Quick answer
Newton's law of gravitation gives F = G m₁m₂ ÷ r². Earth (5.972 × 10²⁴ kg) and a 70 kg person at the surface (6,371 km from the centre) attract with 687.4 N, the person's weight.
Enter both masses and the centre-to-centre distance. The calculator returns the force. Use this gravitational force calculator to check your own figures.
Related tools: Force Calculator: Force from mass and acceleration (Newton's second law). Escape Velocity Calculator: Speed needed to escape a body's gravity from its surface. Centripetal Force Calculator: Force and acceleration for circular motion.
How to use the Gravitational Force Calculator
- Enter mass 1 (kg) (above 0).
- Enter mass 2 (kg) (above 0).
- Enter distance between centers (m) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Mass 1 | A number, in kg | > 0 |
| Mass 2 | A number, in kg | > 0 |
| Distance between centers | A number, in m | > 0 |
Formula and method
Formula
F = G m₁ m₂ ÷ r²
IEEE-754 double precision; shown to the decimals indicated.
G = 6.67430×10⁻¹¹ m³ kg⁻¹ s⁻².
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Mass 1 = 5.972e+24; Mass 2 = 70; Distance between centers = 6371000.0.
| Result | Value |
|---|---|
| Gravitational force | 6.8740e+2 N |
Example 2
Inputs: Mass 1 = 1000; Mass 2 = 1000; Distance between centers = 1.
| Result | Value |
|---|---|
| Gravitational force | 6.6743e-5 N |
Example 3
Inputs: Mass 1 = 7.342e+22; Mass 2 = 5.972e+24; Distance between centers = 384400000.0.
| Result | Value |
|---|---|
| Gravitational force | 1.9805e+20 N |
The first line is the headline result (gravitational force). IEEE-754 double precision; shown to the decimals indicated.
Worked example
F = 6.674 × 10⁻¹¹ × 5.972 × 10²⁴ × 70 ÷ (6.371 × 10⁶)² = 687.4 N, which is 70 × 9.82. Distance is measured between centres, not surfaces.
Inverse square
At twice the distance the force is a quarter. On the Moon's surface the same person would weigh about 114 N. The mutual force on each body is equal and opposite.
How the result changes with mass 1
Holding every other input at the first worked example, this table changes only mass 1. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Mass 1 | Gravitational force |
|---|---|
| 2.986e+24 | 3.4370e+2 N |
| 5.972e+24 | 6.8740e+2 N |
| 1.194e+25 | 1.3743e+3 N |
| 2.389e+25 | 2.7498e+3 N |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Mass 1: entering "0" shows "Mass 1 must be greater than 0." beside that field and no result.
- Distance between centers: entering "0" shows "Distance between centers must be greater than 0." beside that field and no result.
Choosing between the Gravitational Force Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Force Calculator](/science/force-calculator/) | mass and acceleration | Force |
| [Escape Velocity Calculator](/science/escape-velocity-calculator/) | body | Escape velocity |
| [Centripetal Force Calculator](/science/centripetal-force-calculator/) | mass, speed and radius | Centripetal force |
| [Normal Force Calculator](/science/normal-force/) | mass, incline angle and gravitational acceleration | Normal force |
| [Net Force Calculator](/science/net-force-calculator/) | force magnitudes and direction of each force | Net force |
Background: gravity, rotation and optics
Gravity and rotation calculations use a few core relations: a circular orbit has speed v = √(GM ÷ r), torque equals moment of inertia times angular acceleration (τ = Iα), and a thin lens obeys 1/f = 1/dₒ + 1/dᵢ. The moment of inertia depends on both the shape and the axis of rotation.
Use SI units (metres, kilograms, seconds) and check the sign conventions of the formula before interpreting a negative result.
Assumptions and limitations
- Distance is center to center
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for mass 1 and distance between centers to confirm this.
Frequently asked questions
What is G?
6.674 × 10⁻¹¹ N·m²/kg².
Why is it so weak for small objects?
The constant G is only 6.674 × 10⁻¹¹ N·m²/kg², so the pull between everyday objects is a tiny fraction of a newton.
How is weight related?
Weight is the gravitational force at the surface.
What does the Gravitational Force Calculator calculate?
Newtonian gravitational attraction between two masses. It returns Gravitational force.
What formula does the Gravitational Force Calculator use?
F = G m₁ m₂ ÷ r². G = 6.67430×10⁻¹¹ m³ kg⁻¹ s⁻².
What do I need to enter in the gravitational Force Calculator?
You enter Mass 1 (kg), Mass 2 (kg) and Distance between centers (m).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Distance is center to center.
What is an example of a gravitational Force result?
With mass 1 5.972e+24, mass 2 70 and distance between centers 6371000.0, the gravitational force is 6.8740e+2 N.
Related calculators
- Force Calculator — Force from mass and acceleration (Newton's second law).
- Escape Velocity Calculator — Speed needed to escape a body's gravity from its surface.
- Centripetal Force Calculator — Force and acceleration for circular motion.
- Normal Force Calculator — Normal force on an object resting on a flat or inclined surface.
- Net Force Calculator — Resultant of several forces at different angles.
- Friction Force Calculator — Friction force from the coefficient of friction and the normal force.
Sources
- CODATA 2018 / SI exact constants: g₀ = 9.80665 m/s², c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, e = 1.602176634×10⁻¹⁹ C, G = 6.67430×10⁻¹¹ m³/(kg·s²)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.