# Rocket Equation Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Oct 20, 2022

With this rocket equation calculator, you can explore the principles of motion of the vehicles that we call rockets.

The first man to land on the Moon happened 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).

## Tsiolkovsky rocket equation

The 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 (see our specific impulse calculator). Burned propellants are exhausted from the nozzle, and the rocket accelerates as a result of the conservation of momentum.

We should use the Tsiolkovsky rocket equation 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.

💡 You might also want to check out our thrust-to-weight ratio calculator and isentropic flow calculator.

## Rocket equation calculator

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

$\Delta v = v_\text{e} \ln\frac{m_0}{m_f},$

where:

• $\Delta v$ – Change of the velocity of the rocket;
• $v_\text{e}$ – Effective exhaust velocity;
• $m_0$ – Initial mass (rocket and propellants); and
• $m_f$ – Final mass (rocket without propellants).

The change in the velocity of the rocket $\Delta v$ is the difference between the final and the initial velocity of the rocket. The effective exhaust velocity $v_\text{e}$ describes how fast propellants expel from the rocket.

From the above equation, you can see that the greater are $v_\text{e}$ and $m_0$ (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 of fuel, it becomes a redundant mass and should be removed. The change of the velocity $\Delta v$ can be calculated independently for each step with our rocket equation calculator and then linearly summed up $\Delta v = \Delta v_1 + \Delta v_2 + ...$.

An essential advantage of this is that each stage can use a different type of rocket engine that is tuned for particular conditions (lower parts – atmospheric pressure, upper parts – vacuum).

🔎 To learn about the fundamental physics behind rockets, check out the acceleration calculator and conservation of momentum calculator.

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