Gravitational Force Calculator
Apply Newton’s law of gravitation, or find surface gravity and escape velocity.
Please note: Results use idealised models — point masses, no air resistance, ideal gases and uniform materials. Real experiments deviate. Use these for study and estimation, not for engineering sign-off.
What the Gravitational Force Calculator does
Every pair of masses attracts with a force proportional to the product of their masses and inversely proportional to the square of their separation. The same law that keeps the Moon in orbit determines a planet’s surface gravity and the speed needed to escape it.
Formula
F = G × m₁ × m₂ ÷ r²g_surface = G × M ÷ r²v_escape = √(2GM ÷ r)G = 6.6743 × 10⁻¹¹ m³ kg⁻¹ s⁻²
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Calculate | one of 2 options | Yes | — |
| First mass | kg | In some modes | Scientific notation works: 5.972e24 is Earth. Accepts more than 0. Shown Calculate is Force between two masses. |
| Second mass | kg | In some modes | 7.348e22 is the Moon. Accepts more than 0. Shown Calculate is Force between two masses. |
| Mass of the body | kg | In some modes | Accepts more than 0. Shown Calculate is Surface gravity and escape velocity. |
| Distance between centres | number | In some modes | Shown Calculate is Force between two masses. |
| Distance between centres unit | one of 9 options | In some modes | Shown Calculate is Force between two masses. |
| Radius of the body | number | In some modes | Shown Calculate is Surface gravity and escape velocity. |
| Radius of the body unit | one of 9 options | In some modes | Shown Calculate is Surface gravity and escape velocity. |
How to use it
- Choose Calculate.
- Fill in the remaining inputs the form shows for your choice.
- Select Calculate.
Worked example
The gravitational pull between the Earth and the Moon.
- First mass
- 5.972e24 kg
- Second mass
- 7.348e22 kg
- Distance
- 384,400 km
F = 6.6743e−11 × 5.972e24 × 7.348e22 ÷ (3.844e8)² = 1.982 × 10²⁰ N.
Frequently asked questions
Why is gravity so weak between everyday objects?
Because G is tiny. Two 100 kg people a metre apart attract with about 0.67 microneutons — utterly swamped by friction and air movement.
What exactly is escape velocity?
The launch speed at which an object’s kinetic energy just equals the gravitational energy binding it, letting it coast away forever without further thrust.