What is the acceleration of gravity on Earth?

The acceleration due to gravity at the Earth's surface is approximately 9.8 meters per second squared and is often rounded to 9.81. The value of g is calculated using the formula (G * M) / r^2, which gives a value of approximately 9.82. The measured values are slightly less than the theoretical values due to the Earth's rotation and the fact that the Earth is not a perfect sphere.

Why is gravity different on other moons and planets?

Surface gravity is determined by the mass and radius of a celestial body. The Moon has much less mass than Earth, so its surface gravity is only about one sixth that of Earth's. Jupiter, on the other hand, has much more mass, so its surface gravity is about two and a half times that of Earth.

Do heavier objects fall faster?

No. In a vacuum all objects accelerate uniformly with the same acceleration (g) and fall to Earth at the same time if released simultaneously. Although heavier objects experience more gravity, they also require more force to accelerate them so these two effects cancel each other out. In reality feathers drop slowly because of air resistance not gravity.

Can I calculate any celestial body with this calculator?

Yes. You can select a celestial body from the built-in list or choose "Custom" and enter mass and radius of any celestial body including exoplanets. The calculation tool assumes that a celestial body is roughly spherical in shape, so accuracy of results may decrease for bodies with highly irregular shapes.

Acceleration Due to Gravity Calculator

Choose a celestial body

Celestial body

Surface gravity, g

That is about 1 times Earth's gravity, so an object here weighs 1 times what it weighs on Earth.

Weight and free fall (optional)

Mass of an object (optional)

Drop height (optional)

Surface gravity

m/s²

Gravity vs Earth

The acceleration due to gravity is the rate at which an object increases its velocity as it falls towards a massive body. On Earth this acceleration is approximately 9.8 meters per second squared and is usually denoted by "g". This tool will calculate the acceleration due to gravity for any planet, moon or star you specify, or you can enter in the mass and radius of your own custom celestial object.

This tool also answers two common questions: how much an object weighs at a particular location and how it would fall. When you select a celestial body, the surface gravity, object weight, and falling speed values are automatically updated.

What is Earth's acceleration?

All objects with mass attract each other. In the vicinity of large celestial bodies such as planets, this attraction results in a constant acceleration of falling objects. This acceleration is called gravitational acceleration and is represented by "g".

The value of "g" depends only on the particular heavenly body you are standing on and not on the properties of the falling object itself. In a vacuum, a feather and a hammer will have the same rate of acceleration. Thus astronauts can observe both objects hitting the ground at the same time on the moon where there is no air.

Calculation formula

The surface acceleration can be derived from Newton's law of gravitation. If you divide the force that a celestial body exerts on an object by the mass of the falling object, then the mass of your own object is cancelled out.

g = \frac{G M}{r^2}

G is the gravitational constant whose value is 6.6743 times ten to the negative eleventh, with units of newton meters squared per kilogram squared. M is the mass of the celestial body and r is the distance from the center of the celestial body to the point at which the gravity is being calculated. When calculating surface acceleration, r is usually the radius of the celestial body.

For example, the Earth has a mass of about 5.97 times 10 to the power of 24 kilograms and a radius of about 6,371 kilometers. Plugging those values into the formula gives us...

g_{\text{Earth}} = \frac{(6.6743\times10^{-11})(5.97\times10^{24})}{(6.371\times10^{6})^2} \approx 9.82\ \text{m/s}^2

Here's how to use this calculator:

Select a celestial body from the list and the calculator will immediately show you its surface gravity, comparing it to Earth's.

If you want to simulate a celestial body that is not on the list, select Custom and enter the mass and radius of the celestial body. The mass can be entered in kilograms, Earth masses or solar masses so that you can directly enter data from exoplanets regardless of what units they are given in.

Two additional optional input fields allow for more detailed results. By entering the mass of an object, its weight on the selected celestial body can be determined. By entering a drop height, the velocity of the object when it hits the ground and the time taken to fall can be calculated.

Surface gravity of individual bodies in the solar system

By plugging in the mass and radius of each celestial body into the same formula, one obtains the surface gravity listed below. The last column shows the ratio of each celestial body's gravity to Earth's, which is approximately equal to the ratio of values that an identical weighing device would display on that celestial body versus on Earth.

