Gravitational Force Calculator
This gravitational force calculator finds the attraction between two masses using Newton's law of universal gravitation, F = G m1 m2 / r². Enter the two masses and the distance between their centres, and the gravitational force calculator returns the force in newtons. It shows the gravity formula with real numbers, step by step.
Results
The Gravitational Force Calculator is part of our Motion & Force collection. Browse more motion & force to size, convert, and check your work alongside this tool.
What the gravitational force calculator shows
Every mass pulls on every other mass. The pull grows with the size of the masses and falls with the square of the distance between them. The gravitational force calculator puts numbers on that pull for any two objects, from two apples to the Earth and the Moon.
Gravitational force formula calculator
The gravitational force formula calculator applies Newton's law of universal gravitation:
G is the gravitational constant, 6.674 × 10⁻¹¹ N·m²/kg², m₁ and m₂ are the masses, and r is the distance between their centres. Double the distance and the force falls to a quarter, which is the inverse square law.
Gravitational force calculator with steps
A 70 kg person on the Earth's surface: Earth mass 5.972 × 10²⁴ kg, radius 6.371 × 10⁶ m. The gravitational force calculator with steps gives:
That is the person's weight, the same as 70 kg × 9.81 m/s².
How to calculate gravitational force between two objects
To calculate gravitational force between two objects, enter the first mass and the second mass in kilograms and the distance between their centres in metres. The gravitational force calculator returns the force in newtons. For a person on the Earth's surface, use the Earth's mass and radius as mass 1 and distance; scientific notation such as 5.972e24 is accepted.
Reading the gravity formula calculator result
The force acts equally on both objects, in opposite directions. Between everyday objects it is tiny: two 1 kg masses 1 m apart pull with only 6.7 × 10⁻¹¹ N. It only becomes large when at least one mass is planet-sized. The gravity formula calculator measures distance from centre to centre, not surface to surface.
When to use the gravitational force calculator
- Physics homework with the gravitational force calculator
- Checking weight on another planet
- Estimating the pull between the Earth and the Moon
- Showing the inverse square law with numbers
Common gravitational force calculator mistakes
- Surface-to-surface distance. Use centre to centre.
- Forgetting to square r. The distance is squared.
- Kilometres instead of metres. Convert distances to metres.
Tips for accurate results
- Use scientific notation for planetary masses.
- Check your answer against weight = m × g on Earth.
- Keep all units in SI.
Calculations on gravitational force: the inverse square law
Calculations on gravitational force all follow the inverse square law: the force falls with the square of the distance. At twice the Earth's radius, about 12,700 km from the centre, a 70 kg object would weigh only a quarter of what it does at the surface. Gravity also sets how fast a pendulum swings, which the pendulum calculator uses through g.
Gravitational force calculator vs field strength
The force between two objects depends on both masses. Gravitational field strength, or gravitational acceleration, depends only on the body creating the field: g = G M / r². This tool reports the force; divide it by the second mass to get the field strength in m/s².
Gravitational force calculator reference: surface gravity
| Body | Surface gravity | Weight of 70 kg |
|---|---|---|
| Earth | 9.81 m/s² | 687 N |
| Moon | 1.62 m/s² | 113 N |
| Mars | 3.71 m/s² | 260 N |
| Jupiter | 24.79 m/s² | 1,735 N |
Gravitational Force Calculator FAQ
What is the formula for gravitational force?
F = G m1 m2 / r², with G = 6.674 × 10⁻¹¹ N·m²/kg².
Why is gravity between people so small?
G is tiny, so the force only becomes noticeable when one mass is huge, like a planet.
Is the distance measured from the surface?
No, from centre to centre. For an object on Earth, use the Earth's radius.
How is gravitational force related to weight?
Weight is the gravitational force from a planet on an object. On Earth it equals mass times 9.81 m/s².