Math
Gravitational Force Calculator
Solve Newton's law of gravitation F = G m1 m2 / r^2 for force, either mass, or distance. Supports kg, g, lb, solar and Earth masses, m, km, mi, AU, ly.
Gravitational Force Calculator
Given m1, m2, and distance r, compute F = G x m1 x m2 / r^2.
First object's mass. Must be greater than zero.
Second object's mass. Must be greater than zero.
Center-to-center distance between the two masses.
Gravitational force
1.9815e+20 N
Force (N)
1.9815e+20 N
Force (kN)
1.9815e+17 kN
Force (lbf)
4.4545e+19 lbf
Ratio to m1's Earth weight
3.3822e-6
Acceleration of m1
3.3179e-5 m/s^2
Acceleration of m2
0.002697 m/s^2
Mass 1
5.9720e+24 kg
Mass 2
7.3456e+22 kg
Distance
3.8440e+8 m
Frequently Asked Questions about the Gravitational Force Calculator
What is Newton's law of universal gravitation?
Every two masses attract each other along the line joining their centers with force F = G x m1 x m2 / r^2, where G is the gravitational constant (6.6743 x 10^-11 N m^2 / kg^2), m1 and m2 are masses in kilograms, and r is center-to-center distance in meters.
What units does this calculator accept?
Internally everything is SI. Inputs let you pick masses in kg, g, lb, Earth masses (5.972 x 10^24 kg), or solar masses (1.989 x 10^30 kg), and distances in m, km, mi, astronomical units (1 AU = 1.496 x 10^11 m), or light-years. Output is shown in N, kN, and pound-force.
Why is the gravitational force between everyday objects so small?
G is tiny: 6.6743 x 10^-11 N m^2 / kg^2. Two 1 kg masses 1 m apart attract each other with only 6.67 x 10^-11 N, roughly the weight of a single bacterium. Gravity only becomes obvious for very large masses like planets and stars.
How does doubling the distance change the force?
Gravity follows an inverse-square law, so doubling r divides F by four, tripling r divides F by nine. That is why the Sun pulls Earth far harder than the much closer but much less massive Moon.
Why does the calculator show two different accelerations?
Newton's third law says both masses feel the same force, but they do not undergo the same acceleration because a = F / m. Earth and Moon attract each other with the same force (~1.98 x 10^20 N), but the Moon accelerates toward Earth at ~2.7 x 10^-3 m/s^2 while Earth only accelerates toward the Moon at ~3.3 x 10^-5 m/s^2.