Body	Surface gravity (m/s squared)	Compared to Earth
The Sun	274	27.9 times
Jupiter	24.8	2.53 times
Neptune	11.1	1.14 times
Saturn	10.4	1.06 times
Earth	9.82	1.00 times
Venus	8.87	0.90 times
Uranus	8.87	0.90 times
Mars	3.73	0.38 times
Mercury	3.70	0.38 times
The Moon	1.62	0.17 times
Pluto	0.62	0.06 times

Mass or radius calculation

If the surface gravity (g) is known and another unknown quantity is to be determined, then the same formula can be rearranged. If the surface gravity has been measured and the radius is known, then the mass can be calculated, or if the mass is known, then the radius can be calculated.

M = \frac{g\,r^2}{G} \qquad r = \sqrt{\frac{G M}{g}}

Astronomers use this very method to determine the "weight" of planets that are not directly accessible. By observing the fall or orbit of an object they can use these equations to estimate the mass of that celestial body.

Example of calculating free fall:

If the value of g is known, then under the condition that there is no air resistance, one can predict the process by which an object falls from rest. The impact velocity of the object after falling a height h and the time required for it are as follows:

v = \sqrt{2 g h} \qquad t = \sqrt{\frac{2 h}{g}}

If a stone is dropped from the top of a 100-meter tower on Earth, its speed when it hits the ground will be about 44.3 meters per second.

If an object is dropped from a height of 50 meters, it will take approximately 3.2 seconds to hit the ground.

Why do calculated results sometimes differ from 9.81?

While textbooks often state the acceleration of gravity as being 9.81 meters per second squared, using this formula gives a value of about 9.82 meters per second squared. The small gap is real.

The values measured at the Earth's surface are slightly less than the theoretical values resulting from multiplying g by M and dividing by the square of r because of slight centrifugal forces caused by the rotation of the Earth, which are greatest at the equator. The Earth is also not a perfect sphere, and gravity decreases with increasing altitude; on top of Mount Everest, for example, it is about 0.3% less than at sea level.

This calculator is for educational purposes only and provides a rough estimate of values. As all celestial bodies are considered to be homogeneous spheres and air resistance is neglected, the results will deviate from actual measurements.

Frequently asked questions

What is the acceleration of gravity on Earth?: The acceleration due to gravity at the Earth's surface is approximately 9.8 meters per second squared and is often rounded to 9.81. The value of g is calculated using the formula (G * M) / r^2, which gives a value of approximately 9.82. The measured values are slightly less than the theoretical values due to the Earth's rotation and the fact that the Earth is not a perfect sphere.
How is Earth's gravity calculated?: g is calculated as the product of G and M divided by the square of r. G is the gravitational constant whose value is 6.6743 multiplied by ten to the power of minus eleven. M is the mass of the celestial body, and r is the distance from the center of that celestial body. The formula does not contain the mass of the falling object, so the mass of the object itself has no effect on the acceleration due to gravity.
Why is gravity different on other moons and planets?: Surface gravity is determined by the mass and radius of a celestial body. The Moon has much less mass than Earth, so its surface gravity is only about one sixth that of Earth's. Jupiter, on the other hand, has much more mass, so its surface gravity is about two and a half times that of Earth.
Do heavier objects fall faster?: No. In a vacuum all objects accelerate uniformly with the same acceleration (g) and fall to Earth at the same time if released simultaneously. Although heavier objects experience more gravity, they also require more force to accelerate them so these two effects cancel each other out. In reality feathers drop slowly because of air resistance not gravity.
Can I calculate any celestial body with this calculator?: Yes. You can select a celestial body from the built-in list or choose "Custom" and enter mass and radius of any celestial body including exoplanets. The calculation tool assumes that a celestial body is roughly spherical in shape, so accuracy of results may decrease for bodies with highly irregular shapes.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

NASA Planetary Fact Sheet
Mass, radius, and surface gravity for the planets and the Moon.
NIST: Newtonian constant of gravitation G
The CODATA recommended value of the gravitational constant.