Every mass in the universe attracts every other mass. Isaac Newton described the strength of that attraction in 1687 with a single equation, and it still predicts planetary motion, spacecraft trajectories and tides with excellent accuracy. This calculator applies Newton’s law of universal gravitation to two bodies. Enter any three of force, first mass, second mass and distance, and it solves for the fourth, with units that run from kilograms to solar masses and from meters to light-years.
How to use the gravitational force calculator
- Pick what to Solve for: Force, Mass 1, Mass 2 or Distance.
- Enter the First mass (m₁) and Second mass (m₂). Choose kg, g, t or lb for everyday objects, or Moon, Earth, Jupiter or solar masses for astronomy.
- Enter the Distance between centers (r) in m, cm, km, mi, Earth radii, au or ly.
- If you are solving for a mass or a distance, enter the Gravitational force in N, kN, lbf, kgf or dyn.
- Choose the result unit, then read the extras: the gravitational acceleration each mass produces at the other’s position, the potential energy of the pair and the force expressed as an equivalent weight.
Newton’s law of gravitation
The constant is G = 6.67430 × 10⁻¹¹ N·m²/kg². Dividing the force by one mass gives the gravitational field strength created by the other, g = Gm ÷ r2, and the potential energy of the pair is U = −Gm1m2 ÷ r, negative because energy must be added to pull them apart.
Worked example
Your weight, from first principles
The default inputs are Earth (1 Earth mass = 5.9722 × 10²⁴ kg), a 70 kg person, and Earth's mean radius of 6,371 km.
F = 6.6743 × 10⁻¹¹ × 5.9722 × 10²⁴ × 70 ÷ (6,371,000)² = 687.42 N
That is the person's weight, about 154.5 lbf. Dividing by 70 kg gives a field strength of 9.820 m/s², very close to standard gravity (9.80665 m/s²); the small difference comes from using the mean radius and ignoring Earth's spin.
Earth and the Moon. Change the second mass to 1 Moon mass (7.346 × 10²² kg) and the distance to 384,400 km. The calculator returns 1.98 × 10²⁰ N. That enormous force is what keeps the Moon in orbit and raises the ocean tides.
How gravity compares across scales
| Pair | Distance | Force |
|---|---|---|
| Two 70 kg people | 1 m | 3.27 × 10⁻⁷ N |
| 70 kg person and Earth | 6,371 km | 687 N |
| Earth and Moon | 384,400 km | 1.98 × 10²⁰ N |
| Sun and Earth | 1 au | 3.54 × 10²² N |
Gravity is by far the weakest of the fundamental forces. The electric repulsion between two protons is about 10³⁶ times stronger than their gravitational attraction, which you can explore with the Coulomb’s law calculator. Gravity dominates the cosmos only because masses are always positive and add up, whereas positive and negative charges cancel.
When Newton’s law needs help
The formula treats each body as a point or a uniform sphere. It works for planets, moons and people, but irregular objects such as asteroids or a mountain beside you need the mass split into pieces and summed. Inside a body the law changes: halfway to Earth’s center you would feel only the pull of the mass beneath you. Near extremely dense objects such as neutron stars and black holes, general relativity takes over.
For practical follow-ups, the weight calculator uses surface gravity directly, the escape velocity calculator finds the speed needed to break free of a planet, and the orbital period calculator uses the same constant G to time orbits.
Frequently asked questions
What value of G does the calculator use?
G = 6.67430 × 10⁻¹¹ N·m²/kg², the CODATA recommended value. It is the least precisely known fundamental constant, with a relative uncertainty of about 22 parts per million, but that is far smaller than the uncertainty in most masses you will enter.
How strong is gravity between two people?
Tiny. Two 70 kg people standing 1 m apart attract each other with about 3.27 × 10⁻⁷ N, roughly the weight of a grain of fine sand. Gravity only becomes noticeable when at least one mass is planet-sized.
Why does the distance have to be measured between centers?
Newton showed that a uniform sphere pulls on outside objects as if all its mass sat at its center. For you on Earth's surface, r is Earth's radius (about 6,371 km), not zero. Using the gap between surfaces would give an enormous, wrong answer.
Does the heavier object pull harder?
No. By Newton's third law both bodies feel exactly the same force in opposite directions. The lighter one simply accelerates more, which is why an apple falls toward Earth rather than Earth moving noticeably toward the apple.
What happens to the force if I double the distance?
It drops to one quarter, because distance is squared in the denominator. Triple the distance and the force falls to one ninth. This inverse-square behavior is shared by Coulomb's law for electric charges.