Case 1
- Mass of the body
- 5.97210²⁴ kg
- Radius of the body
- 6371000m
9.819973m/s²
Open with these valuesSurface Gravity Calculator
9.819973m/s²
Result: 9.819973 m/s²Surface gravity is the acceleration a body produces at its own surface: g = G × M / r². Earth gives 9.82 m/s², the Moon 1.62 and Jupiter 25.92. Enter the mass in units of 10²⁴ kg — Earth is 5.972 — and the radius in metres. Divide the answer by 9.80665 to read it in Earth gravities.
Worked examples
Case 2
- Mass of the body
- 0.0734210²⁴ kg
- Radius of the body
- 1737400m
1.623381m/s²
Open with these valuesCase 3
- Mass of the body
- 189810²⁴ kg
- Radius of the body
- 69911000m
25.918562m/s²
Open with these valuesHow it's calculated
g = G × M ÷ r²
- StepEnter the mass in units of 10²⁴ kg — Earth is 5.972, the Moon 0.07342.
- StepEnter the radius in metres, from the centre to the surface.
- ResultRead g in m/s²; divide by 9.80665 for the number of Earth gravities.
Reference table
| Mass, radius | Body and Earth gravities | Gravity (m/s²) |
|---|---|---|
| 0.07342, 1737400 | The Moon, 0.17 g | 1.623381 |
| 0.6417, 3389500 | Mars, 0.38 g | 3.727919 |
| 5.972, 6371000 | Earth, 1.00 g | 9.819973 |
| 1898, 69911000 | Jupiter, 2.64 g | 25.918562 |
| 1989000, 695700000 | The Sun, 27.97 g | 274.281490 |
Questions
How do I calculate surface gravity?
Multiply the gravitational constant by the body's mass and divide by its radius squared: g = G × M / r², with G = 6.6743e-11. The mass box counts in units of 10²⁴ kg, so Earth is 5.972 at a radius of 6371000 m. That gives about 9.82 m/s².
What is surface gravity?
Surface gravity is the gravitational acceleration an object feels at the surface of a planet, moon or star. It is measured in metres per second squared and decides how much you would weigh standing there. Earth's is about 9.81 m/s².
Why does the radius matter so much?
Because the radius is squared in the denominator. Doubling a body's radius while keeping its mass divides the surface gravity by four. That is why a very massive but very large planet can still have gentle surface gravity, and why size counts as much as mass.
What does one g mean?
One g is standard gravity, defined as exactly 9.80665 m/s², the conventional value for Earth's surface. Expressing a result as a multiple of g shows how the pull compares with home: the Moon is about 0.17 g, Mars 0.38 g and Jupiter 2.64 g.
Why does Earth come out at 9.82 rather than 9.81?
The formula treats Earth as a uniform sphere of mean radius 6371 km and ignores both its rotation and its flattening. The measured value at the surface runs from 9.78 at the equator to 9.83 at the poles. The 9.82 here is the idealised figure, not a mistake.
What is the difference between surface gravity and weight?
Surface gravity is an acceleration in m/s² and is the same for everyone standing there. Weight is that acceleration times your own mass, so it differs from person to person. Multiply your mass by the surface gravity to find your weight on any body.
Sources and last check
Information, not professional advice.