Chromatography Resolution Calculator
Doubling column length buys only 41% more resolution.
Work out Chromatography Resolution. Doubling column length buys only 41% more resolution. Free, with no account and nothing to install.
When an unretained compound elutes
Only needed for plate height
Resolution (Rs)
1.82
Baseline resolved, under 0.3% overlap
Rs of 1.5 or above is conventionally taken as baseline separation. When resolution is short, selectivity is the most productive thing to change: it enters the resolution equation linearly, while plate count enters under a square root, so doubling the column length buys only about 41% more resolution.
How the Chromatography Resolution Calculator works
Resolution, capacity factor, selectivity, plate count and plate height from two peaks on a chromatogram. Plate count sits under a square root in the resolution equation while selectivity sits outside it, which is why a longer column is usually the least productive fix.
Also known as: hplc resolution between two peaks · theoretical plate count from a peak · capacity factor k prime · why are my peaks not separating
Three factors, and which one to change
The resolution equation splits into three terms: a plate-count term in √N, a selectivity term in (α − 1)/α, and a retention term in k′/(1 + k′). They can be improved independently, and they are not equally worth improving.
Plate count sits under a square root, which is expensive. Doubling column length doubles the plate count and the run time, and returns only √2 — about 41% — more resolution. It also roughly doubles backpressure, which on an HPLC is a hard limit rather than an inconvenience.
Selectivity sits outside the root and is where the leverage is. Moving α from 1.05 to 1.10 nearly doubles resolution at no cost in run time, and it is changed by the chemistry — mobile phase composition, pH, temperature, a different stationary phase. When two peaks will not separate, this is the term to attack first.
The capacity factor and the useful window
k′ is (tR − t₀)/t₀: how many void times a compound spends held on the column, relative to a compound that is not held at all. It is dimensionless and independent of flow rate and column dimensions, which makes it the number worth comparing between instruments.
Below about k′ = 1 a peak elutes too close to the void volume, where unretained material and injection disturbances live, and resolution from anything near it is poor. Above about k′ = 10 the peak is broad and late, the analysis is slow, and sensitivity suffers with no separation gained. Between 2 and 10 is the working range.
Getting there is a mobile phase adjustment. In reversed-phase work, more organic solvent lowers k′ and less raises it — often steeply, since a 10% change in acetonitrile can move k′ by a factor of two or three. Gradient elution exists precisely because a single mobile phase composition rarely keeps every compound in a mixture inside that window.
Plates, plate height and where the band broadening comes from
The theoretical plate is borrowed from distillation, where it was a real tray. In chromatography it is a fiction that happens to be useful: N = 16(tR/w)² counts notional equilibration steps, and higher counts mean narrower peaks. HETP, the plate height, is column length divided by N — smaller is better.
The van Deemter equation breaks HETP into three contributions. The A term is eddy diffusion, from molecules taking different paths through the packing — it is flow-independent and improves with smaller, more uniform particles. The B term is longitudinal diffusion, which matters at low flow and shrinks as flow rises. The C term is resistance to mass transfer, which grows with flow.
B falling and C rising means the curve has a minimum, and that optimum flow rate is where the column runs most efficiently. Sub-2-micron particles flatten the C term enough to push the minimum to much higher flow rates, which is the whole premise of UHPLC — the same separation, several times faster, at pressures that need purpose-built pumps.
Where to go next
The Chromatography Resolution question rarely arrives on its own. These are the ones that usually come with it:
- Molar Conductivity Calculator — Λm = κ/c, plus the degree of dissociation.
- Beer-Lambert Law Calculator — A = εlc, with the linearity limit flagged.
- NMR Chemical Shift Calculator — ppm to hertz, and why only one of them is portable.
- Speed Distance Time Calculator — Any one of the three from the other two, in four units.
Frequently asked questions
What resolution counts as baseline separation?
Rs of 1.5 or above, which leaves under 0.3% overlap between adjacent peaks. Rs of 1.0 still leaves roughly 2%, which is why the working threshold is 1.5.
How is resolution calculated?
Twice the difference in retention times divided by the sum of the two peak widths at base. Using widths at half height instead requires a different constant, so check which convention a value follows.
What is the capacity factor k′?
Retention time minus void time, divided by void time — how long a compound spends in the stationary phase relative to the mobile phase. Values between 2 and 10 are generally the useful working range.
Why is selectivity the best thing to change?
Because it enters the resolution equation linearly while plate count enters under a square root. Doubling column length quadruples analysis time for only about 41% more resolution; a small change in mobile phase composition can do much more.
What are theoretical plates?
A measure of column efficiency borrowed from distillation, counting the notional equilibration steps a column performs. Higher plate counts mean narrower peaks and better separation.
What is HETP?
Height equivalent to a theoretical plate — column length divided by plate count. Smaller is better, and the van Deemter equation describes how it varies with flow rate through a minimum.
Should I measure peak width at base or at half height?
Either, but the constant changes. Width at base uses N = 16(tR/w)²; width at half height uses N = 5.54(tR/w½)². Half-height is easier to measure on a tailing peak, which is why software usually reports it.
What causes peak tailing?
Usually secondary interactions — residual silanols on a silica column interacting with basic analytes is the classic case. Column overload, a void at the column inlet and extra-column dead volume all produce it too. Tailing inflates apparent width and understates the plate count.
What is the van Deemter equation?
HETP = A + B/u + Cu, splitting plate height into eddy diffusion, longitudinal diffusion and mass-transfer resistance. Because B falls and C rises with flow rate, the curve has a minimum — the flow at which the column is most efficient.
Why does UHPLC use sub-2-micron particles?
Smaller particles reduce the A and C terms, flattening the van Deemter curve so efficiency holds at much higher flow rates. The same separation runs several times faster, at the cost of backpressure that needs purpose-built pumps.
How is resolution improved fastest?
By changing selectivity, since it enters the resolution equation linearly while plate count enters under a square root. A small change in mobile phase composition, pH or temperature often beats doubling the column length, which returns only 41% for twice the run time.
What is a good tailing factor?
Between 0.9 and 1.5 for most methods; pharmacopoeial methods often specify 2.0 as the limit. Outside that range, integration becomes unreliable and the plate count no longer means what the equation assumes.
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Related calculators
Molar Conductivity Calculator
Λm = κ/c, plus the degree of dissociation.
OpenBeer-Lambert Law Calculator
A = εlc, with the linearity limit flagged.
OpenNMR Chemical Shift Calculator
ppm to hertz, and why only one of them is portable.
OpenSpeed Distance Time Calculator
Any one of the three from the other two, in four units.
Open