculator

Solve for one element's oxidation state from the formula.

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Formal Charge Calculator

FC = valence − lone electrons − bonds, per atom.

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Van der Waals Equation Calculator

Real gas pressure, and how far it strays from ideal.

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RMS Velocity Calculator

Root-mean-square, mean and most probable molecular speeds.

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Gay-Lussac's Law Calculator

Pressure and temperature at constant volume.

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Avogadro's Law Calculator

Volume and moles at constant temperature and pressure.

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Hess's Law Calculator

Combine reaction steps, reversing and scaling as needed.

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Enthalpy of Reaction Calculator

ΔH°rxn from standard enthalpies of formation.

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Entropy Change Calculator

ΔS°rxn from absolute entropies, where elements are not zero.

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Heat of Fusion and Vaporisation Calculator

Energy for a phase change, where temperature does not move.

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Bomb Calorimeter Calculator

Heat of combustion from a temperature rise.

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Standard Cell Potential Calculator

E°cell, ΔG° and K from two reduction potentials.

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pKa and pKb Calculator

Convert freely between Ka, pKa, Kb and pKb.

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Salt Hydrolysis pH Calculator

Why a dissolved salt is rarely neutral.

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Polyprotic Acid pH Calculator

Diprotic pH from Ka₁, solved exactly rather than approximated.

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Buffer Capacity Calculator

How much acid or base a buffer absorbs before it gives up.

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Limit of Detection Calculator

LOD and LOQ from blank noise and calibration slope.

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Dixon's Q Test Calculator

Whether that one odd measurement can be discarded.

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Standard Addition Calculator

Concentration from the x-intercept, when the matrix interferes.

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Unit Cell Density Calculator

Crystal density from lattice type and edge length.

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Mass Percent Solution Calculator

w/w, w/v and v/v — which are not interchangeable.

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About science & engineering calculations

Physics and chemistry calculations are exact in a way most of this site is not. There is no supplier variation, no regional rate, no fee schedule that changed last quarter — a z-score of 2 is a z-score of 2, and one mole of any gas at standard conditions occupies 22.41 litres whether it is helium or carbon dioxide.

What these tools carry instead is an idealisation. Free fall ignores air resistance, projectile motion ignores drag, the ideal gas law ignores molecular volume, and a voltage divider assumes nothing is drawing current from it. Each of those is exactly right about a world slightly simpler than the real one, and knowing which simplification a page has made is the difference between using its answer and being misled by it. Every page here states its own.

Constants are handled the same way. Standard gravity is 9.80665 m/s² by definition rather than by measurement, and real local gravity runs from about 9.78 at the equator to 9.83 at the poles, so it appears as an editable field rather than a hard-coded fact.

Which one do you need?

I need to work out motion or energy

Speed, distance and time determine each other completely, so any two give the third. For anything accelerating, the velocity and acceleration calculators use the SUVAT relations and report the result in g as well as m/s² — 0.57 g is legible in a way 5.6 m/s² is not. Kinetic energy is where the square matters: doubling speed quadruples the energy, which is why braking distance rises so much faster than speed.

I am building a circuit

The LED resistor calculator rounds up to the next standard value rather than the nearest, because rounding down pushes current past the LED's rating. The resistor and capacitor pages cover series and parallel, which use opposite formulas — resistors add in series, capacitors add in parallel. For filters and timing, the RC time constant page explains where the 63.2% figure comes from.

I am making up a solution

Molarity is moles per litre of solution, not of solvent, so a 1 M solution is topped up to the mark rather than made by adding solute to a full litre. The dilution calculator gives the diluent to add rather than the final volume, which is the number you actually need at the bench.

I need pressure, density or buoyancy

Hydrostatic pressure depends only on depth, fluid density and gravity — the shape and width of the container are irrelevant, which is why a narrow pipe and a wide lake press equally hard at the same depth. The density calculator reports buoyancy as three states rather than two, because a material at exactly the density of water is neutrally buoyant rather than sinking.