Acceleration Due To Gravity Calculator

What it is and when to use it

The acceleration due to gravity, written g, is how quickly an object speeds up when only gravity acts on it. On Earth's surface it is about 9.8 metres per second squared, but the value depends on the mass of the planet, its radius, and how far above the surface you are. This calculator finds g for any spherical body from those inputs and also gives the circular orbital speed at the same distance.

Use it for physics coursework, for comparing surface gravity on the Moon or Mars with Earth, for estimating how much weaker gravity is at orbital altitude, or as a quick sanity check on planetary data. Leave the mass and radius blank to use Earth, or enter another body's values. The height field lets you see how gravity weakens as you move away from the surface.

The formula and how it works

The calculator uses Newton's law of universal gravitation for a spherical body:

g = G x M / r²
G is the gravitational constant, 6.674 x 10^-11 N m² kg^-2.
M is the mass of the body in kilograms.
r is the distance from the centre of the body in metres, equal to the radius plus the height above the surface.
v = sqrt(G x M / r) is the speed of a circular orbit at that distance.

The ratio to Earth standard divides g by 9.80665 m/s squared. The model ignores rotation, atmosphere and departures from a perfect sphere.

Worked example

Use Earth with M = 5.972 x 10²⁴ kg and radius 6371 km, at a height of 400 km. The distance from the centre is r = 6371 + 400 = 6771 km = 6.771 x 10⁶ m. Then G x M = 6.674 x 10^-11 x 5.972 x 10²⁴ = 3.9857 x 10¹⁴.

Dividing by r squared, which is 4.5848 x 10¹³, gives g = 8.694 m/s squared, or 0.887 times Earth's standard value. The circular orbital speed is the square root of 3.9857 x 10¹⁴ / 6.771 x 10⁶, about 7672 m/s or 7.672 km/s. At the surface (height 0) the same inputs give 9.820 m/s squared and 7.910 km/s.

Common mistakes and how to interpret the result

Entering the radius in metres: the field expects kilometres, so 6371 not 6371000.
Measuring height from the centre: the height field is above the surface, and the calculator adds the radius for you.
Confusing weightlessness with zero gravity: gravity in low Earth orbit is still close to its surface value.
Expecting the surface answer to match measured values exactly: rotation and Earth's shape change real gravity by a few tenths of a percent with latitude.

Frequently Asked Questions

Why does the calculator give 9.82 m/s squared for Earth instead of 9.81?

It uses Newton's law of gravitation with Earth's mean radius and treats the planet as a perfect non-rotating sphere. Real measured gravity is about 9.80665 m/s squared as a standard value and varies from about 9.78 at the equator to 9.83 at the poles because Earth spins and bulges at the equator. The spherical model is within about 0.15 percent of the standard value.

How does gravity change with height?

It falls off with the square of the distance from the planet's centre. At 400 km, roughly the altitude of the International Space Station, gravity is still about 89 percent of its surface value. Astronauts feel weightless there because they are in continuous free fall around the Earth, not because gravity has vanished.

Can I use it for other planets and moons?

Yes. Enter the body's mass in kilograms and its mean radius in kilometres. For the Moon use about 7.342e22 kg and 1737.4 km, which gives roughly 1.62 m/s squared. Numbers in scientific notation such as 5.972e24 are accepted by the mass field.

Does the mass of the falling object matter?

Not for the acceleration. The small object's mass cancels out in the formula, which is why a hammer and a feather fall at the same rate in a vacuum. The mass of the object only matters when you compute its weight force, which is that mass multiplied by g.