Gravitational Force Calculator - Newton Law Solver

A gravitational force calculator is a classical-mechanics tool that evaluates Newton law of universal gravitation F = G m1 m2 / r^2 for two point masses m1 and m2 separated by a centre-to-centre distance r, so you can read off the attractive force in newtons plus the gravitational acceleration at that distance in m/s^2.

• • Surface weight checks: Compute the gravitational pull on a person or object at a planet surface.
• • Earth-Moon and Earth-Sun attraction: Compare the gravitational force at the mean separation distance.
• • Inverse-square scaling in the lab: Work out the tiny attraction between two laboratory masses to see how the inverse-square law behaves at metre scale.
• • Back-solve for an unknown mass or distance: Rearrange F = G m1 m2 / r^2 to find one mass or the distance when the other three are known.

The calculator uses the same inverse-square law that Isaac Newton published in 1687 in the Principia and that NASA, NIST, and undergraduate physics courses still use today.

Presets for Earth-person, Earth-Moon, Earth-Sun, and two 1000 kg spheres let you reproduce common textbook values without looking up the constants first.

When you want to see how that attractive force becomes an acceleration on a known mass, the forces and Newton laws calculator applies F = m * a to the same gravitational problem.

The calculator applies F = G m1 m2 / r^2 to whichever variables you provide, returns the solved value in its natural unit, and also reports the gravitational acceleration g at the chosen distance so you can read off surface gravity at the same time.

• F: Gravitational force in newtons (N). Always attractive along the line joining the centres of the two masses.
• G: Newtonian constant of gravitation, 6.67430 x 10^-11 m^3 kg^-1 s^-2 according to NIST CODATA 2018.
• m1: Mass of the first body in kilograms.
• m2: Mass of the second body in kilograms (kg). For a person enter about 70 kg.
• r: Centre-to-centre distance in metres (m). Earth surface uses 6,371,000 m.

The calculator also reports the gravitational acceleration g = F / m2 at the chosen distance. At a planet surface that is the surface gravity, and at orbital radius it is the local g that drives orbital motion.

When the Solve For menu is set to mass 1, mass 2, or distance, the calculator rearranges F = G m1 m2 / r^2 using the force you supply in the known gravitational force field.

According to NIST CODATA - Newtonian constant of gravitation, G = 6.67430 x 10^-11 m^3 kg^-1 s^-2 in CODATA 2018.

According to Wikipedia - Newton's law of universal gravitation, every point mass attracts every other point mass with a force proportional to the product of the two masses and inversely proportional to the square of the distance between them.

Once you know the gravitational force on a satellite, the orbital period calculator uses the same central mass and distance to compute the matching orbital period.

Four ideas from classical gravitation that the calculator keeps separate so each part of F = G m1 m2 / r^2 can be checked on its own.

These four concepts also explain why a back-solve is informative: the known force and three of the four variables in F = G m1 m2 / r^2 always determine the fourth.

For a circular orbit the gravitational pull balances the centrifugal pseudo-force, so the centrifugal force calculator gives the rotational side of the same two-body problem.

Use the gravitational force calculator in five steps.

1. 1 Pick the variable to solve for: Open the Solve For menu and choose force, mass 1, mass 2, or distance.
2. 2 Choose a mass preset or pick custom: Use one of the Earth-person, Earth-Moon, Earth-Sun, or two 1000 kg presets, or pick custom.
3. 3 Enter the two masses in kilograms: Type the mass of each body. For planets use the published mass value; for a person about 70 kg is a default.
4. 4 Enter the centre-to-centre distance in metres: Planet surface distance uses the planet radius; orbital distance adds the orbital altitude.
5. 5 Provide the known force if back-solving: When Solve For is mass 1, mass 2, or distance, enter the known force in newtons.

For a 70 kg person on Earth, set Solve For to gravitational force, Mass Preset to Earth and 70 kg person; the distance field shows 6,371,000 m. The calculator returns F = 687.42 N and g = 9.82 m/s^2. To back out a planet mass from a 5000 N pull on a 1000 kg probe at 7,000,000 m, switch Solve For to mass 1, set m2 = 1000 kg, distance = 7,000,000 m, and known force = 5000 N; the calculator returns m1 = 3.66e24 kg, near Mars.

When you want to see how long a dropped object takes to fall under the same g reported here, the free fall time calculator takes the distance and the acceleration and returns the fall time.

Practical reasons to use this gravitational force calculator instead of rearranging the formula by hand.

• • Four solve-for modes in one tool: Switch between force, mass 1, mass 2, and distance without leaving the page.
• • SI units built in: Masses are entered in kilograms and distance in metres, matching the SI definition of G.
• • Planetary presets ready to compare: Earth-person, Earth-Moon, Earth-Sun, and two 1000 kg spheres cover the most common textbook comparisons.
• • Surface acceleration visible: The gravitational acceleration g is reported beside the force, so surface weight and orbital gravity are on the same screen.
• • Auditable rearrangement: The same G, the same masses, and the same distance always produce the same force, so hand-checks are straightforward.

The calculator is intentionally narrow: it solves one inverse-square law correctly across four solve-for modes and four planetary presets. For relativistic gravity near compact objects you would still need a more specialised model.

For the relativistic clock-rate correction that the inverse-square law cannot reach near compact objects, the gravitational time dilation calculator uses the same central mass and radius in a Schwarzschild model.

What changes the gravitational force the calculator returns, and what it cannot capture.

• • The formula assumes two isolated point or spherical masses. It does not include tidal effects from a third body or relativistic corrections near compact objects.
• • The Earth surface distance uses the published mean radius. Local gravity varies with latitude, altitude, and density anomalies inside the planet.
• • Back-solving for mass or distance assumes the entered force is exact. Real measurements carry uncertainty that the calculator cannot recover from a single input.

The same inverse-square law is the starting point for satellite orbit design, exoplanet discovery, and galaxy dynamics, each of which adds extra physics on top of the static two-body formula.

According to NASA - Moon fact sheet, NASA lists the Moon mass as 7.342 x 10^22 kg and the mean Earth-Moon distance as 384,400 km, which together give the Earth-Moon gravitational force.