Surface Gravity of a Planet Calculator

Background.

Mercury has barely half the mass of Mars, yet you would weigh almost exactly the same on either: 3.70 m/s² against 3.71 m/s². Mercury makes up for its smaller mass with a smaller radius, about 2,440 km against 3,396 km, so its surface sits closer to its centre. That trade between mass and size is the whole of Newton's surface-gravity formula, g₀ = GM/R².

Give a mass and a radius, for a planet, moon, asteroid, exoplanet or invented world, and you get the field at the surface, the body's average density and the amount of that field its spin cancels at the equator. Run it the other way to find the mass a body of a given size needs for a target gravity, or the radius a body of a given mass must have.

Rotation is why two gravities are reported. The 9.80 m/s² JPL lists for Earth is GM/R² with nothing subtracted. A scale on the equator reads less, because part of gravity's pull is used up carrying you round a circle about 40,075 km long once every sidereal day. For Earth that costs a third of a percent; for Jupiter, which turns in under ten hours, it costs almost nine.

What is surface gravity of a planet calculator?

Surface gravity is the acceleration a body's gravity gives a free object at its surface, in metres per second squared. For a spherically symmetric body it is g₀ = GM/R², a consequence of Newton's shell theorem, which lets the whole mass be treated as though it sat at the centre. It does not depend on the mass of the falling object. On a rotating body a scale measures the effective gravity instead: g₀ minus the centripetal acceleration of the ground, a reduction that is largest at the equator and zero at the poles. For the giant planets, which have no solid surface, 'surface' means the level where the atmospheric pressure is one bar.

How to use this calculator.

1. 01Pick what to solve for: surface gravity from mass and radius, the mass that gives a target gravity at a given radius, or the radius that gives a target gravity for a given mass.
2. 02Enter mass in kilograms and radius in metres, multiplying kilometres by 1,000. Earth comes pre-filled with JPL's mass and equatorial radius.
3. 03Match the radius to your purpose: the equatorial radius to compare with an agency's equatorial gravity, the volumetric mean radius to reproduce a published bulk density.
4. 04Enter the sidereal rotation period in hours, or 0 to leave rotation out. A retrograde rotator such as Venus can be entered as a negative period, since only its size matters.
5. 05In the mass and radius modes, enter the target gravity as the non-rotating value GM/R², the kind agencies tabulate.

The formula.

The field is g₀ = GM/R², with G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² from CODATA 2022. Because the radius is squared, size weighs more heavily than mass: double the radius at fixed mass and gravity falls to a quarter, but double it at fixed density and gravity doubles, because the mass grows eightfold.

Rotation adds a centrifugal term at the equator. With ω = 2π/P and P the sidereal period in seconds, a point on the equator travels a circle of radius R and needs a centripetal acceleration ω²R, which comes out of gravity, so g_eff = g₀ − ω²R. Only ω² appears, so the direction of spin makes no difference. If ω²R reaches GM/R², g_eff is zero and the equator is at rotational break-up, which happens once the period falls to 2π√(R³/GM); the result is flagged rather than hidden.

Bulk density is ρ = 3M/(4πR³). The comparison with Earth divides g_eff by the conventional standard gravity, 9.80665 m/s², fixed in 1901 by the 3rd General Conference on Weights and Measures. The inverse modes use M = g₀R²/G and R = √(GM/g₀).

The body is treated as a sphere, so for a flattened, fast-spinning planet the equatorial value runs a few parts in a thousand low; and G itself is known only to about 22 parts per million.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NASA JPL Solar System Dynamics, 'Planetary Physical Parameters': column headers 'Equatorial Radius (km)', 'Mean Radius (km)', 'Mass (×10²⁴ kg)', 'Bulk Density (g cm⁻³)', 'Sidereal Rotation Period (d)' and 'Equatorial Gravity (m s⁻²)'. Earth: 6378.1366 km, 6371.0084 km, 5.97217, 5.5134, 0.99726968 d, 9.80 m/s². Jupiter: 71 492 km, 1898.125, 0.41354 d, 24.79 m/s². The gravity column is noted as 'derived from other referenced values and uncertainties in this table'. Independent, open access. Retrieved 2026-07-29.
2. [2]NIST, CODATA 2022 recommended value of the Newtonian constant of gravitation: G = 6.674 30(15) × 10⁻¹¹ m³ kg⁻¹ s⁻², relative standard uncertainty 2.2 × 10⁻⁵. Independent, open access. Retrieved 2026-07-29.
3. [3]BIPM, 3rd CGPM (1901) Resolution 2, 'Declaration on the unit of mass and on the definition of weight; conventional value of gₙ': adopts 980.665 cm/s² as the conventional standard acceleration due to gravity, and defines weight as a force equal to mass times that acceleration. Independent, open access. Retrieved 2026-07-29.
4. [4]NGA Office of Geomatics, World Geodetic System 1984, standard NGA.STND.0036_1.0.0_WGS84 (revision of 8 July 2014). DEFINING parameters verified on the NGA WGS 84 page and used directly in the worked example: semi-major axis a = 6 378 137.0 m, flattening 1/f = 298.257223563, angular velocity ω = 7 292 115 × 10⁻¹¹ rad/s, geocentric gravitational constant GM = 3.986 004 418 × 10¹⁴ m³/s². The normal equatorial gravity of 9.780 325 3359 m/s² quoted alongside it is a DERIVED constant from the same standard; that derived table was not machine-readable at retrieval, so treat it as a standards-document reference rather than a fetched figure. Retrieved 2026-07-29.
5. [5]Newton, I. (1687). Philosophiae Naturalis Principia Mathematica, Book I, Propositions LXXI and LXXIII — the shell theorem, which is what licenses treating a spherically symmetric planet as a point mass at its centre. Print/bibliographic reference.