How to use it
- Type the First mass in kilograms, for example 70 kg, and the Second mass, for example 5.9722e24 kg.
- Type the Distance between the centres, for example 6371 km.
- Read the Gravitational force and the acceleration of each body toward the other.
- Read the steps below the result to see how each figure is worked out.
Newton's law of gravitation
Newton's law says that two masses attract each other with a force proportional to the product of their masses. The force falls off with the square of the distance between their centres (OpenStax, University Physics Volume 1, section 13.1).
F = G m1 m2 ÷ r²
G = 6.674 30 × 10⁻¹¹ N·m²/kg², the gravitational constant
m1, m2 = the two masses, kg
r = the distance between their centres, m
F = the force, N- Each body accelerates toward the other by a = G × (the other mass) ÷ r². The acceleration does not depend on the body's own mass.
- Doubling the distance makes the force a quarter as large.
- G is about 6.674 × 10⁻¹¹. Henry Cavendish measured it experimentally, about a century after Newton published the law (OpenStax).
Earth's surface
At Earth's surface the acceleration is G × M ÷ R², with M = 5.9722 × 10²⁴ kg and the volumetric mean radius R = 6371.000 km. That gives 9.820 m/s², the surface gravity in the NASA Earth fact sheet. The real surface gravity differs a little between the equator and the poles, and this calculator treats Earth as a sphere.
What this calculator does not include
- General relativity, which matters only in very strong fields, such as near a black hole, or for very precise timing.
- Forces from three or more bodies. Add the force of each pair as a vector.
- Rotation, tides and the shape of a planet that is not a sphere.
Worked example: 70 kg at Earth's surface
The force is F = G × 70 × 5.9722 × 10²⁴ ÷ (6.371 × 10⁶)² = 687.4 N. The acceleration of the 70 kg body toward Earth is G × 5.9722 × 10²⁴ ÷ (6.371 × 10⁶)² = 9.82 m/s², so its weight is 70 × 9.82 = 687.4 N.
| Quantity | Value |
|---|---|
| Force on the 70 kg body | 687.4 N |
| Acceleration of the 70 kg body | 9.82 m/s² |
| Acceleration of Earth | 1.151 × 10⁻²² m/s² |
Frequently asked questions
Why is the acceleration of Earth so small?
The same force is shared by both bodies, and acceleration is force divided by mass. Earth's mass is 5.9722 × 10²⁴ kg, so the 70 kg body moves it only by about 1.15 × 10⁻²² m/s².
Which distance should I type?
The distance between the centres of the two bodies. For an object on Earth's surface use Earth's mean radius, 6371 km; for a satellite, its distance from the centre of Earth.
Why does a small force show as pN?
The prefix keeps the number short. The attraction of two 1 kg masses one metre apart is 66.74 pN, which is 6.674 × 10⁻¹¹ N.
Can I find the weight of an object on another planet?
Yes. The weight is the gravitational force on the object at the planet's surface, so enter the object's mass, the planet's mass and the planet's radius.
Is my data sent to a server?
No. The calculation runs in your browser, and nothing you type is sent to us or stored.
Sources
- OpenStax University Physics Volume 1, section 13.1: Newton's Law of Universal Gravitation
- NIST: Newtonian constant of gravitation G, CODATA 2022 (6.674 30 × 10⁻¹¹ m³/(kg·s²))
- NASA NSSDCA: Earth Fact Sheet (mass 5.9722 × 10²⁴ kg, volumetric mean radius 6371.000 km, surface gravity 9.820 m/s²)
Figures and text last checked on Tuesday, November 10, 2026.