Every mass attracts every other mass. Enter two masses and the distance between their centres to get the gravitational force and the acceleration due to gravity. The defaults give your weight on Earth.
Enter both masses in kg.
Enter the distance between centres in metres.
Read the force and g.
Force: F = G m₁ m₂ ÷ r²
Gravity: g = G M ÷ r²
Newton's law of universal gravitation says every mass pulls on every other mass. This calculator takes two masses in kilograms and the distance between their centres in metres, and returns the gravitational force between them. It also gives g, the acceleration that the first mass produces at that distance, which is the familiar 9.8 m/s² when the first mass is the Earth and the distance is its radius.
The topic appears in Class 9 and Class 11 physics and in JEE and NEET. It explains why you weigh less on the Moon, how satellites like those launched by ISRO stay in orbit, why tides follow the Moon, and why two people standing side by side feel no pull at all. Planetary masses can be typed in scientific notation, such as 5.972e24 for the Earth.
1. Write both masses in kilograms, using powers of ten for planets and stars.
2. Measure r, the distance between the centres of the two masses, in metres. For an object on a planet's surface, r is the planet's radius; at height h, r = R + h.
3. Use G = 6.674 × 10⁻¹¹ N·m²/kg².
4. Compute F = G × m₁ × m₂ ÷ r².
5. Compute the gravitational acceleration due to mass 1: g = G × m₁ ÷ r².
6. Check: F should equal m₂ × g, the weight of mass 2 at that distance.
Think of gravity spreading out from a mass in all directions. At distance r its influence is shared over the surface of a sphere of area 4πr², so the strength per unit area falls as 1 ÷ r². Newton checked this by comparing the Moon's acceleration towards the Earth with the fall of an apple. The Moon is about 60 Earth radii away, and its acceleration is about 1/3600 of 9.8 m/s², just as the inverse square law predicts.
For a uniform sphere, or one made of uniform shells like a planet, the outside gravitational pull is the same as if all its mass were concentrated at the centre. This shell theorem is why r is the distance between centres, not between surfaces. It also means that at the Earth's surface r is about 6.371 × 10⁶ m, and a climb of a few kilometres barely changes g. At the height of the International Space Station, about 400 km, g is still close to 8.7 m/s².
G is extremely small, which is why gravity between everyday objects is imperceptible. Two 70 kg people 1 m apart attract with about 3 × 10⁻⁷ N, far less than the weight of a grain of sand. Gravity dominates astronomy only because planets and stars have enormous masses, and because matter on large scales is electrically neutral, so the much stronger electric forces cancel. Weightlessness in orbit is not absence of gravity; astronauts are in continuous free fall around the Earth.
Neha, who has a mass of 55 kg, imagines standing on the Moon, which has a mass of 7.342 × 10²² kg and a radius of 1.737 × 10⁶ m.
F = G m₁ m₂ ÷ r²: = 6.674 × 10⁻¹¹ × 7.3420 × 10^22 × 55 ÷ (17,37,000)² = 89.3231 N
Gravity produced by mass 1 at that distance: g = G m₁ ÷ r² = 1.6241 m/s²
Answer: Gravitational force 89.3231 N; g due to mass 1 1.6241 m/s²
Measuring distance from the planet's surface instead of from its centre.
Forgetting to square the distance.
Typing powers of ten wrongly, such as 5.972e23 instead of 5.972e24 for the Earth.
Confusing G, the universal constant, with g, the local acceleration due to gravity.
Thinking astronauts are weightless because gravity is zero in orbit.
Class 9, 11, JEE and NEET problems on gravitation.
Comparing weight on the Moon, Mars and other planets.
Finding g at the altitude of aircraft or satellites.
Understanding tides caused by the Moon and the Sun.
Rough estimates for orbital mechanics before using full orbit equations.
How do I find g at a height h?
Use r = R + h, where R is the planet's radius.
Why don't we feel attraction between people?
G is tiny, so the force between everyday masses is far too small to notice.