# Rocket Equation Calculator

Created by Dominik Czernia, PhD candidate
Reviewed by Bogna Szyk
Last updated: Jan 12, 2022

With this rocket equation calculator, you can explore the principles of motion of the vehicles that we call rockets. The first man landing on the moon took place in 1969 during a mission called Apollo 11. From that time, the basics of jet rockets remained the same. One of the simplest cases of the movement of such a rocket can be described using the Tsiolkovsky rocket equation (also called the ideal rocket equation). Read on if you want to learn more about it.

## Tsiolkovsky rocket equation

Ideal rocket equation describes the motion of a device that can apply an acceleration to itself using thrust. Such a rocket burns the propelling fuel and simultaneously reduces its weight. Burned propellants are exhausted from the nozzle, and the rocket accelerates as the result of the conservation of momentum.

Tsiolkovsky rocket equation should be used only in simple cases when no other external forces act on a rocket. In real motion, the rocket has to overcome both air resistance and gravity, which was taken into account by Tsiolkovsky in his further, more complicated, studies.

## Rocket equation calculator

The velocity of a rocket can be estimated with the formula below:

Δv = ve * ln(m0 / mf)

where

• Δv is the change of the velocity of the rocket,
• ve is the effective exhaust velocity,
• m0 is the initial mass (rocket and propellants),
• mf is the final mass (rocket without propellants).

The change of the velocity of the rocket Δv is the difference between the final and the initial velocity of the rocket. The effective exhaust velocity ve describes how fast propellants expel from the rocket. From the above equation you can see that the greater are ve and m0 (more propellant), the higher velocities you can achieve.

## Multistage rocket

You have probably seen many times that rockets consist of several parts that are rejected one after another during the movement of the rocket. When a particular part runs out the fuel, it becomes a redundant mass and should be removed. The change of the velocity Δv can be calculated independently for each step with our rocket equation calculator and then linearly summed up Δv = Δv1 + Δv2 + .... An essential advantage for this is that each stage can use a different type of rocket engine which is tuned for particular conditions (lower parts - atmospheric pressure, upper parts - vacuum).

Dominik Czernia, PhD candidate
Effective exhaust velocity
ft/s
Initial mass
US ton
Final mass
US ton
Change of velocity
mi/s
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