Enter the exhaust velocity, initial mass, and final mass into the calculator to determine the delta-v of a rocket.

Delta-V Formula

The following formula is used to calculate the delta-v of a rocket: 

∆v = Ve * ln(mi / mf)
  • Where ∆v is the change in velocity of the rocket (m/s)
  • Ve is the exhaust velocity (m/s)
  • mi is the initial mass of the rocket (kg)
  • mf is the final mass of the rocket (kg)

This formula assumes a constant exhaust velocity. To calculate delta V, multiply the exhaust velocity by the natural log of the initial mass divided by the final mass.

What is Delta-V?

Definition:

Delta-V, denoted ∆v, is a term used in aerospace to describe the change in velocity of a rocket due to the speed and mass of the exhaust coming out of the rocket.

Delta-V is also a measure of the impulse per unit mass that a rock or spacecraft needs in order to successfully achieve a maneuver such as landing on Mars, etc.

How to calculate Delta-V?

Example:

The following example problem outlines the steps and information needed to calculate the delta-v of a spacecraft.

First, determine the exhaust velocity. For this example, the exhaust velocity is measured to be 500 m/s.

Next, measure/calculate the initial mass of the rocket. In this example, the initial mass is found to be 1000 kg.

Next, measure the final mass of the rocket. For this problem, the final mass is measured to be 400kg.

Finally, calculate the delta-v using the formula above:

∆v = Ve * ln(mi / mf)

∆v = 500 * ln(1000 /400)

∆v = 458.14 m/s