THE NUMORIX GUIDE
How to use the Gravitational Force Calculator
Last reviewed September 14, 2026
What this calculator does
Newton's law of universal gravitation is F = G m_1 m_2 / r^2.
Formula and method
Newton's law of universal gravitation is F = G m_1 m_2 / r^2. The engine uses G = 6.674e-11 N*m^2/kg^2 and returns the force magnitude in newtons.
Variables and inputs
Masses m_1 and m_2 are entered in kilograms and distance r in meters. The default values approximate Earth and the Moon: 5.972e24 kg, 7.342e22 kg, and 3.844e8 m; the UI requires all three inputs to be positive.
Worked example
For the default Earth-Moon values: F = (6.674e-11)(5.972e24)(7.342e22)/(3.844e8)^2 = 1.9804e20 N. This is the attractive force magnitude along the line joining the centers.
How to interpret the result
The force grows with either mass and falls with the square of center-to-center distance. The scalar result does not show the equal-and-opposite force on the other body or the direction vector.
Common mistakes to avoid
Square the separation distance only after putting it in meters, and measure from center to center for astronomical bodies. Do not substitute local surface gravity g for G, because G is the universal constant in this equation.
Assumptions and limitations
The point-mass or spherically symmetric approximation ignores extended-body shape, rotation, nearby bodies, orbital dynamics, and relativistic effects. The engine hardcodes a rounded G value and does not validate inputs when called outside the UI.
Practical use and checks
The Gravitational Force Calculator applies Newton's inverse-square law to two masses and their center-to-center separation. Enter mass1 = 1 kg, mass2 = 1 kg, and distance = 1 m as a simple check; the force should be about 6.674e-11 N. For an Earth-Moon scale calculation, use center-to-center distance rather than the gap between surfaces. The result is a force magnitude, so it does not show the equal-and-opposite vector directions on the two bodies. Masses increase the force linearly, while doubling distance reduces it to one quarter. Use kilograms and meters, and do not substitute local acceleration g for the universal constant G. The point-mass approximation is useful for separated spherical bodies and basic orbital estimates, but it ignores body shape, rotation, nearby masses, tidal effects, and relativistic corrections. A zero separation makes the formula undefined, and negative masses or distances are not physical inputs even if a raw function can perform arithmetic. The hardcoded G value is rounded relative to a measured constant, so do not treat the last displayed digits as experimental precision. For a real trajectory or structural decision, include all important bodies and define the reference frame instead of using this scalar pairwise force as a complete dynamics model.