Escape Velocity Calculator

Created by Dominik Czernia, PhD candidate
Last updated: Jun 23, 2022

Our escape velocity calculator serves as a quick way of estimating the escape velocity formula for any planet or star you want. You can immediately use the tool next to the text or check the article below to learn what the escape velocity of Earth is and how to use the escape speed formula in practice.

The escape velocity calculator uses the considerations of the gravitational force definition. We have prepared a separate article about this force. Be sure to check it!

Escape velocity formula

The escape velocity equation is simple to remember, and it originates from comparing the gravitational and centrifugal force formulae. It has the following form:

ve=2GMRv_e = \sqrt{\frac{2GM}{R}}

where:

  • vev_e - The escape velocity, which is the minimum speed an object needs to leave the surface of a celestial body, e.g., a planet;
  • G6.67×1011 m3kg1s2G \approx 6.67\times10^{-11} \text{ m}^3 \cdot \text{kg}^{-1} \cdot \text{s}^{-2} - The universal gravitational constant. It is also helpful if you need to know how to calculate orbital period.
  • MM - The mass of the celestial body;
  • RR - The radius of the celestial body.

You can use the escape velocity equation to estimate the amount of work (or energy) you need to put into the object to leave a planet permanently. To do so, find the escape velocity and use its value, e.g., in the Omni Calculator's work calculator with a final speed of 0 m/s.

How to use the escape velocity calculator

To use the built-in escape speed formula in our tool, you need to provide it with two inputs:

  1. Mass\text{Mass} - The planet's mass you want to escape from. If you want to find the escape velocity of Earth, change the units to weights of the Earth\text{weights of the Earth} and type in the number 11. The value of 1 Earth1 \text{ Earth} equals about 5.972×1024 kg5.972\times10^{24} \text{ kg}.
  2. Radius\text{Radius} - The planet's radius. Similarly, you can select appropriate units of Earth radii\text{Earth radii} and enter 1 R⊕1 \text{ R⊕} which is about 6,371 km6,371 \text{ km}.
  3. The escape velocity calculator will quickly find the escape velocity, which you can display in various units. For Earth, it has a constant value of about 11.2 km/s or 25 mph.

If you need more calculations regarding the Earth's orbit, our satellite velocity calculator might be precisely the tool you're looking for. Be sure to check it!

Dominik Czernia, PhD candidate
Escape velocity equation
Mass (M)
Earths
Radius (R)
R⊕
First cosmic velocity
mi/s
Escape velocity (vₑ)
mi/s
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