Article — Acceleration Due to Gravity Calculator
Acceleration due to gravity calculator
Acceleration due to gravity, symbol g, is the rate at which any object accelerates downward under gravity alone. On Earth, the defined standard value is 9.80665 m/s² (32.174 ft/s²). Real local values range from 9.764 m/s² near the equator to 9.834 m/s² at the poles. On the Moon, g is 1.62 m/s². On Jupiter cloud-top, 24.79 m/s². On Pluto, just 0.62 m/s².
Newton law of gravitation, g = GM/(R+h)², governs the result. The value depends on the body mass, radius, the distance from its centre, and — for rotating bodies — the latitude. For Earth, the centrifugal effect of rotation reduces effective gravity by about 0.034 m/s² at the equator, with no reduction at the poles.
What is acceleration due to gravity?
Acceleration due to gravity is the rate of change of velocity that an object experiences solely from gravitational attraction. In free fall near a massive body, every object accelerates at g, independent of its mass — Galileo demonstrated this principle in the 16th century and Newton formalised it in 1687. The unit is metres per second squared (m/s²) in SI, or feet per second squared (ft/s²) in US customary.
The standard value g₀ = 9.80665 m/s² is a defined constant set by the 3rd General Conference on Weights and Measures in 1901. It is the conventional value used to convert between mass and weight in engineering, metrology, and definitions of pressure units (1 standard atmosphere = ρ_Hg × g₀ × h_Hg). Local g varies because Earth is not a perfect sphere and rotates.
The acceleration due to gravity formula
Newton inverse-square law gives the gravitational acceleration as a function of distance from a body's centre.
g = GM / r² Newton inverse-square lawr = R + h distance from body's centreg_eff = g − ω²r cos²(latitude) rotating body correctionG = 6.6743 × 10⁻¹¹ m³/(kg·s²) gravitational constantg₀ = 9.80665 m/s² defined standard gravity (Earth)The inverse-square scaling means doubling the distance from the centre reduces g by a factor of four. Tripling it reduces g by a factor of nine. That is why g drops measurably with altitude even on small scales: each kilometre of elevation reduces Earth surface gravity by about 0.0031 m/s², a 0.03% change per km that is easily detected by precision gravimeters.
Gravity by celestial body
Surface gravity varies dramatically across the solar system. Compact bodies with high density (like Earth) have higher surface gravity than larger but less dense gas giants relative to their mass.
- Sun: 274 m/s². 28× Earth. Crushing — a 70 kg person would weigh 19,200 N (4,300 lb).
- Mercury: 3.70 m/s². 38% of Earth.
- Venus: 8.87 m/s². 90% of Earth.
- Earth: 9.80665 m/s² mean (9.78 equator → 9.83 pole).
- Moon: 1.62 m/s². 16.5% of Earth.
- Mars: 3.71 m/s². 38% of Earth (similar to Mercury).
- Jupiter (cloud-top): 24.79 m/s². 253% of Earth.
- Saturn (cloud-top): 10.44 m/s². 106% of Earth.
- Uranus (cloud-top): 8.87 m/s². 90% of Earth.
- Neptune (cloud-top): 11.15 m/s². 114% of Earth.
- Pluto: 0.62 m/s². 6.3% of Earth.
Gravity at altitude
Earth surface gravity decreases predictably with altitude. The fractional change is approximately −2h/R for small h. A 1,000 m gain reduces g by 0.031% (about 0.0031 m/s²). A 10 km gain reduces it by 0.31%. The ISS at 408 km altitude experiences g = 8.69 m/s² — 88.6% of surface gravity. Astronauts float because they orbit at high horizontal velocity, not because gravity has disappeared.
The free-fall sensation in orbit is not the absence of gravity but the absence of a normal force. Astronauts and the station fall together at the same g, so there is no contact force between them — exactly the situation in a freely falling elevator. The ISS gravitational acceleration is 8.69 m/s², roughly 88.6% of surface gravity. Calling Earth orbit "zero gravity" is convenient shorthand; "microgravity" or "free fall" is more accurate.
Gravity by latitude on Earth
Two effects make Earth gravity stronger at the poles than at the equator. First, Earth bulges at the equator — its equatorial radius (6,378 km) is 21 km larger than its polar radius (6,357 km). Points at the equator sit farther from Earth's centre of mass, so gravitational attraction is weaker. Second, Earth rotation produces a centrifugal acceleration that opposes gravity and is maximum at the equator, zero at the poles.
The International Gravity Formula 1980 captures both effects empirically. At sea level, gravity by latitude follows g(φ) = 9.780327 × [1 + 0.0053024 sin²φ − 0.0000058 sin²(2φ)] m/s². Equator: 9.780 m/s². 45°: 9.806 m/s². Poles: 9.832 m/s². The 0.5% variation matters for precision weighing, oil-and-gas reservoir mapping, and satellite geodesy.
Acceleration due to gravity vs weight
Mass measures the amount of matter and is invariant — the same kilogram on Earth, Moon, or in deep space. Weight measures the gravitational force on that mass and equals mass × g, which varies with location. The two are often conflated in everyday speech but represent different physical quantities.
A bathroom scale measures the force between you and the floor — your weight. It then divides by the standard Earth gravity (9.80665 m/s²) and displays the result as if it were mass. Take the same scale to the Moon and it would read about 16.5% of your Earth value, even though your mass has not changed. True mass-measuring instruments (balances) compare you to a reference mass and give correct readings regardless of g.
A 70 kg person weighs 687 N at sea level on Earth, 113 N on the Moon, 260 N on Mars, 1,735 N at Jupiter cloud-top, and 19,200 N at the Sun surface. Their mass is 70 kg everywhere. The weight values are direct outputs of W = mg, where g comes from this calculator and m is the invariant mass.
Common gravity calculation mistakes
Always distinguish between gravitational acceleration g (a property of the location) and the acceleration of an object (which can differ if other forces act). A skydiver in free fall accelerates at 9.81 m/s² initially, then less as air drag builds up — until terminal velocity, where acceleration is zero even though gravity has not changed. Forces, not gravity alone, set the net acceleration.
The first common error is forgetting that Newton law gives gravity from the centre of mass, not the surface. The relevant distance is R + h, not just h. For a 1 km altitude over Earth, r = 6,372 km, not 1 km. Using just h gives an answer about a million times too large.
The second error is mixing up g (acceleration) and G (universal gravitational constant). G is the fundamental constant 6.6743 × 10⁻¹¹ m³/(kg·s²), present in every gravitational equation regardless of body. g varies with body, location, and altitude. The Newton inverse-square law g = GM/r² shows how G turns body mass and radius into local g.
The third error is using g = 10 m/s² in serious calculations. The 2% error from rounding 9.81 to 10 silently propagates through every step. For homework or back-of-envelope estimates, g = 10 is fine; for engineering work, use 9.81 or the local value from a gravimeter table.