Gravitational Force Converter
Convert gravitational force between units instantly. Includes conversion tables, common equivalents, and calculation formulas.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
F = G * m1 * m2 / r^2
The gravitational force F in Newtons equals the gravitational constant G (6.674e-11) multiplied by both masses (m1 and m2 in kg) divided by the square of the distance r between their centers (in meters). The result can be converted to dynes (multiply by 1e5), pounds-force (divide by 4.44822), or kilogram-force (divide by 9.80665).
Worked Examples
Example 1: Weight of a Person on Earth
Problem:Calculate the gravitational force on a 70 kg person on Earth's surface (mass 5.972e24 kg, radius 6,371 km).
Solution:F = G * m1 * m2 / r^2\nF = 6.674e-11 * 5.972e24 * 70 / (6.371e6)^2\nF = 2.789e16 / 4.059e13 = 686.95 N
Result:Gravitational force = 686.95 N (about 154.4 lbf)
Example 2: Earth-Moon Gravitational Force
Problem:Find the gravitational force between Earth (5.972e24 kg) and Moon (7.342e22 kg) at 384,400 km apart.
Solution:F = G * m1 * m2 / r^2\nF = 6.674e-11 * 5.972e24 * 7.342e22 / (3.844e8)^2\nF = 2.926e37 / 1.478e17 = 1.98e20 N
Result:Earth-Moon gravitational force = 1.98 x 10^20 N
Frequently Asked Questions
Why does gravitational force decrease with the square of distance?
The inverse-square relationship arises from geometry. Gravitational influence radiates outward from a mass in all directions, spreading over the surface of an expanding sphere. Since the surface area of a sphere is 4*pi*r^2, the gravitational field strength (force per unit area) decreases proportionally to 1/r^2. Doubling the distance reduces the force to one-quarter, tripling it reduces force to one-ninth, and so on. This same principle applies to light intensity and other radially spreading phenomena.
How strong is Earth's gravitational pull on a person?
For a 70 kg person standing on Earth's surface (radius 6,371 km from center, Earth mass 5.972e24 kg), Newton's law gives a gravitational force of about 686 Newtons or roughly 154 pounds-force. This matches the familiar calculation of weight = mass times gravitational acceleration (70 kg * 9.81 m/s^2 = 686.7 N). The force decreases with altitude: at the International Space Station's orbit (about 408 km altitude), it is still about 89% of surface gravity.
What is the gravitational constant G and how was it measured?
The gravitational constant G equals 6.67430e-11 N*m^2/kg^2 and was first measured by Henry Cavendish in 1798 using a torsion balance experiment. He suspended a horizontal bar with small lead balls from a thin wire and measured the tiny twist caused by placing large lead spheres nearby. Modern measurements use similar principles with improved precision. G remains one of the least precisely known fundamental constants because gravitational forces between laboratory-scale objects are extremely small.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy