Gravitational Acceleration Calculator Formula
Understand the math behind the gravitational acceleration calculator. Each variable explained with a worked example.
Formulas Used
Surface Gravity
gravity = 6.674e-11 * mass / pow(radius, 2)In Earth g
gravity_g = (6.674e-11 * mass / pow(radius, 2)) / 9.80665Variables
| Variable | Description | Default |
|---|---|---|
mass | Body Mass(kg) | 5.972e+24 |
radius | Body Radius(m) | 6371000 |
How It Works
Surface Gravitational Acceleration
Formula
g = G M / r²
Divide by 9.80665 m/s² to express in multiples of Earth's standard gravity.
Worked Example
Confirm Earth's surface gravity.
mass = 5.972e+24radius = 6371000
- 01g = G M / r²
- 02G M = 6.674e-11 × 5.972e24 = 3.986e14
- 03r² = (6.371e6)² = 4.059e13
- 04g = 3.986e14 / 4.059e13 ≈ 9.82 m/s²
Frequently Asked Questions
Why does Mars have lower gravity than Earth?
Mars has about 11% of Earth's mass and 53% of its radius, giving about 38% of Earth's surface gravity.
Does this formula work above the surface?
Yes, replace r with the distance from the centre (body radius + altitude). Gravity decreases as 1/r².
What is standard gravity?
Standard gravity is defined as exactly 9.80665 m/s².
Ready to run the numbers?
Open Gravitational Acceleration Calculator