# Rocket Equation Calculator

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).

Read on if you want to learn more about it.

## 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:

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.