BYTETOOLS

Gravitational Force Calculator

Apply Newton's law of universal gravitation to find force, mass or separation, plus surface gravity and escape velocity with presets for every planet.

1.9806e+20 N
Force
3.3163e-5 m/s²
Acceleration of m₁
0.0027 m/s²
Acceleration of m₂
384,400,000 m
Separation used

F = G·m₁·m₂ ÷ r²

  • F = 6.6743e-11 × 5.9722e+24 kg × 7.3420e+22 kg ÷ (384,400,000 m)² = 1.9806e+20 N
  • Both bodies feel the same size of force in opposite directions (Newton's third law), but the lighter one accelerates more: a = F ÷ m.
  • Doubling the separation quarters the force — that is what "inverse square" means.
  • G = 6.67430e-11 m³·kg⁻¹·s⁻² (CODATA 2018).

Newton's law of universal gravitation treats both bodies as point masses (or perfect uniform spheres), so r is always measured centre to centre. The body presets use NASA fact-sheet masses and equatorial radii; computed surface gravity matches the published column to three significant figures, and Earth comes out at 9.80 m/s² with an escape velocity of 11.18 km/s. General relativity supersedes this formula near very dense objects, but for planets, satellites and everyday masses the Newtonian answer is correct to far more digits than you need.

What is the Gravitational Force Calculator?

Newton's law of universal gravitation gives the pull between two masses as F = G·m₁·m₂ ÷ r², with G = 6.67430 × 10⁻¹¹ m³·kg⁻¹·s⁻² and r measured centre to centre. Doubling the separation quarters the force.

  • Force, surface gravity and escape velocity from one set of inputs
  • Solves F = Gm₁m₂/r² for force, either mass or the separation
  • Mass units up to Earth masses and solar masses; distances up to light-years
  • Presets for the Sun, all eight planets, the Moon and Pluto from NASA data
  • Circular orbit speed and per-body acceleration reported alongside the answer
  • Runs 100% locally in your browser — no uploads, no accounts

How to use the Gravitational Force Calculator

  1. 1

    Choose the calculation: force between two masses, surface gravity, or escape velocity.

  2. 2

    For the force mode, pick which of F, m₁, m₂ or r you want to solve for.

  3. 3

    Enter the masses and separation with their unit dropdowns; scientific notation such as 5.97e24 is accepted.

  4. 4

    For gravity or escape velocity, select a body preset to fill in its mass and radius, then edit either value.

  5. 5

    Read the result tiles and copy the working, which includes the value of G used.

About the Gravitational Force Calculator

The ByteTools Gravitational Force Calculator covers three related problems. It solves F = G·m₁·m₂ ÷ r² for the force, either mass or the separation; it works out surface gravity from g = G·M ÷ R²; and it gives escape velocity from v = √(2GM ÷ r), along with the circular orbit speed at the same radius, which is always escape velocity divided by √2.

Masses can be entered in kilograms, tonnes, pounds, Earth masses or solar masses, and distances in metres, kilometres, miles, Earth radii, astronomical units or light-years. Presets carry NASA fact-sheet masses and equatorial radii for the Sun, all eight planets, the Moon and Pluto, so Earth comes out at 9.80 m/s² with an escape velocity of 11.18 km/s.

All of this runs as JavaScript inside your browser. Nothing you enter is uploaded or saved, the answers update as you type, and the page continues to work offline once loaded — handy for astronomy coursework away from a connection.

Frequently asked questions

What is the formula for gravitational force?

Newton's law of universal gravitation is F = G·m₁·m₂ ÷ r², where G is 6.67430 × 10⁻¹¹ m³·kg⁻¹·s⁻². Both bodies feel the same size of force in opposite directions, but the lighter one accelerates far more because a = F ÷ m.

What is the escape velocity from Earth?

Escape velocity from Earth's surface is about 11.18 km/s, or roughly 25,000 mph, from v = √(2GM ÷ r). It does not depend on the mass of the object escaping, and it ignores air resistance, which real rockets must still overcome.

How do you calculate surface gravity?

Surface gravity is g = G·M ÷ R², using the body's mass and its radius. Earth's figures give 9.80 m/s², while the Moon comes out near 1.62 m/s², about one sixth of Earth's.

Should r be measured from the surface or the centre?

Always from the centre. The formula treats each body as a point mass, which is exactly right for a uniform sphere, so an object sitting on Earth's surface is 6378 km from the centre, not zero metres away.

Is Newton's law still accurate today?

For planets, satellites and everyday masses it is correct to far more digits than you need. General relativity supersedes it near very dense objects or at very high speeds, such as close to a neutron star or in Mercury's orbital precession.

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