Standard gravity, g₀

A fixed, conventional value for the acceleration due to gravity, used for the kilogram-force, g-force ratings and standard weights. It is a convention rather than a measurement, and not the value anywhere in particular.

g₀ = 9.80665 m/s²

Exact by definition, so it has no uncertainty at all.

In other units

Values marked … are exact, but their decimals run on, so they stop at ten significant figures instead of being rounded.

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.

Standard gravity in SI units and in other units
Quantity	Value
g₀	9.80665 m/s²
g₀	32.17404855… ft/s²
g₀	980.665 cm/s²
1 kgf	9.80665 N

g₀ in ft/s²

9.80665 m/s² ÷ 0.3048 m/ft
= 32.17404855… ft/s²

g₀ in cm/s²

9.80665 m/s² × 100 cm/m
= 980.665 cm/s²

A centimetre per second squared is also called a gal, the unit geophysicists measure gravity in.

1 kgf in N

1 kg × 9.80665 m/s²
= 9.80665 N

The kilogram-force is the weight of one kilogram under standard gravity.

Where the value comes from

The 3rd General Conference on Weights and Measures adopted it in 1901, declaring 980.665 cm/s² the standard acceleration due to gravity, a figure already written into the laws of some countries. The same declaration settled the difference between mass and weight: a body’s standard weight is its mass times this acceleration.

The number came from a measurement made at the International Bureau of Weights and Measures, near Paris, in 1888, divided by a theoretical factor meant to convert it to sea level at a latitude of 45°. Nothing has redefined it since, so it is a fixed convention rather than the gravity at any real place. CODATA lists it as exact, under the symbol gₙ.

Which form to use

Use 9.80665 m/s² wherever a standard or a unit calls for it: the kilogram-force, g-force ratings, standard weights. In a school problem 9.81 m/s² is the usual figure; it differs from g₀ by 0.034 percent, far less than real gravity varies over the Earth.

At sea level, gravity runs from about 9.78 m/s² at the equator to about 9.83 m/s² at the poles, roughly half a percent. Two effects add together: the Earth’s rotation throws the surface outward most strongly at the equator, and the equatorial bulge puts the surface there further from the centre.

Gravity also falls with height, by about 3 × 10⁻⁶ m/s² for every metre climbed, roughly 0.003 m/s² per kilometre. On a mountain that shows in the fourth significant figure; across the globe the change with latitude is larger.

Common mistakes

Treating g₀ as the gravity where you are. It is a convention, and local gravity can differ from it in the second decimal place.
Confusing g, an acceleration, with G, the gravitational constant, which is 6.67430(15) × 10⁻¹¹ m³/(kg·s²) and a different quantity altogether.
Reading a g-force as a force. A 5 g manoeuvre is an acceleration of 5 × 9.80665 m/s²; the force that goes with it depends on the mass.

Tools that use it

Gravitational Potential Energy Calculator takes it as the default value of g.
Kinetic Energy Calculator gives the height a body would have to fall to gain its energy.
Force Calculator (F = ma) shows the acceleration in g and the weight on Earth.
Centrifuge RCF Calculator expresses relative centrifugal force as a multiple of it.
Centripetal Force Calculator shows the acceleration in g.
Gravitational Force Calculator compares the force with the weight of the smaller mass.
Conservation of Energy Simulator pulls the cart along the track, so it sets every potential energy and speed.
Free Fall Calculator takes it as g on Earth, for the fall time, impact speed and terminal speed.

Related constants

Gravitational constant, G = 6.67430(15) × 10⁻¹¹ m³/(kg·s²)