Gravitational Force CalculatorF = Gm₁m₂ ÷ r²
Newton’s law of universal gravitation: every two masses attract each other with a force F = Gm₁m₂ ÷ r², where G = 6.674 × 10⁻¹¹ N·m²/kg². Enter two masses and the distance between their centres to get the gravitational force. Or find the gravitational acceleration g at any altitude, from the ISS to geostationary orbit.
Formula verified against OpenStax — University Physics, Volume 1 · NIST — CODATA 2022 Fundamental Physical Constants
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Masses & distance
r is measured centre to centre. Masses accept kg, Earth masses or solar masses.
Step-by-step working
What is gravitational force?
Gravitational force is the attraction between any two objects that have mass. Newton’s law of universal gravitation says it grows with the product of the masses and weakens with the square of the distance between them.
The same law that makes an apple fall keeps the Moon in orbit and holds galaxies together. Einstein’s general relativity refines it near very massive or fast-moving objects, but Newton’s equation is accurate for almost all everyday and spaceflight calculations.
Quick answers
How do you calculate the gravitational force between two objects?
Multiply G by both masses and divide by the distance squared: F = Gm₁m₂ ÷ r². Two 1,000 kg cars 2 m apart attract with 1.67 × 10⁻⁵ N, far too small to notice.
What is the value of G?
G = 6.67430 × 10⁻¹¹ N·m²/kg² (CODATA 2022). It is the least precisely known fundamental constant, with an uncertainty of about 22 parts per million.
How does gravity change with altitude?
It drops with the square of the distance from Earth’s centre. At the ISS (408 km up) g is still 8.67 m/s², about 88% of surface gravity.
How is gravitational force related to weight?
Weight is the gravitational force from Earth on you, W = mg, where g = GM ÷ R². For weight on the Moon or Mars, see the free fall calculator planet presets.
Newton’s law of universal gravitation
Valid for point masses and for spheres measured from their centres. G is the CODATA 2022 value.
| Symbol | Meaning | SI unit |
|---|---|---|
| F | Gravitational force on each mass | N |
| G | Gravitational constant | N·m²/kg² |
| m₁, m₂ | The two masses | kg |
| r | Distance between centres | m |
| g | Gravitational field strength | m/s² (N/kg) |
How to calculate gravitational force
- Convert both masses to kg and the distance to metres, measured centre to centre.
- Multiply the masses together and by G.
- Divide by r².
- Remember the pair: each mass feels the same force, pointing towards the other.
Worked example: your weight from Newton’s law
What force does Earth (5.9722 × 10²⁴ kg, mean radius 6,371 km) exert on a 70 kg person at the surface?
F = 687.4 N, which matches 70 kg × 9.82 m/s²
Two 70 kg people standing 1 m apart attract each other with just 3.27 × 10⁻⁷ N, about the weight of a grain of fine sand. Earth and the Moon pull on each other with 1.98 × 10²⁰ N.
Gravity at different altitudes above Earth
g = GM ÷ (R + h)² with M = 5.9722 × 10²⁴ kg and R = 6,371 km.
| Location | Altitude | g (m/s²) | % of surface |
|---|---|---|---|
| Sea level (mean) | 0 km | 9.82 | 100% |
| Mount Everest summit | 8.8 km | 9.79 | 99.7% |
| International Space Station | 408 km | 8.67 | 88.3% |
| GPS satellites | 20,200 km | 0.56 | 5.7% |
| Geostationary orbit | 35,786 km | 0.22 | 2.3% |
| Moon’s distance | 378,000 km | 0.0027 | 0.03% |
Common mistakes to avoid
- Measuring r from the surface. For planets and stars, r runs from the centre, so add the radius to any altitude.
- Forgetting to square r. The inverse-square law is the heart of the equation.
- Thinking gravity disappears in orbit. It is still about 90% of surface strength at the ISS.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Gravitational Force Calculator: frequently asked questions
F = Gm₁m₂ ÷ r², where G = 6.674 × 10⁻¹¹ N·m²/kg², m₁ and m₂ are the masses and r the distance between their centres.
Because G is tiny. Everyday masses produce forces millions of times smaller than their weight, so only planet-sized masses produce noticeable gravity.
No. It weakens with distance but never reaches exactly zero. It just becomes negligible compared with other influences.
Yes. By Newton’s third law each mass feels an equal and opposite force. The lighter object accelerates more because a = F ÷ m.
G is the universal gravitational constant. g is the local gravitational acceleration, about 9.81 m/s² on Earth’s surface, which depends on the planet’s mass and radius.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 13.1–13.2, Newton’s Law of Universal Gravitation
- NIST — CODATA 2022 Fundamental Physical Constants — G = 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻²
- NASA NSSDC — Planetary Fact Sheet — Earth and Moon masses and radii
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.