Time Dilation Calculator

About the Time Dilation Calculator

Time dilation is one of the most remarkable predictions of Einstein's special relativity: a moving clock ticks slower than a stationary one. The faster you travel, the more pronounced the effect becomes, governed by the Lorentz factor γ = 1/√(1 − v²/c²). At everyday speeds the effect is negligibly small, but as you approach the speed of light, time slows dramatically.

This effect is not theoretical speculation — it has been confirmed countless times. GPS satellites must correct for time dilation to maintain accuracy, cosmic ray muons survive to reach Earth's surface because their internal clocks run slow, and precision atomic clocks flown on aircraft have measured exactly the predicted difference.

This calculator computes the Lorentz factor and time dilation for any velocity from walking speed to 99.999% of light speed. Enter a proper time experienced by a moving traveler and see how much time passes for a stationary observer, or explore the comprehensive comparison table spanning 14 orders of magnitude in speed.

When This Page Helps

Time dilation connects fundamental physics to practical technology (GPS) and science fiction scenarios (interstellar travel). This calculator makes the math accessible and provides the comprehensive speed-comparison table that textbooks rarely include, from everyday speeds to near-light velocities.

How to Use the Inputs

1. Enter the velocity as a fraction of c (e.g. 0.9), in km/s, or m/s.
2. Enter the proper time — time experienced by the traveler.
3. Select the time unit (seconds, minutes, hours, days, or years).
4. Use preset buttons for common relativistic speeds.
5. Review the Lorentz factor, observer time, and time difference.
6. Explore the full comparison table from walking speed to 99.999% c.

Example Calculation

Tips & Best Practices

• At 10% c, γ ≈ 1.005 — barely noticeable time dilation.
• At 86.6% c, γ = 2 — time passes at half speed for the traveler.
• At 99.5% c, γ ≈ 10 — a 1-year trip ages Earth by a decade.
• GPS corrections account for both special and general relativistic time dilation.
• Cosmic ray muons with γ ≈ 25 survive long enough to reach Earth's surface.

When To Use This Calculator

Calculate special relativistic time dilation from velocity. Find the Lorentz factor, dilated time, and compare effects at various speeds from walking to near-light. Use it when you need a repeatable calculation in the physics / astronomy category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Frequently Asked Questions

• What is time dilation?

  A consequence of special relativity where a moving clock runs slower than a stationary clock. The effect increases with speed and is described by the Lorentz factor γ.

• Is time dilation real?

  Yes. It has been experimentally confirmed many times, including with atomic clocks on aircraft, GPS satellite corrections, and the extended lifetime of cosmic ray muons.

• What is the twin paradox?

  If one twin travels at high speed and returns, they will have aged less than the twin who stayed home. This is not a paradox but a real prediction confirmed by experiment.

• How is this different from gravitational time dilation?

  Special relativistic time dilation is caused by velocity (moving clocks run slow). Gravitational time dilation is caused by gravity (clocks in stronger gravity run slow). Both effects are real and additive.

• Does time dilation affect GPS?

  Yes. GPS satellites orbit at ~3.87 km/s, causing their clocks to tick about 7 microseconds/day slower due to velocity. This is partially offset by gravitational effects (45 μs/day faster). Without corrections, GPS would drift by ~10 km/day.

• Can you reach the speed of light?

  No. As v approaches c, γ approaches infinity, meaning infinite energy would be needed. Only massless particles (like photons) travel at c.