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Escape velocity calculator

A-level Fields and space

The minimum speed needed at the surface to escape from a planet’s gravitational field.

v = √(2G M / r)

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

11200 m/s
N m²/kg²

Working

  1. Write the equation
    v = √(2G M / r)
  2. Constants used
    G = 6.67 × 10−11 N m²/kg²
  3. Substitute the values
    v = √(2 × (6.67 × 10−11) × (5.97 × 1024) ÷ (6.37 × 106))
  4. Calculate
    v = 11181.4 m/s
  5. Give the answer to 3 significant figures
    v = 11200 m/s
    In standard form: 1.12 × 104 m/s

Worked example

Find v, the escape velocity. Given: mass of the planet M = 5.97 × 10²⁴ kg; radius of the planet r = 6.37 × 10⁶ m; gravitational constant G = 6.67 × 10⁻¹¹ N m²/kg².

  1. Write the equation
    v = √(2G M / r)
  2. Constants used
    G = 6.67 × 10−11 N m²/kg²
  3. Substitute the values
    v = √(2 × (6.67 × 10−11) × (5.97 × 1024) ÷ (6.37 × 106))
  4. Calculate
    v = 11181.4 m/s
  5. Give the answer to 3 significant figures
    v = 11200 m/s
    In standard form: 1.12 × 104 m/s

Symbols and units

SymbolQuantitySI unit
vEscape velocitym/s
GGravitational constant (constant)N m²/kg²
MMass of the planetkg
rRadius of the planetm

Escape velocity: rearranged

  • To find escape velocity: v = √(2G M / r)
  • To find mass of the planet: M = v2 r / (2G)
  • To find radius of the planet: r = 2G M / v2

Exam tip

It does not depend on the mass of the object that is escaping.

Common questions

What is the formula for escape velocity?

The equation is v = √(2G M / r), where v is the escape velocity (m/s); M is the mass of the planet (kg); r is the radius of the planet (m); G is the gravitational constant (N m²/kg²).

What units should I use for escape velocity?

In SI units: escape velocity in m/s, gravitational constant in N m²/kg², mass of the planet in kg, radius of the planet in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange v = √(2G M / r)?

Rearranging gives these forms: to find escape velocity: v = √(2G M / r). to find mass of the planet: M = v² r / (2G). to find radius of the planet: r = 2G M / v².

Practise escape velocity questions

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Related

Read the full explanation on the Escape speed formula page. More fields and space equations: Coulomb’s law, Uniform electric field, Electric field strength, Field of a point charge, Newton’s law of gravitation, Gravitational field strength, Gravitational potential, Orbital period. See the full list on the a-level physics equation calculator page.