Acceleration Due to Gravity Calculator

What this calculator does

Acceleration due to gravity is the rate at which any mass accelerates toward the centre of a larger body, purely because of that body’s gravity. It depends on only two things: how much mass the larger body has, and how far you are from its centre. This calculator applies the acceleration due to gravity formula directly, rather than looking up a pre-set value for a handful of planets, so it works for any mass and distance you enter, including points above a surface.

The formula comes straight from Newton’s law of universal gravitation. Divide out the mass of the smaller object and what is left over is the gravitational field strength at that point, expressed in metres per second squared. At Earth’s surface that works out to the familiar 9.8 m/s², but the same arithmetic answers the question for any moon, planet or hypothetical body.

The formula

Formulag = G × M / r² (G = 6.674×10⁻¹¹ N·m²/kg²)

g equals the gravitational constant G multiplied by the mass of the body, divided by the square of the distance from its centre. G is a fixed constant, 6.674×10⁻¹¹ N·m²/kg², so the only things that change the answer are the mass you enter and how far away you are.

Term	Meaning
g	Acceleration due to gravity at that point, in m/s².
G	The gravitational constant, 6.674×10⁻¹¹ N·m²/kg², fixed for the universe.
M	Mass of the larger body, in kilograms.
r	Distance from the centre of that body to the point being measured, in metres.

The inputs explained

Field	What to enter
Mass (kg)	The mass of the body you are calculating gravity for, in kilograms. Use scientific notation freely, such as 5.972e24 for Earth.
Distance from centre (m)	Distance from the centre of that body, in metres. At the surface, this is the body’s radius.

When to use it

Checking how to calculate acceleration due to gravity for a known planet

Enter a body’s published mass and radius to see how its surface gravity compares with Earth’s, and confirm the arithmetic behind commonly quoted figures.

Gravity above a surface

Increasing the distance beyond a body’s radius shows how quickly gravity weakens with altitude, since it falls off with the square of distance, not linearly.

Working with a hypothetical or fictional body

Because the calculator takes raw mass and radius rather than a fixed list of planets, it also answers the acceleration due to gravity calculator question for made-up or newly discovered bodies once their mass and radius are known.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How does mass alone change gravity, at a fixed radius?

Holding the radius fixed at Earth’s value and increasing only the mass isolates what mass by itself does to surface gravity.

Radius held at Earth’s (6,371 km), mass increasing

Mass	Acceleration due to gravity	As a multiple of Earth gravity
7.348e+22 kg	0.1208 m/s²	0.012×
6.390e+23 kg	1.051 m/s²	0.107×
5.972e+24 kg	9.820 m/s²	1.001×
1.898e+27 kg	3,120.81 m/s²	318.234×

These masses span the Moon’s to Jupiter’s, but every row uses Earth’s radius rather than each body’s real one, so this isolates the effect of mass alone: with radius held fixed, gravity rises in direct proportion to mass. A real body’s gravity also depends on its own radius, which is why Mars and Jupiter do not simply follow their mass ratio to Earth.

How much does gravity weaken with altitude above Earth?

Earth’s mass stays fixed at 5.972×10²⁴ kg; only the distance from the centre changes.

Earth’s mass held fixed, distance from centre increasing

Distance from Earth’s centre	Acceleration due to gravity	As a multiple of Earth gravity
6,371 km	9.820 m/s²	1.001×
6,771 km	8.694 m/s²	0.887×
7,371 km	7.336 m/s²	0.748×
8,371 km	5.688 m/s²	0.580×
13,371 km	2.229 m/s²	0.227×

Moving just 400 km further from the centre (roughly the altitude of the International Space Station) barely changes g, because 400 km is small next to Earth’s 6,371 km radius; gravity only drops noticeably once the distance itself has grown substantially.

Questions

How do you calculate acceleration due to gravity?

Multiply the gravitational constant G by the mass of the body, then divide by the square of the distance from its centre: g = GM/r². G is always 6.674×10⁻¹¹ N·m²/kg², so only mass and distance change the result.

What is the acceleration due to gravity formula based on?

It comes from Newton’s law of universal gravitation, F = GMm/r², with the smaller object’s mass m divided out. What remains, GM/r², is the gravitational field strength, independent of whatever object is falling through it.

Why is gravity different on other planets?

Surface gravity depends on both mass and radius, not mass alone. Mars has roughly a tenth of Earth’s mass but also a smaller radius, so its surface gravity works out to about 38 percent of Earth’s rather than 10 percent.

Does acceleration due to gravity depend on the falling object’s own mass?

No. The formula only uses the mass of the larger body being orbited or stood on. A feather and a hammer accelerate at the same rate in a vacuum because the falling object’s own mass cancels out of the equation.

For gravity already reduced to a single per-planet value, see the weight on other planets calculator. For acceleration from a change in speed instead of gravity, see the acceleration calculator.