Escape Velocity Calculator
Calculate the escape velocity of any celestial body using v_e = √(2GM/R). Enter mass (kg) and radius (m). Earth's escape velocity is ~11,186 m/s.
How to use this tool
- Enter body mass m and body radius r in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your escape velocity and the full breakdown beneath it.
Escape velocity is the minimum speed needed to leave a body's gravitational field without further propulsion: v_e = √(2GM/R), where G = 6.674×10⁻¹¹ N·m²/kg², M is mass and R is radius.
Formula
ve = √(2GM ÷ R)
Where: G = 6.674 × 10−11 N·m²/kg² (gravitational constant), M = body mass (kg), R = body radius (m).
How it works
Escape velocity is the minimum speed an object needs to escape a celestial body's gravitational field without further propulsion. It is derived by equating the object's kinetic energy to the magnitude of its gravitational potential energy: ½mv2 = GMm/R, which simplifies to the formula above.
The calculator uses G = 6.674 × 10−11 N·m²/kg² and returns the result in both m/s and km/s. It assumes a spherically symmetric, non-rotating body; rotation and atmospheric drag are not accounted for.
Worked example
Worked example (Earth)
- Given: Earth's mass M = 5.972 × 10²⁴ kg, Earth's radius R = 6 371 000 m, G = 6.674 × 10⁻¹¹.
- Compute 2GM = 2 × 6.674×10⁻¹¹ × 5.972×10²⁴ = 7.972×10¹⁴.
- Divide by R: 7.972×10¹⁴ ÷ 6 371 000 ≈ 1.2512×10⁸.
- vₑ = √(1.2512×10⁸) ≈ 11 185.73 m/s.
Escape velocity = 11185.73 m/s (approximately 11.186 km/s).
Key terms
- Escape velocity
- The minimum speed required for an object to break free from a body's gravitational pull, starting from its surface, with no further thrust.
- Gravitational constant (G)
- A fundamental physical constant equal to 6.674 × 10⁻¹¹ N·m²/kg², describing the strength of gravitational attraction.
- Gravitational potential energy
- The energy stored in an object due to its position in a gravitational field, equal to −GMm/R at the surface.
- Celestial body
- A natural object in space such as a planet, moon, or asteroid with sufficient mass to exert significant gravity.
- Kinetic energy
- Energy possessed by an object due to its motion, equal to ½mv².
Frequently asked questions
- What is Earth's escape velocity?
- Approximately 11.2 km/s (≈ 40,270 km/h). Rockets don't need to reach this speed instantly — they can achieve escape with continuous thrust at lower speeds.
- Does atmosphere affect escape velocity?
- Escape velocity is a theoretical value ignoring atmosphere. In practice, air resistance means rockets must carry extra fuel.