# Acceleration due to Gravity Calculator

Created by Purnima Singh, PhD
Last updated: Feb 02, 2023

If you have ever wondered how free-falling objects would behave on different planets, our acceleration due to gravity calculator can help you find out that.

Continue reading to know what acceleration due to gravity is and how to calculate its value on any celestial body. You will also find an example of calculating the magnitude of the acceleration due to gravity using our tool.

## What is the acceleration due to gravity?

As the name suggests, the acceleration due to gravity is the acceleration experienced by a body when it falls freely under the influence of gravity alone. We use the symbol $g$ to denote it. The SI unit of $g$ is m/s2.

Acceleration due to gravity or $g$ is a vector quantity, and it is directed towards the center of the celestial body under consideration.

## Acceleration due to gravity formula

The formula for determining the magnitude of the acceleration due to gravity $g$ at the surface of any celestial body is:

$\small g = \frac{G \ M}{R^2}$

where:

• $M$ – Mass of the celestial body in kg;
• $G = 6.674 \times 10^{-11}\ \mathrm{m^3\ kg^{-1}\ s^{-2}}$ – Universal gravitational constant; and
• $R$ – Radius of the celestial body in m.

🙋 The acceleration due to gravity experienced by an object is independent of its mass.

## How to calculate the acceleration due to gravity on Earth

As an example, let us calculate the acceleration due to gravity on the surface of Earth. We know that:

• Mass of earth, $M = 5.972 \times 10^{24}\ \text{kg}$; and
• Radius of Earth, $R = 6. 371 \times 10^6 \ \text{m}$

substituting these values in the formula of acceleration due to gravity, we get:

\!\footnotesize \begin{align*} g & = \frac{G \ M}{R^2}\\ \\ & = \frac{6.674 \times 10^{-11}\ \mathrm{m^3 kg^{-1} s^{-2}} \times 5.972 \times 10^{24}\ \text{kg}} {(6. 371 \times 10^6 \ \text{m})^2} \\ \\ & = 9.8\ \mathrm{m/ s^2} \end{align*}

Hence the magnitude of the acceleration due to gravity on the surface of Earth is 9.8 m/s2. In the next section, you will see how to determine the value of $g$ using our gravitational acceleration calculator.

## How to use the acceleration due to gravity calculator

Now let us calculate the same problem as above using the acceleration due to gravity calculator:

1. Type the mass of the Earth as 5.972 e24.

2. Enter the radius of the Earth as 6371 km or 6371000 m.

3. The tool will calculate the magnitude of the acceleration due to gravity on the surface of Earth as 9.8 m/s2.

## Other similar calculators

If you liked this gravitational acceleration calculator, do check out our other tools on gravitation, namely:

## FAQ

### How do I calculate the acceleration due to gravity on Mars?

To calculate the acceleration due to gravity on the surface of Mars, follow the given steps:

1. Take the square of the radius of Mars (3,390 km or 3.390 × 10⁶ m). You will get 1.1492 × 10¹³ m².

2. Divide the mass of Mars (6.4185 x 10²³ kg) by the square of its radius in m.

3. Multiply the result by G, i.e., the universal gravitation constant.

4. You will get the value of acceleration due to gravity on Mars, i.e., 3.7 m/s².

### How do I calculate the acceleration due to gravity on the Moon?

To calculate the acceleration due to gravity on the Moon, proceed as follows:

1. Divide the mass of the Moon (7.346 x 10²² kg) by the square of its radius (1737.4 km).

2. Multiply the result from step 1 with 6.674×10⁻¹¹ m³/kg s², i.e., the value of G.

3. Congrats! You have calculated the acceleration due to gravity on the surface of the Moon as 1.6 m/s².

Purnima Singh, PhD
g = GM/R²
Mass (M)
lb
mi
Acceleration due to gravity (g)
ft/s²
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