Acceleration Due to Gravity Calculator
Compute the gravitational acceleration at the surface or any altitude above a planet or moon. Enter the body's mass and radius — defaults are set to Earth — plus an optional altitude, and get g in m/s², its ratio to Earth's 9.81 m/s², and the escape velocity.
km
km
Acceleration of a freely-falling object at the given altitude
- 1
Total radius R + h
(6,371 + 0) km × 1 000 = 6,371,000 m - 2
G × M (numerator)
6.674×10⁻¹¹ × 5.972×10²⁴ = 398,571,280,000,000 m³/s²G = 6.674×10⁻¹¹ N·m²/kg²; body mass converted to SI kg. - 3
Gravitational acceleration g = G × M ÷ r²
398,571,280,000,000 ÷ (6,371,000)² = 9.8195 m/s²
How does this calculator work?
Gravitational acceleration obeys g = GM / (R+h)², where G = 6.674 × 10⁻¹¹ N·m²/kg². Enter a body's mass and radius plus any altitude above the surface. Earth's surface gives g ≈ 9.81 m/s²; the value drops with altitude following an inverse-square law.
Formula
How this is calculated
Newton's law of universal gravitation says that the force on a mass m near a spherical body of mass M is F = GMm/r², where r is the distance from the body's centre. Dividing both sides by m gives the gravitational acceleration g = GM/r², which is the same for any object regardless of its own mass — it depends only on the large body and the distance.
At the surface, r equals the body's radius R; at an altitude h above the surface, r = R + h. Because g falls as the square of the distance, the field weakens rapidly: at two Earth radii from the centre (about 6371 km altitude), g is only one-quarter of the surface value. The ISS, for instance, orbits at about 408 km altitude where g ≈ 8.7 m/s²; astronauts feel weightless not because gravity is absent but because the station and its occupants are in the same free fall.
The escape velocity — the minimum speed to leave the body's gravity without further thrust — follows as √(2GM/r). These formulas assume a spherical, non-rotating body, which is a good first approximation for planets and moons; true surface gravity varies slightly with latitude due to the Earth's oblateness and rotation.
Frequently asked questions
Gravitational acceleration follows an inverse-square law: g = GM/r². Doubling your distance from the body's centre (not the surface) reduces g to one-quarter. At the ISS orbit (~408 km) gravity is still about 89% of the surface value — weightlessness is due to free fall, not absent gravity.
The Moon's surface gravity is about 1.62 m/s² (≈ 0.165 g), and Mars is about 3.72 m/s² (≈ 0.379 g) — set mass to 0.0735 and radius to 1737 km for the Moon, or mass to 0.6417 and radius to 3390 km for Mars.
Escape velocity is the minimum speed at which a projectile fired from the surface can escape without further thrust: v_esc = √(2GM/r). For Earth it is about 11.2 km/s. It is related to g at the surface by v_esc = √(2 × g_surface × R).
TG we-Calculate Editorial Team. (2026). Acceleration Due to Gravity Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/acceleration-due-to-gravity-calculator
TG we-Calculate Editorial Team. "Acceleration Due to Gravity Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/acceleration-due-to-gravity-calculator.
TG we-Calculate Editorial Team, "Acceleration Due to Gravity Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/acceleration-due-to-gravity-calculator
@misc{wecalculate_acceleration_due_to_gravity_calculator, title = {Acceleration Due to Gravity Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/acceleration-due-to-gravity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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