Gravitational Force Calculator: F = G m1 m2 / r^2

The attraction between two masses, from Newton's law of gravitation.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • F = \frac{Gm_1m_2}{r^2}
  • r = \sqrt{\frac{Gm_1m_2}{F}}
  • m_2 = \frac{Fr^2}{Gm_1}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the gravitational force: gravitational force = (6.6743e-11 x first mass x second mass) / (distance between the centres^2)
  2. Put the values in (every value in its SI unit): gravitational force = (6.6743e-11 x 5.972e+24 x 70) / (6.371e+6^2)
  3. The answer: gravitational force: 687.398 N
  4. The same answer in other units: 0.687398 kN; 70.0951 kgf

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Distance between the centres; Gravitational force (leave it as it is if this is what you are finding) 686.6 N; Second mass (leave it as it is if this is what you are finding) 70 kg.

  1. The formula, arranged to find the distance between the centres: distance between the centres = square root of ((6.6743e-11 x first mass x second mass) / (gravitational force))
  2. Put the values in (every value in its SI unit): distance between the centres = square root of ((6.6743e-11 x 5.972e+24 x 70) / (686.6))
  3. The answer: distance between the centres: 6.3747e+6 m
  4. The same answer in other units: 6374.7 km; 3961.06 miles

Common questions

What is Newton's law of gravitation?

Every mass attracts every other mass with a force proportional to the product of the masses and inversely proportional to the square of the distance between their centres.

What is the value of G?

6.6743e-11 newton square metres per kilogram squared.

How does this give the weight of a person?

Put in the Earth's mass and radius and the person's mass. A 70 kg person gets a force of about 687 N.

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Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any physics text (Newton's law of gravitation). G from the 2018 CODATA values.

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