Relativistic Velocity Addition Calculator

Relativistic Velocity Addition

When two objects move at significant fractions of the speed of light, simple addition no longer holds. Einstein's special relativity gives a corrected formula that keeps combined speeds below the speed of light.

Formula

$$u = \frac{v + w}{1 + \frac{vw}{c^2}}$$

Here $v$ and $w$ are the velocities being combined, $u$ is the result, and $c = 299{,}792{,}458$ m/s is the speed of light in vacuum. Enter velocities in km/s; the calculator converts internally.

Why Classical Addition Fails

At everyday speeds, $vw/c^2$ is negligible and $u \approx v + w$. Near light speed, the denominator grows and prevents $u$ from exceeding $c$. Two objects each moving at 0.6c relative to a reference frame combine to about 0.88c, not 1.2c.

Related tools: Electron Speed Calculator and UFO Travel Calculator.

Frequently Asked Questions

Why cannot two light-speed velocities add to 2c?

Special relativity requires that no information or matter exceeds the speed of light. The relativistic formula ensures the combined velocity stays below c.

When does the relativistic correction matter?

When either velocity exceeds roughly 10% of light speed (about 30,000 km/s), the correction becomes noticeable. Below that, classical addition is a good approximation.

Are the velocities in the same reference frame?

Yes. Both v and w must be measured relative to the same observer or frame before applying the formula.

What units should I use?

Enter velocities in km/s. The calculator uses c = 299,792,458 m/s internally and displays the result in km/s.

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Velocity Addition Calculator