Velocity Addition Calculator

Einstein’s Velocity Addition Formula

In everyday experience, velocities simply add together, but special relativity requires a modified formula to ensure nothing ever exceeds the speed of light: w_combined = (u + w) / (1 + uw/c²), where u and w are expressed as fractions of c.

At low speeds, the denominator is essentially 1 and this reduces to ordinary Newtonian addition. But as speeds approach c, the formula automatically prevents the combined velocity from ever reaching or exceeding the speed of light — for example, adding 0.9c and 0.9c gives roughly 0.994c under this formula, not 1.8c. This is one of the clearest illustrations of how special relativity departs from classical mechanics at high speed.