`M = { a * ( r )^2}/{G}`

Enter a value for all fields

The Planet's Mass from Acceleration and Radius calculator computes the mass of planet or moon based on the radius (r), acceleration due to gravity on the surface (a) and the universal gravitational constant (G).

INSTRUCTIONS: Choose units and enter the following:

• (r)  Radius of Planet
• (a)  Acceleration due to gravity on the surface of Planet

Planetary Mass (M): The calculator returns the mass (M) in kilograms.  However, this can be automatically converted into other mass units via the pull-down menu including the following:

• Earth Masses
• Jupiter Masses
• Solar Masses

The Math / Science

This calculator computes the mass of a planet given the acceleration at the surface and the radius of the planet.  The formula for the mass of a planet based on its radius and the acceleration due to gravity on its surface is:

M = a⋅r²/G

where:

• M = Mass of the Planet
• a = acceleration due to gravity on the planet surface
• r = radius of the planet
• G = universal gravitational constant

Astronomy Calculators

• Kepler's 3^rd Law formula T² = (4π • R³)/(G • M)
  • (M) - mass of the system. 
  • (T) - period of the orbit.
  • (R) - separation distance between the two objects.
  • (G) - universal gravity constant
• Small Angle Formula
  • (α) - angle
  • (D) - distance to astronomical object
  • (S) - size or diameter of astronomical object
• Flux and Magnitude formulas
  • Change in Magnitude from Flux Ratio
  • Flux Ratio from Magnitudes
• Telescope formulas
  • Resolving Power of a Telescope
  • Magnification of a Telescope
• Mass formulas
  • Mass from Luminosity
  • Mass from Acceleration and Radius
  • Mass from Speed and Separation
  • Mass of extra-solar planet from mass of star, radius of star orbit and radius of exoplanet orbit
  • Mass of extra-solar planet from mass and velocity of star and velocity of planet
• Relative Size Formulas
  • Relative Size from Relative Temperature and Luminosity
  • Relative Temperature from Relative Size and Luminosity
  • Relative Luminosity from Relative Temperature and Size
• Wavelength Formulas
  • Velocity from shift in Wavelength and Unshifted Wavelength
  • Wavelength Shift from Wavelength and Speed
  • Blackbody Wavelength from Temperature
  • Blackbody Temperature from Peak Wavelength
  • Photon Energy from Wavelength
  • Photon Wavelength from Energy
• Luminosity and other Formulas
  • Distance from absolute and apparent magnitude
  • Radius from Speed and Period
  • Speed of Circular Motion
  • Hubble Time
  • Luminosity from Mass

Related Astro Calculators:

• Kepler's 3^rd Law Calc has Kepler's 3^rd law solved for each parameter.
• Astronomy Calculator contains basic formulas for a college level Introduction to Astronomy
• Exoplanet Calculator contains formulas for studying planets outside of our Solar System.
• Astronomical Distance Calculator provides the distance from the Earth to numerous astronomical bodies (e.g. Sun, Moon, planets, stars, Milky Way's Center and Edge, Andromeda Galaxy)
• Astronomical Distance Travel Time Calculator computes the time to travel to distant parts of space at different velocities.
• Ellipse Calculator
• 3D Vector Calculator:
• Drake Equation Calculator
• Seager Equation Calculator
• Friedman Equation Calculator
• Exoplanet Calculator contains formulas for studying planets outside of our Solar System.
• Astronomical Distance Calculator provides the distance from the Earth to numerous astronomical bodies (e.g. Sun, Moon, planets, stars, Milky Way's Center and Edge, Andromeda Galaxy)
• Astronomical Distance Travel Time Calculator computes the time to travel to distant parts of space at different velocities.
• Radius of Perigee
• Radius of Apogee