Time Dilation Calculator: How Much Slower Does a Fast Clock Tick?

Frequently asked questions

How do you calculate time dilation?

Find the Lorentz factor, then multiply or divide. The factor is γ = 1 / √(1 − v²/c²), where v is the speed and c is the speed of light. The time on the stationary observer's clock is γ times the time on the moving clock, and the moving clock's time is the observer's time divided by γ. For 0.6c, γ = 1.25, so 10 years on the moving clock is 12.5 years for the observer. The calculator does this as you type: enter the Velocity and either time field.

What is the Lorentz factor?

It is the number γ (gamma) that says how many times slower a moving clock ticks, as measured by someone who is not moving with it. It equals 1 at rest and grows without limit as the speed approaches the speed of light. At 90% of c it is 2.294157, at 99% it is 7.0888, and at 99.9999% it is about 707. The Lorentz factor card shows γ for whatever Velocity is entered.

How much time dilation is there at 90 percent of the speed of light?

At 90% of c the Lorentz factor is 2.294157, so one year on the moving object's clock is 2.2941573 years for the stationary observer. That is the starting example when the page loads. Type 1 in Moving object time and Stationary observer time reads 2.2941573 years; type 10 and it reads 22.941573 years.

How much time dilation is there at half the speed of light?

At 50% of c, γ = 1.154701, so the moving clock runs about 13.4% slow: one year on board is about 1.1547 years for the observer, a difference of roughly 56 days. Set Velocity to 50 with the unit on % of c to see the exact figure for any time span.

What happens to time at the speed of light?

The formula has no answer there: at v = c the Lorentz factor would divide by zero, and in special relativity nothing with mass can reach that speed. The calculator accepts a speed from 0 up to, but not including, the speed of light. Anything at or above it shows the message 'Enter a speed from 0 up to, but not including, the speed of light.' You can still get very close, for example 99.9999 gives γ of about 707.

At what speed does time dilation become noticeable?

Not until a sizeable fraction of the speed of light. At 1% of c, γ is 1.00005, which is only about 26 minutes per year. At 10% of c it is 1.005038, about 1.8 days per year. Around 50% of c the effect is roughly 15%, and past 90% it grows quickly. At the speeds of cars, planes and rockets the difference is far too small to notice.

Does this calculator do gravitational time dilation, acceleration or a black hole?

No. It covers special relativity only: two objects at a constant relative speed. Gravity (general relativity), acceleration and black-hole horizons need different formulas, and the tool does not handle them. It also does not output length contraction or relativistic mass; the only result besides the other clock's time is the Lorentz factor.

Can I use it for the twin paradox?

Only the simplified part. The moving twin's time and the stay-at-home twin's time are related by the same γ as long as the speed is constant, so you can see how much older the observer gets over, say, 20 years of travel at 0.99c (about 141.8 years). The turnaround acceleration that makes the twin paradox a paradox is not modelled, so treat the answer as the cruising phase.

Can I enter the speed in km/s or mph instead of a percent of c?

Yes. Press Units, then pick km/s or mph under Velocity unit. The number already in the Velocity field is converted for you, so 90% of c becomes about 269,813 km/s or about 603,555,000 mph. The calculator uses c = 299,792.458 km/s, which is about 670,616,629 mph, and rejects any speed at or above it.

How long is a year in the calculator?

A Julian year of 365.25 days. Under Units, Time unit lets you switch between Years, Days, Hours and Seconds, and the number already entered is converted. The conversion does not change the answer, only the unit it is shown in.

Can I type very large or very small numbers?

Yes. Scientific notation such as 2.5e3 is accepted in the fields. Times must be 0 or more, otherwise you get the message 'Enter a time of 0 or more.' When γ reaches a million or more it is shown in scientific notation.

Is anything I type uploaded?

No. The formula runs in your browser as you type, so nothing is sent anywhere.