Time Dilation Calculator
See how motion stretches time in special relativity. Enter a speed as a fraction of the speed of light, or as a real speed (m/s, km/s, km/h, or mph), and a proper time to get the Lorentz factor and the dilated time.
Example: with Speed input Fraction of light speed (c) · Speed as fraction of c 0.5 · Actual speed 149896229 · Speed unit m/s · Proper time (at rest) 10 → Lorentz factor (γ): 1.154701.
- Dilated time (observed)11.5470 years (from 10 years at rest)
- Speed and slowdownv = 149,896,229 m/s (50.00% of c); moving clock runs 13.40% slower
Computed by the calculator below using its default values. Change any input to see your own numbers.
γ = 1 / √(1 − v²/c²), with c = 299,792,458 m/s. A clock moving at speed v ticks slower than a stationary one by the factor γ. At 50% of light speed γ is about 1.155.
Why moving clocks run slow
Special relativity rests on one strange fact: the speed of light is the same for every observer, no matter how fast they move. To keep light's speed constant, time and space must adjust. The consequence is time dilation — a clock moving relative to you ticks slower than your own by the Lorentz factor γ = 1/√(1 − v²/c²).
At everyday speeds the effect is minuscule because v/c is tiny, so γ sits at essentially 1. It only becomes dramatic as speed approaches c. At half light speed a moving clock loses about 13 percent; at 99 percent of c it runs seven times slower.
Not just theory
Time dilation is measured daily. GPS satellites move fast enough that their clocks tick slightly slow from motion — an effect engineers must correct, alongside a larger gravitational shift, or positions would drift by kilometers within a day. Particle accelerators see short-lived particles last far longer at high speed, exactly as γ predicts.
The famous twin paradox follows directly: a traveler moving near light speed ages less than a twin who stays home. There is no trick — the moving twin's proper time really is stretched by γ when compared in the stay-at-home frame.
How it’s calculated
Lorentz factor γ = 1/√(1 − v²/c²) with c = 299,792,458 m/s. Speed can be entered as a fraction of c (β) or as an actual speed converted to m/s (km/s ×1,000; km/h ÷3.6; mph ×0.44704). Dilated time = γ × proper time. The slowdown percentage is (1 − 1/γ) × 100.
Covers special-relativistic time dilation from relative velocity only, for constant-velocity motion. It excludes gravitational time dilation and acceleration effects, and requires v < c.
Lorentz factor at different speeds
| Speed (fraction of c) | Lorentz factor γ | 1 year at rest becomes |
|---|---|---|
| 0.10 c | 1.005 | 1.005 years |
| 0.50 c | 1.1547 | 1.155 years |
| 0.90 c | 2.294 | 2.294 years |
| 0.99 c | 7.089 | 7.089 years |
| 0.999 c | 22.366 | 22.37 years |
Computed with γ = 1/√(1 − v²/c²), c = 299,792,458 m/s.
Common mistakes
- Entering a speed at or above c — the formula only applies for v less than the speed of light.
- Mixing up which clock is slow: the clock moving relative to the observer is the one that ticks slow.
- Expecting a big effect at ordinary speeds; below a few percent of c, γ is indistinguishable from 1.
- Forgetting gravitational time dilation, a separate effect not included here.
Frequently asked questions
What is the time dilation formula?
Moving time equals proper time times the Lorentz factor γ = 1/√(1 − v²/c²), where v is the relative speed and c is the speed of light. The larger v is, the larger γ and the greater the dilation.
What is the Lorentz factor?
It is the number γ that tells how much time stretches, lengths contract, and momentum grows at speed v. It equals 1/√(1 − v²/c²), starting at 1 for rest and rising toward infinity as v approaches c.
How do I enter speed as a fraction of light speed?
Choose the fraction-of-c mode and type a value between 0 and 1 — for example 0.5 for half light speed. You can also switch to actual-speed mode and enter m/s, km/s, km/h, or mph.
Is time dilation real or just theoretical?
It is real and measured. GPS satellite clocks, fast-moving particles, and precise atomic clocks flown on aircraft all confirm that moving clocks run slow exactly as the formula predicts.
Why does everyday motion not slow time noticeably?
Because ordinary speeds are a tiny fraction of light speed, so v²/c² is nearly zero and γ is essentially 1. The effect only grows large as speed nears c.