Gravitational Potential Calculator

How it works

1. 1Enter the source mass M in kilograms (scientific notation such as 5.972e24 for Earth is accepted) and the distance r from its centre in metres.
2. 2The calculator computes V = −G·M ÷ r, where G = 6.674×10⁻¹¹ N·m²/kg². The result is the gravitational potential in joules per kilogram.
3. 3The result panel shows V in J/kg; the stat grid shows the magnitude in MJ/kg and notes that V is negative and rises toward 0 with distance.

Use cases

• Astrophysics and orbital mechanics — the energy per unit mass to move between orbits.
• Geophysics — the potential at Earth’s surface or satellite altitude for geodetic work.
• Physics education — verifying Earth’s surface potential (≈ −62.6 MJ/kg).

Frequently asked questions

What is the formula and what do the symbols mean?

V = −G·M ÷ r, where G ≈ 6.674×10⁻¹¹ N·m²/kg², M is the source mass in kg, and r is the distance from the centre in metres, giving J/kg. For Earth at the surface, V ≈ −6.26×10⁷ J/kg (≈ −62.6 MJ/kg).

Why is gravitational potential always negative?

The zero reference is at infinity. As a unit mass falls in from infinity, gravity does positive work, so the potential at any finite r is negative. The deeper into the well (smaller r), the more negative V becomes.

What is the difference between potential (J/kg) and potential energy (J)?

Potential V is the energy per unit mass: V = −GM ÷ r. Potential energy U is for a specific mass m: U = m·V = −GMm ÷ r. A 70 kg astronaut at Earth’s surface has U ≈ 70 × (−6.26×10⁷) ≈ −4.38×10⁹ J, while V is −6.26×10⁷ J/kg regardless of mass.