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Gravitational field strength calculator
Fields and space
The gravitational field strength at a distance from the centre of a planet or star.
g = G M / 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
Working
- Write the equationg = G M / r2
- Constants usedG = 6.67 × 10−11 N m²/kg²
- Substitute the valuesg = (6.67 × 10−11) × (5.97 × 1024) ÷ (6.37 × 106)2
- Calculateg = 9.81344 N/kg
- Give the answer to 3 significant figuresg = 9.81 N/kg
Worked example
Find g, the gravitational field strength. Given: mass of the planet or star M = 5.97 × 10²⁴ kg; distance from the centre r = 6.37 × 10⁶ m; gravitational constant G = 6.67 × 10⁻¹¹ N m²/kg².
- Write the equationg = G M / r2
- Constants usedG = 6.67 × 10−11 N m²/kg²
- Substitute the valuesg = (6.67 × 10−11) × (5.97 × 1024) ÷ (6.37 × 106)2
- Calculateg = 9.81344 N/kg
- Give the answer to 3 significant figuresg = 9.81 N/kg
Symbols and units
| Symbol | Quantity | SI unit |
|---|---|---|
| g | Gravitational field strength | N/kg |
| G | Gravitational constant (constant) | N m²/kg² |
| M | Mass of the planet or star | kg |
| r | Distance from the centre | m |
Gravitational field strength: rearranged
- To find gravitational field strength: g = G M / r2
- To find mass of the planet or star: M = g r2 / G
- To find distance from the centre: r = √(G M / g)
Exam tip
On the surface r is the radius of the planet. The field falls with the square of the distance.
Common questions
What is the formula for gravitational field strength?
The equation is g = G M / r², where g is the gravitational field strength (N/kg); M is the mass of the planet or star (kg); r is the distance from the centre (m); G is the gravitational constant (N m²/kg²).
What units should I use for gravitational field strength?
In SI units: gravitational field strength in N/kg, gravitational constant in N m²/kg², mass of the planet or star in kg, distance from the centre in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.
How do I rearrange g = G M / r²?
Rearranging gives these forms: to find gravitational field strength: g = G M / r². to find mass of the planet or star: M = g r² / G. to find distance from the centre: r = √(G M / g).
Practise gravitational field strength questions
Press the button for a question with random numbers. Work it out on paper first, then type your answer.
Related
Read the full explanation on the Gravitational field and orbit formula page. More fields and space equations: Coulomb’s law, Uniform electric field, Electric field strength, Field of a point charge, Newton’s law of gravitation, Gravitational potential, Orbital period, Escape velocity. See the full list on the a-level physics equation calculator page.