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Gravitational Force Calculator

Find the gravitational force between two masses.

Result

6.874e+2 N

How it is calculated

The tool uses Newton's law of gravitation:

F = G × m1 × m2 / r²

G is fixed at 6.674×10-11 N·m²/kg². Masses m1 and m2 are in kilograms and the distance r is in metres, measured between the centres of the two bodies, not between their surfaces. The distance must be above zero or nothing is shown. The result is in newtons and printed in scientific notation with four significant digits, so 6.874e+2 means 6.874 × 10² = 687.4 N. Very large numbers can be typed in that form too, such as 5.972e24.

Worked example

The pull of the Earth on a 70 kg person standing on the ground: m1 = 5.972e24 kg, m2 = 70 kg, r = 6.371e6 m (Earth's radius, since the centre is that far down).

  1. G × m1 × m2 = 6.674e-11 × 5.972e24 × 70 ≈ 2.790e16
  2. r² = (6.371e6)² ≈ 4.059e13
  3. F = 2.790e16 / 4.059e13 ≈ 6.874e+2 N

That is about 687 N, the person's weight.

Try this example →

Common mistakes

  • Using the distance between surfaces instead of between centres: for planets and people on them, r is the planet's radius plus any height.
  • Entering masses in grams or tonnes, or distance in kilometres: the formula expects kilograms and metres, so a kilometre figure makes the force a million times too large.
  • Misreading the exponent: e-7 is a tiny force and e+2 is hundreds of newtons, so check the sign of the exponent.
  • Expecting force to halve when distance doubles: it falls to one quarter, because r is squared.

About this calculator

This calculator applies Newton's law of universal gravitation, F = G(m₁m₂)/r², where G is the gravitational constant (6.674×10⁻¹¹ N·m²/kg²), to find the attractive force between two masses separated by a given distance.

Physics students use it for mechanics and astronomy homework, and it's the same formula used (in more elaborate form) to calculate orbital mechanics, satellite trajectories, and the gravitational pull between planets and stars. Because the force falls off with the square of distance, the calculator makes it easy to see why doubling the distance between two objects cuts the gravitational force to a quarter, not to a half.

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