Physics
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Relativistic Velocity Addition Calculator.
Combine collinear velocities using special-relativistic velocity addition.
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Results update as you type.
Results update automatically as you type.
Use Cases
Physics homework and exam prep
Quickly verify relativistic velocity addition problems for special relativity assignments or to understand how velocities combine at high speeds.
Example: Check the combined velocity of a spaceship moving at 0.6c relative to Earth and a probe launched at 0.8c relative to the spaceship.
Astrophysics and particle physics
Estimate the resultant velocity of particles or objects moving at relativistic speeds in different reference frames, such as cosmic rays or particles in accelerators.
Example: Calculate the speed of a particle ejected from a relativistic jet moving at 0.9c.
Frequently Asked Questions
- What is relativistic velocity addition?
- In special relativity, velocities don't simply add like in classical mechanics. The relativistic velocity addition formula accounts for the constancy of the speed of light, giving the correct combined velocity when two objects move along the same line.
- How do I use this calculator?
- Enter the object's velocity and the frame's velocity in meters per second (m/s). The calculator will compute the relativistic sum using the formula (u+v)/(1+uv/c^2), where c is the speed of light.
- Can the result exceed the speed of light?
- No. The formula ensures that if both input velocities are less than the speed of light, the resulting velocity is always less than the speed of light. This aligns with the principle that nothing can travel faster than light.
Tips & Common Mistakes
Tips
- Ensure both velocities are entered in meters per second (m/s). If you have speeds in other units, convert them first.
- For velocities much smaller than the speed of light, the result will be nearly the same as simple addition, but this calculator gives the exact relativistic value.
- Remember that the speed of light is approximately 3 × 10^8 m/s. You can use this to check if your inputs are realistic.
- If you need to add more than two velocities, apply the formula iteratively: first combine two, then combine the result with the next velocity.
Common Mistakes to Avoid
- Forgetting to convert velocities to m/s before entering them. For example, using km/s without conversion will give incorrect results.
- Assuming that the result is simply the sum of the two velocities, which is only an approximation at low speeds and fails at relativistic speeds.
- Entering velocities greater than the speed of light, which is physically impossible and will produce an error or meaningless result.
Last updated: August 13, 2026