Enter the gravitational constant, the mass of the planet or celestial body, and radius into the calculator to determine the surface gravity. This calculator can also evaluate any of the variables given the others are known.

Surface Gravity Formula

The following formula is used to calculate the surface gravity of a planet or celestial body. 

g = (G * M) / r^2

Variables:

  • g is the surface gravity
  • G is the gravitational constant
  • M is the mass of the planet or celestial body
  • r is the radius of the planet or celestial body

To calculate the surface gravity, multiply the gravitational constant by the mass of the planet or celestial body. Then, divide this result by the square of the radius of the planet or celestial body. The result is the surface gravity.

What is a Surface Gravity?

Surface gravity refers to the gravitational force experienced at the surface of a celestial body like a planet, moon, or star. It determines the weight of an object on that body and influences the body’s escape velocity, atmosphere retention, and the formation of natural satellites. Surface gravity is typically measured in relation to Earth’s gravity (g), with Earth’s surface gravity being 1g. It varies based on the mass of the celestial body and its radius.

How to Calculate Surface Gravity?

The following steps outline how to calculate the Surface Gravity using the given formula:

  1. First, determine the value of the gravitational constant (G).
  2. Next, determine the mass of the planet or celestial body (M).
  3. Next, determine the radius of the planet or celestial body (r).
  4. Next, substitute the values of G, M, and r into the formula: g = (G * M) / r^2.
  5. Finally, calculate the Surface Gravity (g).
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge:

gravitational constant (G) = 6.67430 x 10^-11 N(m/kg)^2

mass of the planet or celestial body (M) = 5.972 x 10^24 kg

radius of the planet or celestial body (r) = 6.371 x 10^6 m