Enter Known Values
Use center-to-center distance. Select a solve mode to find force, a missing mass, or the required separation.
Formula Used
F = G × m₁ × m₂ ÷ r²
F is gravitational force in newtons. G is the universal gravitational constant. m₁ and m₂ are masses in kilograms. r is center separation in meters.
For advanced solve modes, the calculator uses m₁ = Fr² ÷ (Gm₂), m₂ = Fr² ÷ (Gm₁), and r = √(Gm₁m₂ ÷ F).
How to Use This Calculator
- Select the quantity you want to calculate.
- Enter positive values for the remaining known fields.
- Choose units beside each measurement.
- Use center-to-center distance, not surface spacing.
- Keep the default constant unless your study requires another value.
- Press the calculate button and review the SI conversion details.
- Download CSV or PDF when you need a saved record.
Example Data
| Object 1 mass | Object 2 mass | Center separation | Calculated force |
|---|---|---|---|
| 1,000 kg | 2,000 kg | 10 m | 1.334860 × 10−6 N |
| 5,000 kg | 8,000 kg | 50 m | 1.067888 × 10−6 N |
| 1 Earth mass | 1 Moon mass | 384,400 km | 1.982110 × 1020 N |
Understanding Mutual Gravitational Attraction
Gravity Between Objects
Gravity is the attraction between every pair of objects. It acts across empty space and pulls inward. The strength depends on both masses and their separation. Bigger masses create a stronger attraction. Greater separation reduces the force rapidly. This calculator applies Newton’s universal law of gravitation. It converts selected units before performing the calculation. That keeps the result consistent with scientific units. The displayed force describes the pull each object exerts. Both objects experience equal force in opposite directions.
Mass and Separation Effects
Mass matters because gravitational force grows directly with it. Double one mass and the force doubles. Double both masses and the force becomes four times larger. Distance has a stronger effect on results. Double the separation and force falls to one quarter. Triple the separation and force becomes one ninth. This inverse square behavior explains many orbital patterns. It shows why nearby objects attract strongly. Use center-to-center distance whenever object sizes are important. Surface distance can give misleading results for spheres.
Units and Scientific Notation
The calculator accepts mass and distance units. Kilograms and meters are scientific choices. Grams, pounds, tonnes, feet, miles, and astronomical units work. Every entry is converted into SI values internally. The universal constant then produces force in newtons. Results can display in newtons, kilonewtons, meganewtons, pounds-force, or dynes. Scientific notation helps with extremely small results. It prevents long decimal strings from hiding digits. Select units carefully before submitting your calculation. Incorrect units often cause the largest avoidable errors.
Finding an Unknown Value
Advanced modes rearrange the gravitational equation. You may solve for object one’s mass. You may solve for object two’s mass. You may also solve for center separation distance. Those modes need a known force. The calculator converts force into newtons automatically. It returns the missing quantity in your selected unit. Check every known input is positive. Zero distance has no physical meaning. A negative mass or force is invalid. Review units beside fields before calculating.
Reading the Result Details
The result section includes the main answer. It shows SI mass values used internally. It shows center distance used by the equation. It reports each object’s gravitational acceleration. Acceleration equals force divided by that object’s mass. Smaller objects accelerate more under the same mutual force. The force remains equal for both objects. This distinction is useful when comparing satellites and planets. Download a result summary as CSV. A PDF copy is available for reports. Keep significant figures appropriate for your input accuracy.
Limits of the Simple Model
Newton’s equation assumes point masses or spheres. For spheres, measure distance between their centers. The equation works well when bodies do not overlap. It does not model tides, rotation, relativistic effects, or uneven shapes. Very dense or large objects may need advanced models. Orbital motion also needs velocity and direction information. This tool only calculates instantaneous gravitational attraction. Use verified measurements whenever decisions depend on the result. Compare estimates against known examples for a quick reasonableness check. Always state units when sharing gravitational force calculations.
Frequently Asked Questions
1. What formula does this calculator use?
It uses Newton’s universal gravitation equation: F = Gm₁m₂/r². The tool rearranges this equation when you choose a missing mass or center separation as the unknown quantity.
2. Why must distance be measured between centers?
The standard equation treats objects as point masses or spheres. For spheres, their mass acts as though concentrated at the center. Center separation therefore gives the correct distance for the model.
3. Can I use pounds and feet?
Yes. Select pounds for mass and feet for distance. The calculator converts them to kilograms and meters internally, then completes the calculation using consistent scientific units.
4. Why is my calculated force extremely small?
The gravitational constant is very small. Everyday objects have measurable mass, but their mutual attraction is usually tiny unless their masses are enormous or their centers are very close.
5. Does each object feel the same force?
Yes. Each object experiences equal force magnitude in opposite directions. Their accelerations can differ because acceleration equals force divided by mass.
6. What does the gravitational constant represent?
G sets the scale of gravitational attraction in SI units. Its default value is 6.67430 × 10−11 N·m²/kg². You can replace it for controlled classroom exercises.
7. Can I calculate the mass needed for a chosen force?
Yes. Select either object mass as the target. Enter the other mass, center separation, known force, and gravitational constant. The tool returns the missing mass in your chosen unit.
8. Can this calculate orbital speed?
No. This page calculates instantaneous mutual gravitational force only. Orbital speed additionally depends on the system’s geometry, central mass, and the chosen orbit.
9. What happens when I double the separation?
The force becomes one quarter as large. Gravitational force follows an inverse square relationship, so distance changes have a powerful effect on the result.
10. Are negative values allowed?
No. This calculator accepts positive masses, positive separation, positive known force, and a positive constant. Those values match the physical assumptions used by the equation.
11. When is this simple model less reliable?
Use a more advanced model for irregular nearby objects, tidal effects, rotating systems, extreme gravity, or relativistic conditions. This equation is strongest for point masses and non-overlapping spherical bodies.