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Newton’s law of gravitation calculator

A-level Fields and space

The gravitational force between two point masses, or two spheres measured from their centres.

F = G m1 m2 / r2

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

1.07 × 10−8 N
N m²/kg²

Working

  1. Write the equation
    F = G m1 m2 / r2
  2. Constants used
    G = 6.67 × 10−11 N m²/kg²
  3. Substitute the values
    F = (6.67 × 10−11) × 5 × 8 ÷ 0.52
  4. Calculate
    F = 1.0672 × 10−8 N
  5. Give the answer to 3 significant figures
    F = 1.07 × 10−8 N

Worked example

Find F, the gravitational force. Given: mass m1 = 5.00 kg; mass m2 = 8.00 kg; distance between the centres r = 0.500 m; gravitational constant G = 6.67 × 10⁻¹¹ N m²/kg².

  1. Write the equation
    F = G m1 m2 / r2
  2. Constants used
    G = 6.67 × 10−11 N m²/kg²
  3. Substitute the values
    F = (6.67 × 10−11) × 5 × 8 ÷ 0.52
  4. Calculate
    F = 1.0672 × 10−8 N
  5. Give the answer to 3 significant figures
    F = 1.07 × 10−8 N

Symbols and units

SymbolQuantitySI unit
FGravitational forceN
GGravitational constant (constant)N m²/kg²
m1Masskg
m2Masskg
rDistance between the centresm

Newton’s law of gravitation: rearranged

  • To find gravitational force: F = G m1 m2 / r2
  • To find mass: m1 = F r2 / (G m2)
  • To find mass: m2 = F r2 / (G m1)
  • To find distance between the centres: r = √(G m1 m2 / F)

Exam tip

Measure r between the centres of the masses, not the surfaces.

Common questions

What is the formula for newton’s law of gravitation?

The equation is F = G m1 m2 / r², where F is the gravitational force (N); m1 is the mass (kg); m2 is the mass (kg); r is the distance between the centres (m); G is the gravitational constant (N m²/kg²).

What units should I use for newton’s law of gravitation?

In SI units: gravitational force in N, gravitational constant in N m²/kg², mass in kg, mass in kg, distance between the centres in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange F = G m1 m2 / r²?

Rearranging gives these forms: to find gravitational force: F = G m1 m2 / r². to find mass: m1 = F r² / (G m2). to find mass: m2 = F r² / (G m1). to find distance between the centres: r = √(G m1 m2 / F).

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Related

Read the full explanation on the Newton’s law of gravitation formula page. More fields and space equations: Coulomb’s law, Uniform electric field, Electric field strength, Field of a point charge, Gravitational field strength, Gravitational potential, Orbital period, Escape velocity. See the full list on the a-level physics equation calculator page.