Gravitational constant, G

The constant in Newton’s law of gravitation, F = Gm₁m₂/r², and in Einstein’s general relativity. CODATA calls it the Newtonian constant of gravitation, and it is the one measured constant in this site’s table.

G = 6.67430(15) × 10⁻¹¹ m³/(kg·s²)

CODATA 2022, measured. Standard uncertainty 0.00015 × 10⁻¹¹ m³/(kg·s²), which is 2.2 × 10⁻⁵ of the value.

In other units

Measured values are in CODATA’s concise form: the digits in brackets are the standard uncertainty in the last two places, so 6.67430(15) means 6.67430 ± 0.00015.

Gravitational constant in SI units and in other units
Quantity	Value
G	6.67430(15) × 10⁻¹¹ m³/(kg·s²)
G	6.67430(15) × 10⁻¹¹ N·m²/kg²
G	6.67430(15) × 10⁻⁸ cm³/(g·s²)

G in N·m²/kg²

1 N = 1 kg·m/s², so N·m²/kg² = m³/(kg·s²)
= 6.67430(15) × 10⁻¹¹ N·m²/kg²

The same number: the two units are the same thing written two ways.

G in cm³/(g·s²)

6.67430(15) × 10⁻¹¹ m³/(kg·s²) × 10⁶ cm³/m³ ÷ 1000 g/kg
= 6.67430(15) × 10⁻⁸ cm³/(g·s²)

The value in the centimetre-gram-second units of older physics texts.

Where the value comes from

G cannot be derived from anything else; it has to be measured, and gravity between laboratory masses is feeble. The classic method is Henry Cavendish’s torsion balance of 1798: large lead spheres pull on small ones hung from a fine wire, and the twist of the wire gives the force.

Modern experiments use refined torsion balances, pendulums and atom interferometers, and their results disagree with one another by more than their stated uncertainties. CODATA’s value therefore carries a relative uncertainty of 2.2 × 10⁻⁵, about 1 part in 45,000, and the 2018 adjustment gave the same 6.67430(15) × 10⁻¹¹.

Which form to use

Quote a gravitational result to no more than five significant figures; the sixth is not known. Use masses in kilograms and distances in metres between centres, and the force comes out in newtons.

Astronomy mostly sidesteps G. The product GM for the Sun or the Earth is known far more precisely than either factor, from the orbits of planets and satellites, so orbital calculations use GM directly.

Common mistakes

Confusing G with g. G is the same everywhere; g at a planet’s surface is GM/r² and changes from place to place.
Measuring the distance between surfaces rather than centres, or forgetting to square it.
Printing G to seven or more figures. Its uncertainty already reaches the fifth significant figure, so the extra digits are noise.

Tools that use it

Gravitational Force Calculator computes F = Gm₁m₂/r² and the field Gm/r² with it.

Related constants

Standard gravity, g₀ = 9.80665 m/s²