T' = t / SQRT(1 – (v² / c²))

(Equation Diagram)

Equation Explained

T' = Rate multiplier that the spacecraft experiences time at.

t = Rate Multiplier of a reference point you want to calculate from. Usually 1.

v = Velocity of the spacecraft in m/sec

c = Velocity of the speed of light. Is 299,792,458 m/sec.

Example

A spacecraft is travelling at “point one light” or 10% of light speed (29,979,246 m/sec). What is the time dilation on board compared to a fixed reference point?

1 / SQRT (1 – 29,979,246² / 299,792,458²) = 1.00504 times that of fixed reference.

This means that after 3,600 seconds have passed on the fixed reference point, 3,618 will have passed on the vehicle. The effect is not noticeable at lower fractions of cee, but as you approach light-speed it grows asymptotically; e.g. at “point nine light”; time dilation will occur at a rate of 2.29416 that of a fixed point; and at “point nine nine light”, the multiplier is 7.08881.