Gravitational Force Calculator

Calculate

Mass 1 (m₁) (kg)

Mass 2 (m₂) (kg)

Separation r (m)

Enter values above to calculate

Calculate Reset

How it calculates

1

G = 6.674×10⁻¹¹ N·m²/kg²

2

F = G × m₁ × m₂ / r²

3

Result in newtons (always attractive)

Formula

F = Gm₁m₂/r²

Variable Table

→ General Relativity article

How to Use This Calculator

This gravitational force calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.

Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.

Assumptions and Limits

The formula F = Gm₁m₂/r² is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.

Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.

Worked Example

Common Mistakes

• Gravity is always attractive — there is no negative gravitational charge
• r is centre-to-centre distance, not surface separation
• G (6.674×10⁻¹¹) is tiny, so gravity is weak unless masses are astronomical

Related

Frequently Asked Questions

What is the gravitational constant G?

G = 6.674×10⁻¹¹ N·m²/kg² — one of the least precisely measured fundamental constants.

Why is gravity so weak?

G is extremely small. Gravity dominates at astronomical scales only because mass always adds up (it has no opposite charge to cancel it).