Coulomb's Law Force Calculator

Calculate

Charge q₁ (C)

Charge q₂ (C)

Separation r (m)

Enter values above to calculate

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How it calculates

1

k = 8.99×10⁹ N·m²/C² (Coulomb constant)

2

F = k × |q₁| × |q₂| / r²

3

Positive result = magnitude; direction: attractive if opposite signs, repulsive if same

Formula

F = kq₁q₂/r²

Variable Table

→ Coulomb's Law article

How to Use This Calculator

This coulomb's law 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 = kq₁q₂/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

• Force is attractive for unlike charges, repulsive for like charges
• F ∝ 1/r² — doubling distance reduces force by 4×
• Use SI units: charge in coulombs, distance in metres

Related

Frequently Asked Questions

What is the Coulomb constant k?

k = 1/(4πε₀) = 8.99×10⁹ N·m²/C². ε₀ = 8.854×10⁻¹² F/m is the permittivity of free space.

How does Coulombs Law compare to gravity?

Both are inverse-square laws, but electrostatic force is ~10³⁶ times stronger than gravity between two protons.