Length Contraction & Time Dilation Calculator
One factor, γ, does all of it.
Work out Length Contraction & Time Dilation. One factor, γ, does all of it. States the assumption instead of hiding it.
Lorentz factor γ
1.999824
Strongly relativistic — Newtonian formulas are badly wrong here.
Everything here comes from one number: γ = 1/√(1 − v²/c²). Length contracts by γ, time dilates by γ, momentum and effective mass both scale by γ. Presenting them separately would hide that they are one phenomenon seen from different angles. At everyday speeds γ is 1.0000000001 and nothing is measurable. It only reaches 1.005 at 10% of light speed, 1.15 at half, and 2 at 86.6% — which is why relativity stayed hidden until people started accelerating particles. The kinetic energy term is what makes c unreachable. As γ grows without bound, so does the energy needed for each further increment of speed, and reaching c would take infinite energy for anything with mass. Muons created in the upper atmosphere reach the ground only because their dilated lifetime buys them the time.
How the Length Contraction & Time Dilation Calculator works
Length contraction, time dilation, relativistic mass and momentum from a single speed. All four come from the Lorentz factor, and separating them into unrelated calculators hides that they are one phenomenon.
Also known as: lorentz factor calculator · time dilation at 0.9c · how much do lengths contract · why cant anything reach light speed
Frequently asked questions
What is the Lorentz factor?
γ = 1/√(1 − v²/c²). It is 1 at rest, 1.005 at 10% of light speed, and exactly 2 at 86.6%. Everything in special relativity scales by it.
At what speed does relativity start to matter?
Around 10% of light speed, where corrections reach about half a percent. Below that γ is so close to 1 that Newtonian mechanics is indistinguishable from relativity in almost any measurement.
Is time dilation real or an illusion?
Entirely real and routinely measured. GPS satellites need relativistic corrections or they would drift by about 10 km a day, and muons created in the upper atmosphere only reach the ground because their dilated lifetime buys them the time.
Why can't anything reach the speed of light?
Because kinetic energy is (γ−1)mc², and γ grows without bound as v approaches c. Reaching c would take infinite energy for anything with mass, which is why accelerators spend enormous energy on the last fraction of a percent.
Is relativistic mass a real thing?
It is a valid bookkeeping device and most physicists now avoid the term, preferring to keep mass invariant and put γ into momentum and energy instead. The predictions are identical either way.
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