Gravitational Force Converter
Convert gravitational force between units instantly. Includes conversion tables, common equivalents, and calculation formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Gravitational Force Converter
Calculator
Adjust values & calculateEnter your values below. Every result is computed in your browser โ no data is sent to any server.
Formula: F = G * m1 * m2 / r^2
Worked example โ Gravitational force = 686.95 N (about 154.4 lbf)
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 F = 6.674e-11 * 5.972e24 * 70 / (6.371e6)^2 F = 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 F = 6.674e-11 * 5.972e24 * 7.342e22 / (3.844e8)^2 F = 2.926e37 / 1.478e17 = 1.98e20 N
Result:Earth-Moon gravitational force = 1.98 x 10^20 N
Frequently Asked Questions
What is Newton's Law of Universal Gravitation?
Newton's Law of Universal Gravitation states that every object with mass attracts every other object with mass through a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is F = G * m1 * m2 / r^2, where G is the gravitational constant (6.674e-11 N*m^2/kg^2). This law accurately describes gravitational interactions for most everyday and astronomical scenarios, though Einstein's General Relativity provides corrections needed for extreme conditions.
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 for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
Related Calculators
๐งฎForce Converter
Calculate force converter with inputs, formulas, and instant results.
๐งฎNewtons to Pounds-Force Converter (N, lbf, kgf)
Convert between Newtons, pounds-force, kilogram-force, and dynes.
๐งฎNm to Kgf-Cm Converter
Convert torque between Newton-meters and kilogram-force centimeters.
๐งฎTorque Unit Converter
Calculate torque unit converter with inputs, formulas, and instant results.
๐งฎElectrical Resistance Converter (ฮฉ, kฮฉ, Mฮฉ)
Calculate electrical resistance unit converter with inputs, formulas, and instant results.
๐งฎTime Unit Converter
Calculate time unit converter with inputs, formulas, and instant results.
๐งฎArea Converter
Calculate area converter with inputs, formulas, and instant results.
๐งฎAresto Hectares Converter
Calculate aresto hectares converter with inputs, formulas, and instant results.