Acceleration due to Gravity Calculator
Find the acceleration due to gravity (g) on Earth, the Moon, Mars, or any other celestial body. Select a planet preset or enter a custom mass and radius, add an altitude above the surface, and the calculator shows you g in both m/s^2 and ft/s^2 together with the step-by-step derivation from Newton's law of gravitation.
What is acceleration due to gravity?
Acceleration due to gravity (symbol g) is the rate at which a freely falling object speeds up toward the center of a massive body, ignoring air resistance. At Earth's surface this value averages 9.80665 m/s^2, meaning every second a falling object gains about 9.8 metres per second of downward velocity. Because the gravitational force depends on mass and distance through Newton's law of universal gravitation, g differs on every planet, moon and star, and even decreases as you climb higher above a surface.
The formula and how to use this calculator
The governing equation is g = G M / (R + h)^2, where G is the universal gravitational constant (6.674 x 10^-11 m^3 kg^-1 s^-2), M is the mass of the celestial body in kilograms, R is its mean radius in metres, and h is your altitude above the surface. Selecting a planet preset fills M and R automatically. You can then adjust the altitude, for example 408,000 m for the International Space Station, to see how gravity weakens with height. Switch the output unit between m/s^2 and ft/s^2 at any time. The relative-to-Earth output converts the result to g-force units so you can immediately compare any body to familiar Earth gravity.
How gravity varies with altitude
Because gravity follows an inverse-square law, doubling your distance from the center of a body reduces g to one quarter of its surface value. At 400 km above Earth (approximately the ISS orbit) g is about 8.69 m/s^2, roughly 89% of the surface value. This is why astronauts appear weightless: they and the space station are both in free fall around Earth, so there is no contact force pressing them against the floor. At 35,786 km (geostationary orbit) g drops to about 0.22 m/s^2, less than 3% of the surface value. The chart below shows how g declines continuously from the surface to 2,000 km altitude for the body you have selected.
Gravity on other planets: practical implications
On the Moon (g = 1.62 m/s^2, about 17% of Earth) objects fall six times more slowly and astronauts can leap far higher than on Earth. Mars has about 38% of Earth gravity, which is thought to be enough to partially mitigate some health effects of long-duration spaceflight but still raises concerns about bone density and muscle loss over years. Jupiter's surface gravity of 24.8 m/s^2 is about 2.5 times Earth's: a 70 kg person would weigh about 175 kg there. The Sun's surface gravity of 274 m/s^2 is 28 times that of Earth. Understanding these differences matters for spacecraft landing systems, rocket propellant budgets, structural engineering of habitats, and even simple questions like how far a ball would travel when thrown.
Surface gravity across the solar system
| Body | Surface gravity (m/s^2) | Relative to Earth (g) | Surface gravity (ft/s^2) |
|---|---|---|---|
| Mercury | 3.70 | 0.38 | 12.14 |
| Venus | 8.87 | 0.90 | 29.10 |
| Earth | 9.81 | 1.00 | 32.17 |
| Moon | 1.62 | 0.17 | 5.32 |
| Mars | 3.72 | 0.38 | 12.21 |
| Jupiter | 24.79 | 2.53 | 81.33 |
| Saturn | 10.44 | 1.06 | 34.25 |
| Uranus | 8.87 | 0.90 | 29.10 |
| Neptune | 11.15 | 1.14 | 36.58 |
| Sun | 274.0 | 27.94 | 898.9 |
Standard surface gravitational acceleration for major solar-system bodies (altitude = 0).
Frequently asked questions
What is the standard acceleration due to gravity on Earth?
The internationally defined standard value is exactly 9.80665 m/s^2 (approximately 32.174 ft/s^2). In practice, the measured surface value ranges from about 9.764 m/s^2 at the equator to 9.832 m/s^2 at the poles because Earth is slightly flattened at the poles and rotates, which reduces the effective gravitational pull at the equator.
Why does gravity decrease with altitude?
Newton's law of gravitation states that the gravitational force between two masses decreases with the square of the distance between them. As you move farther from the center of Earth (or any body), the distance r in g = GM / r^2 grows, so g shrinks. Doubling your distance from the center reduces g to one quarter. At the ISS altitude of about 408 km, g is still around 88-89% of its sea-level value, which is why orbit is not "zero gravity" but rather continuous free fall.
Is gravity the same everywhere on Earth?
No. Earth's gravity varies by about 0.7% from the equator (lower) to the poles (higher). The main causes are Earth's oblate shape (the poles are closer to the center), the centrifugal effect of rotation (strongest at the equator), and local variations in rock density. Precision instruments called gravimeters detect these differences for applications such as underground mineral mapping and geodesy.
How is this calculator different from a g-force calculator?
This calculator finds the gravitational acceleration produced by a planetary body - the natural free-fall acceleration at a given location. A g-force calculator, by contrast, finds the apparent weight experienced during acceleration, braking, or circular motion relative to Earth's surface gravity. The two concepts share the same unit (g) but measure different physical situations.
Can I use this for free-fall problems?
Yes. The g value this calculator gives is exactly the constant acceleration you use in kinematic equations for free fall, such as v = g x t for speed after time t, or d = (1/2) g t^2 for distance fallen from rest in time t. Enter the altitude where the object starts falling to get the local g, then use that value in your kinematic equations. Note that real-world falls also involve air drag, which this calculator does not model.