Gravitational Potential Energy (General)

U = -\frac{Gm_1 m_2}{r}

General gravitational potential energy (negative).

Variables

Potential energy

Gravitational PE

In SI units: kg·m²/s²

Gravitational constant

6.674×10⁻¹¹

In SI units: m³/(kg·s²)

Allowed values: greater than 0

N·m²/kg²

m₁

Mass 1

First mass

Allowed values: 0 or more

m₂

Mass 2

Second mass

Allowed values: 0 or more

Distance

Separation

Allowed values: greater than 0

Derivation

U = -∫F dr = -Gm₁m₂/r (zero at infinity).

Your notes

0/5000

Constants in this formula

Gravitational Constant

6.674 30 × 10⁻¹¹ ± 0.000 15 × 10⁻¹¹. Measured (CODATA 2018).

N·m²/kg²

Check value

Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

G = 6.674 30 × 10⁻¹¹ N·m²/kg² (Gravitational constant)
m₁ = 2 kg (Mass 1)
m₂ = 3 kg (Mass 2)
r = 4 m (Distance)

Result: U = -1.001145 × 10⁻¹⁰ J

Other mechanics formulas with the same quantities

Gravitational Field (Gravitation) shares Gravitational constant, Distance
Center of Mass (Two Objects) (Dynamics) shares Mass 1, Mass 2
Orbital Velocity (Gravitation) shares Gravitational constant
Orbital Period (Gravitation) shares Gravitational constant
Surface Gravity (Gravitation) shares Gravitational constant
Geosynchronous Orbit Radius (Gravitation) shares Gravitational constant

Where this formula is listed

Mechanics formulas, under Gravitation.
In the mechanics list it comes after Gravitational Field and before Orbital Velocity.
Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Gravitational Potential Energy (General) formula?

Gravitational Potential Energy (General) is written U = −Gm₁m₂/r. General gravitational potential energy (negative). It belongs to Mechanics, under Gravitation.

What are the units in U = −Gm₁m₂/r?

In SI units, U is potential energy, measured in kg·m²/s²; G is gravitational constant, measured in m³/(kg·s²); m₁ is mass 1, measured in kg; m₂ is mass 2, measured in kg; r is distance, measured in m.

How is the Gravitational Potential Energy (General) formula derived?

U = -∫F dr = -Gm₁m₂/r (zero at infinity). The result is U = −Gm₁m₂/r.