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Gravitational Force Calculator

Find the gravitational pull between two masses with Newton’s law, and each body’s field.

By Nitin Raturi · Last reviewed

Your worksheet

How to use the Gravitational Force Calculator

Find the pull between any two masses.

  1. Enter both masses in kilograms.
  2. Enter the distance between their centres in metres.
  3. Read the force and each body’s gravitational field.

Good to know

  • Type very large or small numbers as 5.972e24 or 1e-3.

F = G m₁ m₂ ÷ r². Type large values as 5.972e24.

First mass (kg)

The mass of one body.

How to fill it in

  • Enter kilograms; type 5.972e24 for Earth.

Example

Earth and a 70 kg person at the surface: 687.3981 N, a field of 9.8200 m/s².

Second mass (kg)

The mass of the other body.

How to fill it in

  • Enter kilograms; the Moon is 7.342e22.

Example

Earth and the Moon attract with 1.980 × 10²⁰ N.

Distance between centres (m)

From the centre of one body to the centre of the other.

How to fill it in

  • For a person on Earth, use Earth’s radius, about 6.371e6 m.

Example

Two 9,000 kg vehicles 10 m apart: 5.406 × 10⁻⁵ N; two people 1 m apart: 2.803 × 10⁻⁷ N.

Gravitational force

5.406 × 10⁻⁵ N

Masses of 9,000.0000 kg and 9,000.0000 kg, 10.0000 m apart centre to centre, attract each other with 5.406 × 10⁻⁵ N.

Force on each mass
5.406 × 10⁻⁵ N
Field of mass 1 at that distance
6.007 × 10⁻⁹ m/s²
Field of mass 2 at that distance
6.007 × 10⁻⁹ m/s²

Point masses or spheres, with r between their centres. G = 6.674 30 × 10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA). Each mass feels the same force.

ChangelogHow we test this calculatorEmbed this calculator

How this calculator works

  1. Step 1Massesm₁ × m₂More mass, more pull.
  2. Step 2Distance÷ r²Inverse square of the separation.
  3. Step 3Force× GG = 6.674 30 × 10⁻¹¹.

Every two masses attract each other. The force grows with both masses and falls with the square of the distance between their centres.

G is tiny, so the pull between everyday objects is far too small to notice. Only planet-sized masses produce forces we feel.

Worked example: OpenStax Example 13.1

Two 9,000 kg vehicles, 10 m apart
F
G m₁ m₂ ÷ r²
  1. m₁ × m₂9,000 × 9,0008.1 × 10⁷ kg²
  2. ÷ r²÷ 10²8.1 × 10⁵
  3. Force× 6.674 30 × 10⁻¹¹5.406 × 10⁻⁵ N

OpenStax, with G = 6.67 × 10⁻¹¹, gives 5.4 × 10⁻⁵ N.

Read the result

  • Two people, 1 m apart2.803 × 10⁻⁷ NFar too small to feel.
  • Earth and the Moon1.980 × 10²⁰ NKeeps the Moon in orbit.

A 70 kg person on Earth’s surface feels 687.3981 N, which is their weight; Earth’s field there is 9.8200 m/s².

Assumptions and limits

  • Spheres or pointsMeasure r between centres.
  • Measured GCODATA value with small uncertainty.
  • Not relativityNewtonian gravity only.
  • Equal and oppositeBoth masses feel the same force.

Newton's law of gravity sets weight on every planet and the swing of a pendulum.

To see what a mass weighs on other planets, use the weight calculator. The pendulum calculator shows how gravity sets a swing’s period.

Common mistakes

  • Mistake: Measuring from the surfaces.

    Instead: Use centre-to-centre distance.

  • Mistake: Forgetting to square r.

    Instead: Twice the distance gives a quarter of the force.

Checking the method

A separate script works out each body’s field first, in exact fractions, and reproduces OpenStax Example 13.1.

Read how we test our calculators, or browse more maths calculators.

Frequently asked questions

What is the force between two 9,000 kg masses 10 m apart?

5.406 × 10⁻⁵ N, as in OpenStax Example 13.1 (5.4 × 10⁻⁵ N).

How strongly do Earth and the Moon attract?

With centres 3.844 × 10⁸ m apart, 1.980 × 10²⁰ N.

What force does Earth exert on a 70 kg person?

687.3981 N at the surface: the person’s weight.

Do two people attract each other?

Yes, but only with 2.803 × 10⁻⁷ N at 1 m.

What value of G does it use?

G = 6.674 30 × 10⁻¹¹ m³ kg⁻¹ s⁻², the CODATA value from NIST.

Sources and methodology

The formulas are standard time-value-of-money results. We check every figure against golden values worked out independently, by closed form and by month-by-month simulation; see the methodology.

Written and maintained by Nitin Raturi, a software engineer (about the author). Last reviewed 4 Nov 2026; next review due by . Found an error? Tell us.

Changelog

  • : Initial release.