MotionLab

Time Dilation Calculator

Moving clocks tick slower — the faster you go, the more time stretches for a stationary observer.

Proper time Δt₀ (s)

Velocity (fraction of c)

Dilated time Δt′ (s)

2.294

Δt′ = γΔt₀

Lorentz factor γ: 2.294
Length contraction L′/L₀: 0.436

What you entered

Proper time Δt₀ (s): 1Velocity (fraction of c): 0.9

1
β = v/c
0.9= 0.9
2
γ = 1 ÷ √(1 − β²)
1 ÷ √(1 − 0.9²)= 2.2942
3
Dilated time Δt′ = γ × Δt₀
2.2942 × 1= 2.2942 s
4
Length contraction factor L′/L₀ = 1/γ
1 ÷ 2.2942= 0.4359

Result

Dilated time Δt′ (s): 2.294

At 90.0% the speed of light (γ = 2.294), 1 s of proper time appears as 2.294 s to a stationary observer.

Relativistic time dilation and length contraction

For one second of proper time at a fraction of light speed. Gamma is the Lorentz factor; contracted length is for a one-unit object.

Speed (fraction of c)	Dilated time (s)	Lorentz factor	Contracted length
0.1	1.0050	1.0050	0.9950
0.5	1.1547	1.1547	0.8660
0.9	2.2942	2.2942	0.4359
0.99	7.0888	7.0888	0.1411
0.999	22.3663	22.3663	0.0447

At 10% of light speed the effect is only half a percent, which is why relativity is invisible in everyday life - even at orbital speeds the correction is tiny, though GPS satellites do need it to avoid drifting by kilometres a day. The effect accelerates sharply near c: going from 0.9 to 0.999 multiplies the dilation nearly tenfold, and it grows without limit as speed approaches c, which is one way to see why massive objects cannot reach it. Length contraction is the exact reciprocal of time dilation, and both are symmetric - each observer sees the other's clock running slow.

Time dilation is real, not just theory

GPS satellites orbit at about 14,000 km/h and their onboard clocks tick ~7 μs/day slower due to special relativity (partially offset by general relativity). Without corrections, GPS positions would drift by ~10 km per day — time dilation has practical engineering consequences.

The twin paradox in numbers

At 90% the speed of light (v/c = 0.9), γ ≈ 2.29 — meaning one year for the traveler equals 2.29 years back on Earth. At 99.9% c, γ ≈ 22.4 — the traveler ages just 16 days while Earth ages a full year.

Frequently asked questions

Astronauts on the ISS orbit at 7,660 m/s. How much time dilation do they experience?

v/c = 7660/3×10⁸ = 2.55×10⁻⁵. γ = 1/√(1 − v²/c²) ≈ 1.0000000003. After 6 months, they age about 0.005 seconds less than people on Earth. Tiny — but GPS satellites must correct for this or positions drift by km/day.

At what speed does time dilation become noticeable?

At 10% of light speed (0.1c = 30,000 km/s), γ = 1.005 — a 0.5% effect. At 50% c, γ = 1.155 (15.5% slower). At 99% c, γ = 7.09. Below about 10% c, the effect is negligibly small for most purposes but still measurable with atomic clocks.

Is time dilation real or just a measurement trick?

Completely real. Muons created in the upper atmosphere by cosmic rays should decay in ~2.2 μs and never reach Earth's surface. But they travel at ~0.998c (γ ≈ 15.8), so they 'live' 15.8× longer in our frame and easily reach ground-based detectors. This was experimentally confirmed in the 1960s.

Does time dilation affect aging?

Yes — a twin traveling at 90% c for 10 years returns to find their Earth twin has aged 22.9 years (γ ≈ 2.29). The traveling twin is biologically younger. This isn't just clocks ticking differently — all physical processes, including aging, slow by the same factor.