Gravitational Field Strength Calculator

About the Gravitational Field Strength

This calculator finds the surface gravity, or gravitational field strength, of a planet, moon, or any other roughly spherical body from its mass and radius. It is useful for comparing how strongly gravity pulls at the surface of different worlds, or for building physics problems that need surface gravity for a body other than Earth.

How It Works

You enter the body's mass in units of 10 to the 24th power kilograms and its radius in kilometers. The calculator converts both to base SI units (kilograms and meters), then applies Newton's law of gravitation evaluated at the surface, where the distance term equals the radius. If the radius is zero or negative, it returns 0 m/s squared instead of attempting an undefined division.

g = G x M / r^2, where G = 6.674 x 10^-11 N*m^2/kg^2, M is the body's mass in kg, and r is its radius in meters.

Formula & Methodology

By hand, first convert the entered mass to kilograms by multiplying the 10^24 kg figure by 10^24, and convert the radius to meters by multiplying the kilometer value by 1000. Multiply G by the mass in kilograms, then divide by the radius in meters squared. The result is the surface gravitational acceleration in meters per second squared, which is numerically the same as the field strength in newtons per kilogram.

Examples

Earth's surface gravity

With mass 5.97 x 10^24 kg and radius 6,371 km, the calculator gives g = (6.674x10^-11 x 5.97x10^24) / (6,371,000)^2, approximately 9.82 m/s squared, close to Earth's commonly cited 9.81 m/s squared.

The Moon's weaker pull

Using the Moon's mass of about 0.0735 x 10^24 kg and radius 1,737 km, the same formula gives roughly 1.63 m/s squared, showing why an object weighs about a sixth as much on the lunar surface as on Earth.

Advantages

Turns a two-step unit conversion and inverse-square calculation into a single instant result.
Makes it simple to compare surface gravity across different planets, moons, or hypothetical bodies just by changing mass and radius.
Guards against a division-by-zero error when radius is left blank or entered incorrectly.

Common Mistakes

Entering mass as a raw number instead of in the requested 10^24 kg units, which throws the result off by many orders of magnitude.
Forgetting that radius must be entered in kilometers, not meters, since the calculator performs the km-to-meter conversion internally.
Assuming surface gravity depends only on mass, when in fact a smaller radius increases surface gravity for the same mass because gravity scales inversely with radius squared.

Edge Cases to Watch For

A radius entered as zero or negative returns a surface gravity of 0 m/s squared rather than an error or an infinite value.
The formula assumes a spherically symmetric mass distribution, so irregular bodies such as asteroids have field strength that varies by location, making this a useful average rather than an exact value everywhere on the surface.
This computes surface gravity only. Below the surface, field strength decreases roughly linearly toward the center for a uniform sphere, a different relationship than the inverse-square law used here.

Common Use Cases

Astronomy and physics students calculating surface gravity for planets, moons, or exoplanets in coursework.
Science writers or hobbyists estimating how much an object would weigh on another world.
Educators building comparison tables of surface gravity across the solar system.

Frequently asked questions

Why is Mars's surface gravity so much lower than Earth's despite having a similar composition?

Surface gravity depends on both mass and radius, and Mars has only about 11% of Earth's mass but 53% of Earth's radius - since gravity scales directly with mass but inversely with radius squared, the much smaller mass dominates, leaving Mars with roughly 38% of Earth's surface gravity even though the two planets are made of broadly similar rocky material.