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Coulomb’s law calculator

A-level Fields and space

The force between two point charges. It is repulsive for like charges and attractive for unlike charges.

F = Q₁ Q₂ / (4πε₀ r²)

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

FElectrostatic force to find 5.40 N

Q₁Charge

Q₂Charge

ε₀Permittivity of free space constant F/m

rSeparation of the charges

Significant figures

Working

Write the equation
F = Q₁ Q₂ / (4πε₀ r²)
Constants used
ε₀ = 8.85 × 10⁻¹² F/m
Substitute the values
F = (2 × 10⁻⁶) × (3 × 10⁻⁶) ÷ (4π × (8.85 × 10⁻¹²) × 0.1²)
Calculate
F = 5.39508 N
Give the answer to 3 significant figures
F = 5.40 N

Worked example

Find F, the electrostatic force. Given: charge Q1 = 2.00 × 10⁻⁶ C; charge Q2 = 3.00 × 10⁻⁶ C; separation of the charges r = 0.100 m; permittivity of free space ε0 = 8.85 × 10⁻¹² F/m.

Write the equation
F = Q₁ Q₂ / (4πε₀ r²)
Constants used
ε₀ = 8.85 × 10⁻¹² F/m
Substitute the values
F = (2 × 10⁻⁶) × (3 × 10⁻⁶) ÷ (4π × (8.85 × 10⁻¹²) × 0.1²)
Calculate
F = 5.39508 N
Give the answer to 3 significant figures
F = 5.40 N

Symbols and units

Symbol	Quantity	SI unit
F	Electrostatic force	N
Q₁	Charge	C
Q₂	Charge	C
ε₀	Permittivity of free space (constant)	F/m
r	Separation of the charges	m

Coulomb’s law: rearranged

To find electrostatic force: F = Q₁ Q₂ / (4πε₀ r²)
To find charge: Q₁ = 4πF ε₀ r² / Q₂
To find charge: Q₂ = 4πF ε₀ r² / Q₁
To find separation of the charges: r = √(Q₁ Q₂ / (4πF ε₀))

Exam tip

Use the sign of each charge only to decide the direction. The size uses the magnitudes.

Common questions

What is the formula for coulomb’s law?

The equation is F = Q1 Q2 / (4πε0 r²), where F is the electrostatic force (N); Q1 is the charge (C); Q2 is the charge (C); r is the separation of the charges (m); ε0 is the permittivity of free space (F/m).

What units should I use for coulomb’s law?

In SI units: electrostatic force in N, charge in C, charge in C, permittivity of free space in F/m, separation of the charges in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange F = Q1 Q2 / (4πε0 r²)?

Rearranging gives these forms: to find electrostatic force: F = Q1 Q2 / (4πε0 r²). to find charge: Q1 = 4πF ε0 r² / Q2. to find charge: Q2 = 4πF ε0 r² / Q1. to find separation of the charges: r = √(Q1 Q2 / (4πF ε0)).

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Read the full explanation on the Coulomb force between two point charges formula page. More fields and space equations: Uniform electric field, Electric field strength, Field of a point charge, Newton’s law of gravitation, Gravitational field strength, Gravitational potential, Orbital period, Escape velocity. See the full list on the a-level physics equation calculator page.