Time Dilation Calculator

Discover how time varies at high speeds with the Time Dilation Calculator – your tool for delving into the realms of special relativity.

Dilated time1.666666667 s1 s of proper time looks like this from outside — MOVING clocks run slow, so the outside reading is the larger one

Lorentz factor γ1.666666667at 0.8c — every relativistic effect below is this one number applied somewhere

Speed2.39834e+8 m/s

Time gained per second0.666667 scomputed from a series in β² rather than by subtracting 1 from γ, which would lose every significant figure at everyday speeds

Contracted length6 m10 m at rest, shortened along the direction of motion only — the transverse dimensions are untouched

Rest energy8.98755e+16 JE = mc² for 1 kg — 2.148e+7 tonnes of TNT, which is what makes the equation famous

Relativistic kinetic energy5.9917e+16 J(γ−1)mc² — NOT ½mv², which would give 2.87602e+16 J and is -52% out at this speed

Total energy1.49793e+17 Jγmc² — rest energy plus kinetic energy

Relativistic momentum3.99723e+8 kg·m/s

Check: E² = (pc)² + (mc²)²1×the energy–momentum relation, which must come out at exactly 1

Relativistic velocity sum0.8c(u+v)/(1+uv/c²) — the naive sum would be 1c, which is faster than light and therefore wrong

Adding c to anythingstill exactly cput u = 1 and the formula gives (1+v)/(1+v) = 1 for every v — light travels at c in every frame, which is the postulate the whole theory is built on, recovered here as arithmetic

Does it fit?YES in the barn's framea 10 m pole contracts to 6 m against a 8 m barn

The barn in the pole's frame4.8 mcontracted too — so from the pole's point of view the barn is SHORTER and the pole certainly does not fit. Both frames are right

Simultaneity offset between the doors35.5802 nsthe two doors close at the SAME time in the barn frame and this far apart in the pole frame. The paradox dissolves because "both doors shut at once" is not a frame-independent statement

How far the far end travels anyway8 mthe tip cannot know the head was stopped for at least 33.3564 ns, so it keeps going that much further — MORE than the 8 m depth, so it reaches the bottom regardless

Why nothing can be rigidsignals travel at c at mosta rigid body would transmit a push instantly, which would carry information faster than light. Assuming one is exactly what generates the bug-and-rivet paradox

The formula

γ = 1/√(1−β²); t = γt₀; L = L₀/γ; w = (u+v)/(1+uv/c²)

One number, many effects

Time dilation, length contraction, the growth of momentum and the energy of a moving body are all the same Lorentz factor applied in different places. At 0.8c it is 5/3 exactly; at walking pace it differs from 1 by about 10⁻¹⁷, which is why relativity went unnoticed for so long and why this calculator computes γ − 1 from a series rather than by subtraction — a double simply cannot represent that difference from 1.

Velocity addition makes c a limit

Add 0.5c to 0.5c and you get 0.8c, not c. Add c to anything at all and you get exactly c, because (1+v)/(1+v) is 1 for every v. The speed of light is not a speed that happens to be hard to reach; it is the value that every frame agrees on, and the addition formula turns that postulate into arithmetic.

The barn-pole paradox is about simultaneity

A pole too long for a barn at rest fits inside it when moving fast enough, because it contracts. But in the pole's own frame the barn is the thing that contracts, and the pole certainly does not fit. Both descriptions are correct.

The resolution is that "both doors shut at the same moment" is not a frame-independent statement. In the barn's frame they shut together; in the pole's frame they shut at measurably different times, first one and then the other, with the pole never wholly enclosed. The offset is computed above, and it is a real number rather than a hand-wave.

The bug-and-rivet version turns on the same point plus one more: nothing is rigid. When a rivet head stops, the tip cannot know for at least the time light takes to cross it, so it keeps travelling. Rigid bodies are impossible in relativity, and assuming one is what generates the paradox.