Use this calculator to find gravitational force, distance between centers, or one missing mass using Newton's law with clear unit conversions.
Advanced options
How to use our Gravitational Force Calculator
- Choose Solve for to pick the value you want: force, distance, Mass 1, or Mass 2.
- Select Unit system. SI uses kg, m, and N. US customary uses lbm, ft, and lbf.
- Enter Mass 1 (selected unit) and Mass 2 (selected unit) unless one of them is the value you want to solve for.
- Enter Distance between centers (selected unit), not the surface gap between the objects.
- If you are solving for distance or a mass, also enter Gravitational force input (selected force unit) with a value greater than 0.
- Optional: open Advanced options to use Optional presets, change Number display, or adjust Gravitational constant G (m^3/(kg*s^2)) if your class uses a rounded value.
- Click Calculate.
- Check the result by reading Answer (selected solve-for) and the reference outputs. A quick sanity check is that a larger distance should make force much smaller, while larger masses should make force larger.
Definitions
Solve for: The quantity the calculator will find for you: force, distance, Mass 1, or Mass 2.
Mass 1 (selected unit): The mass of the first object. In SI use kilograms. In US customary use pounds-mass, written lbm.
Mass 2 (selected unit): The mass of the second object, using the same unit system as Mass 1.
Distance between centers (selected unit): The straight-line distance from one object's center to the other object's center, which is the distance used in Newton's gravitation formula [2].
Gravitational force input (selected force unit): A known force value used only when you solve for distance, Mass 1, or Mass 2.
Gravitational constant G: The constant that sets the strength of gravity in the formula. The standard value used here is 6.67430 x 10^-11 m^3/(kg*s^2) [1].
Newton (N): The SI unit of force.
Pounds-force (lbf): A US customary force unit shown as a converted reference output.
Common mistakes and quick fixes
Mistake: Entering the surface gap in Distance between centers (selected unit) instead of the center-to-center distance.
Fix: Use the distance from the center of one object to the center of the other. For objects touching, this is about radius 1 plus radius 2.
Mistake: Typing weight units into Mass 1 (selected unit) or Mass 2 (selected unit) when Unit system is US customary.
Fix: Enter mass in lbm, not force in lbf. The force result appears separately in Gravitational force (F) in pounds-force (US customary) .
Mistake: Leaving Gravitational force input (selected force unit) blank when Solve for is set to distance, Mass 1, or Mass 2.
Fix: Fill in the known force value before calculating. That input is required for those solve-for modes.
Mistake: Mixing SI and US values after changing Unit system .
Fix: Recheck every visible field after switching units. The labels tell you whether to enter kg or lbm, and m or ft.
Mistake: Changing Optional presets and forgetting that Distance between centers (selected unit) is still your job to enter.
Fix: Presets fill masses only. Enter the correct center-to-center distance for your situation.
Mistake: Thinking a negative answer should appear in Gravitational force (F) in newtons because gravity pulls inward.
Fix: This calculator shows force magnitude, so the force outputs are positive. Use the value size, not a sign, to compare strength.
Limitations & Key Assumptions / Boundary Conditions
- This calculator uses Newton's law of universal gravitation, which works well for typical homework and many astronomy-style problems but is not a relativity model.
- It treats each object as if its mass acts from its center, so you must enter center-to-center distance, not surface gap.
- All entered masses, distances, and force inputs must be greater than 0. Zero or negative values are not physical for this setup and will trigger an error.
- US customary entries are converted to SI internally, then the results are converted back for display.
- Presets fill masses only. They do not fill distance, and they do not account for changing orbital distance or object shape.
- Very large or very small answers may display in scientific notation depending on your Number display settings, even though the internal math keeps full numeric precision.
- The calculator cannot tell whether your distance is a surface gap by mistake, so always review the Notes or warnings output.
Methodology
Core equation
This calculator uses Newton's law of universal gravitation to find the magnitude of the force between two masses [2][3].
F = G * m1 * m2 / r^2
Here, F is force in newtons, G is the gravitational constant, m1 and m2 are masses in kilograms, and r is the center-to-center distance in meters. The standard value used for G is 6.67430 x 10^-11 m^3/(kg*s^2) [1].
Solve-for modes
If you choose a different target in Solve for, the same equation is rearranged.
r = sqrt(G * m1 * m2 / F)
m1 = F * r^2 / (G * m2)
m2 = F * r^2 / (G * m1)
These forms only work when all known inputs are positive and no denominator is zero.
Unit conversion
If you pick US customary, the calculator converts your entries to SI first, does the physics in SI, then converts some results back for display.
kg = lbm * 0.45359237
m = ft * 0.3048
lbf = N / 4.4482216152605
Worked mini-example
Suppose m1 = 5.972e24 kg, m2 = 1 kg, r = 6.371e6 m, and standard G. Then:
F = 6.67430e-11 * 5.972e24 * 1 / (6.371e6)^2
F is about 9.82 N
That is why an object of mass 1 kg near Earth's surface feels about 9.82 N of gravitational force in this simplified two-body setup.
Output interpretation
A larger force means stronger attraction. If distance doubles, the force becomes one-fourth as large because distance is squared in the denominator. If one mass doubles, the force doubles.
Assumptions used by this calculator
This method assumes point-mass or center-based distance, uses positive magnitudes only, and does not model air resistance, rotation, tides, or relativistic effects. Results can differ from real-world measurements when those effects matter.