Gravitational Force Calculator

What does the calculator return besides the force?

It returns the force F = G·m₁·m₂ ÷ r² in newtons and the acceleration F ÷ m₂ that mass 2 experiences toward mass 1. With the defaults (Earth, 70 kg, 6.371×10⁶ m) that is 687.3672 N and 9.8195 m/s². The force on mass 1 is equal in size and opposite in direction, but mass 1’s acceleration would be F ÷ m₁, which the tool does not display.

Why is my answer different from my bathroom-scale weight?

The calculator gives the pure gravitational attraction for the mass and distance you typed. A real weight reading also depends on your actual distance from Earth’s centre, which changes with latitude and altitude, and on Earth’s rotation. The default 9.8195 m/s² uses the single radius 6.371×10⁶ m, so it will not match a local measured value exactly.

What counts as the distance r?

The distance between the centres of the two bodies, not between their surfaces. To find the force on a person standing on Earth, use Earth’s radius, since you are about one radius from the centre. For an object one Earth radius above the surface, the centre distance is two radii, and the result is a quarter of the surface force (171.8418 N for 70 kg).

What happens if I enter zero or a negative number?

Masses and distance must all be positive numbers. A zero or negative mass returns “Masses must be positive”, a zero or negative distance returns “Distance must be positive”, and clearing a box counts as 0, so it returns the same message for that field. No force is calculated in those cases.

Can I type very large or very small numbers?

Yes, in scientific notation: 5.972e24 means 5.972×10²⁴. Results below 0.001 N or above one billion N are shown in exponential form, for example 1.9820e+20 N for the Earth–Moon pair. Inputs are also echoed in exponential form, so a 70 kg mass appears as 7.0000e+1.

Does it work inside a planet or for non-spherical objects?

No. The formula treats each body as a point mass, which also holds outside a uniform sphere. Inside a planet, only the mass closer to the centre than you pulls on you in a simple way, and the formula with the full mass would overstate the force. Irregular shapes such as asteroids need a more detailed model.

Is the constant G adjustable?

No. The code uses a fixed G = 6.674×10⁻¹¹ N·m²/kg², shown in the results. Published values of G are known only to roughly four or five significant figures, so results beyond about four digits are an artefact of the inputs rather than a measurement.

Does it account for relativity or for a third body?

No. It is Newton’s two-body law only. The Earth–Moon example ignores the Sun’s pull on the Moon, and nothing here models orbits, tides or relativistic corrections.