Time Dilation Calculator

According to special relativity, time is not absolute; it depends entirely on the observer's frame of reference. The core equation implemented by this calculator is derived from the Lorentz factor:

t' = t / sqrt(1 - (v^2 / c^2))

Where t' represents the dilated time observed from a stationary frame, t is the proper time interval measured in the moving frame, v is the relative velocity of the moving object, and c is the constant speed of light in a vacuum (approximately 299,792,458 meters per second). As the velocity approaches the speed of light, the denominator approaches zero, causing the observed time interval to grow exponentially larger.

Imagine a futuristic spacecraft traveling at a constant velocity of 200,000,000 meters per second (about 67% the speed of light) relative to Earth. Suppose an astronaut inside the ship measures a stationary time interval or clock tick of 10 seconds. To calculate the dilated time elapsed from the perspective of an observer back on Earth, we apply our formula:

1. Square the velocity: (200,000,000)^2 = 4.0 x 10^16

2. Square the speed of light: (299,792,458)^2 = 8.98755 x 10^16

3. Divide velocity squared by lightspeed squared: 4.0 x 10^16 / 8.98755 x 10^16 = 0.445

4. Subtract from one: 1 - 0.445 = 0.555

5. Take the square root: sqrt(0.555) = 0.745

6. Divide the proper time by this result: 10 / 0.745 = 13.42 seconds.

Thus, for every 10 seconds that pass for the astronaut, approximately 13.42 seconds pass for the observer on Earth.

When computing relativistic effects, always ensure your velocity units are consistent with the speed of light, typically expressed in meters per second. Keep in mind that noticeable time dilation only occurs at extreme velocities—typically exceeding 10% of the speed of light. For everyday terrestrial speeds, the Lorentz factor remains so close to 1 that relativistic differences are practically undetectable without atomic clocks.