Gravitational Force Calculator
Every pair of masses pulls on each other with a force set by Newton's law of universal gravitation. Enter two masses and their centre-to-centre separation to find the attractive force in newtons, or flip the calculator to solve for an unknown mass or distance. Switch between metric and imperial units, pick a planet preset, and see the gravitational field strength (acceleration) each mass experiences.
Formula
Worked example
A 70 kg person on Earth's surface (r = 6.371 × 10⁶ m): F = (6.674×10⁻¹¹ × 5.972×10²⁴ × 70) ÷ (6.371×10⁶)² ≈ 686.5 N, their weight. Field strength on the person: 686.5 / 70 ≈ 9.807 m/s² (standard gravity).
Newton's law of universal gravitation
Newton's law of universal gravitation states that every particle of matter attracts every other particle with a force directed along the line joining their centres. The magnitude is: F = G × m₁ × m₂ / r², where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²), m₁ and m₂ are the masses in kilograms, and r is the centre-to-centre distance in metres. The result is the attractive force in newtons. Because G is so small, gravity is the weakest of the four fundamental forces and only becomes significant when at least one mass is enormous, such as a planet or a star.
Why the inverse-square law matters
The r² in the denominator means gravity weakens rapidly with distance: move twice as far apart and the force drops to one quarter; move ten times as far and it drops to one hundredth. This inverse-square behaviour governs orbital periods, escape velocities and tidal effects. The force is always mutual and equal on both bodies in line with Newton's third law, but the resulting acceleration is not equal. A small object near a large one accelerates strongly toward it, while the large object barely moves, which is why a dropped apple rushes toward Earth while the Earth's response is immeasurably small.
Gravitational field strength and weight
Gravitational field strength (g) is the force per unit mass at a given point in a gravitational field: g = F / m (in N/kg, which equals m/s²). On Earth's surface this is about 9.807 m/s². On the Moon it is roughly 1.62 m/s² and on Mars about 3.72 m/s². Weight is simply the gravitational force an object feels: W = m × g. This calculator reports the field strength each body experiences and expresses the total force as an equivalent mass (weight in kilograms-force) so you can check answers against familiar numbers.
Reverse-solving for mass or distance
The same formula can be rearranged to find an unknown mass or separation when the force is already known. To find mass 1: m₁ = F × r² / (G × m₂). To find mass 2: m₂ = F × r² / (G × m₁). To find the distance: r = square root of (G × m₁ × m₂ / F). These rearrangements are how astronomers determine the mass of planets and stars from observed orbital data, and how the Cavendish experiment first measured G.
Gravitational force in familiar situations
| Scenario | Mass 1 (kg) | Mass 2 (kg) | Distance (m) | Force (N) | Field on m₂ (m/s²) |
|---|---|---|---|---|---|
| Two 1 kg balls, 1 m apart | 1 | 1 | 1 | 6.67 × 10⁻¹¹ | 6.67 × 10⁻¹¹ |
| 70 kg person on Earth surface | 5.97 × 10²⁴ | 70 | 6.37 × 10⁶ | 686.5 | 9.807 |
| 70 kg person on Moon surface | 7.34 × 10²² | 70 | 1.74 × 10⁶ | 113.5 | 1.62 |
| 70 kg person on Mars surface | 6.42 × 10²³ | 70 | 3.39 × 10⁶ | 261.4 | 3.73 |
| Earth-Moon system | 5.97 × 10²⁴ | 7.35 × 10²² | 3.84 × 10⁸ | 1.98 × 10²⁰ | 0.00270 |
| Earth-Sun system | 5.97 × 10²⁴ | 1.99 × 10³⁰ | 1.50 × 10¹¹ | 3.54 × 10²² | 5.93 × 10⁻³ |
How the same formula spans more than thirty orders of magnitude depending on the masses and distance.
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 6.674 × 10⁻¹¹ N·m²/kg², m₁ and m₂ are the two masses in kilograms, and r is the centre-to-centre distance in metres. The result is the attractive force in newtons.
How do I solve for mass or distance instead of force?
Use the Solve for dropdown at the top of the calculator. Selecting Mass 1, Mass 2, or Distance rearranges the formula so you enter the known force along with the remaining two known values. Mass 1 = F × r² / (G × m₂), and Distance = square root of (G × m₁ × m₂ / F).
What is gravitational field strength?
Gravitational field strength (g) is the force per unit mass at a location, measured in N/kg or equivalently m/s². It equals the acceleration a free-falling object gains. On Earth's surface g is about 9.807 m/s², on the Moon 1.62 m/s², and on Mars 3.73 m/s². This calculator shows the field strength each body experiences: divide the total force by the mass of that body.
Why is the gravitational force between everyday objects so small?
Because the gravitational constant G is only 6.674 × 10⁻¹¹, the force between ordinary masses is minuscule. Two 1 kg balls one metre apart attract with about 6.7 × 10⁻¹¹ N, far too weak to notice. Gravity becomes appreciable only when one mass is planet-sized.
What distance should I use in the calculation?
Use the distance between the centres of mass of the two objects, not the gap between their surfaces. For an object on a planet's surface, that distance is the planet's radius, since a uniform spherical body acts as if all its mass is concentrated at its centre (shell theorem).
Can I use pounds and feet instead of kilograms and metres?
Yes. Each mass and distance input has a unit selector. Switch Mass inputs to lb and the distance input to ft or mi as needed. The calculator converts to SI for the computation and then converts the force back to your chosen unit (N, kN, or lbf).