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Velocity Addition Calculator

Make use of the flexible Velocity Addition Calculator tool to determine the relative projectile velocity of an object easily & instantly. All you need to do is provide the required input fields such as the spaceship velocity, projectile velocity and press the calculate button to check the output within no time.

Choose option to calculate
Projectile velocity(w)
Space velocity(v)

Velocity Addition Calculator: Get the detailed process to find the relative projectile velocity of an object. This online Velocity Addition Calculator tool provides an accurate answer and detailed explanation to solve it. Find the velocity addition formula and more details about it in the following sections. Get the solved example questions on velocity addition.

How to Find Relative Projectile Velocity?

The following are the steps to solve the relative projectile velocity of an object.

  • Get the spaceship velocity, projectile velocity details.
  • Add those velocities and multiply them.
  • Divide the product by the square of the speed of the light.
  • Add 1 to the result.
  • Divide the sum of velocities by the result from above step to obtain the relative projectile velocity.

Relativistic Velocity Addition Formula

The sum of the spaceship speed and fired projectile speed is equal to the projectile travelling speed.

The relativistic velocity addition equation is as follows:

u = (v + w) /(1 + (v * w)/c²)


c is the speed of the light and its value is 299,792,458 m/s

v is the speed of the spaceship

w is the speed of the projectile as seen from the spaceship

u is the speed of the projectile as seen outside of the spaceship


Question: If the spaceship heading directly towards the earth is half of the speed of the light sends a signal to us on alaser-produced beam of light. Given that, the light leaves the ship at a speed c and spaceship velocity is 0.500c. Calculate the speed at whicch it approaches the earth?


Given that

Spaceship velocity v = 0.5c

projectile velocity w = c

Relative projectile velocity u = (v + w) /(1 + (v * w)/c²)

u = (0.5c + c) /(1 + (0.5c * c)/c²)

= 1.5c/(1 + 0.5c²/c²

= 1.5c/(1 + 0.5)

= 1.5c/(1.5)

= c

Therefore, the relative projectile speed is c.

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Frequently Asked Questions on Velocity Addition Calculator

1. What is the formula of relative velocity?

The relativistic velocity addition formula is u = (v + w)(1 + (v x w)/c²). Here, v is the speed of the spaceship, w is the speed of the projectile from the spaceship, u is the speed of the projectile outside of the spaceship.

2. How to find relativistic velocity addition?

Relative velocity addition can be calculated by substituting the spaceship velocity and projectile velocity details in the formula. Solve the equation and get the result.

3. What is the relativity of velocity?

Relativistic velocity addition is the velocities of an object moving at a relativistic speed. An observer of electromagnetic radiation sees relativistic Doppler effects if the source of the radiation is moving relative to the observer.

4. How to use the velocity addition calculator?

A free and user-friendly velocity addition calculator is used to calculate the relative projectile velocity. Enter spaceship velocity, projectile velocity details and hit the calculate button to check the relative projectile velocity as result.

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