Coulomb's law calculator with electric field strength

Coulomb's law gives the force between two point charges: F = kQ₁Q₂ ÷ r², where k = 8.99 × 10⁹ N m²/C² and r is the distance between them. Two 3 µC charges 0.2 m apart push each other away with 2.02 N. This Coulomb's law calculator works out that force with each step, takes charges in coulombs, millicoulombs, microcoulombs, nanocoulombs or electron charges, and also finds the electric field strength around a charge or between two plates.

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Electric Force Calculator

Calculate Coulomb's law electric force

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How to use the Coulomb's law calculator

1. Open the Electric Force Calculator and choose Force, Radial Field or Uniform Field.
2. For Force, type each charge as a number and a power of ten, with its sign: 2 and −6 for 2 µC, or set the charge unit to µC and type 2 and 0. Charges can be in C, mC, µC, nC or elementary charges, e.
3. Type the distance between the centres of the charges, also as a number and a power of ten, in m, cm, mm or nm, among others.
4. Read the force in newtons, with the working. A positive force means the charges repel; a negative one means they attract.
5. The graph shows how the size of the force falls with distance, with your distance marked. For practice, press Random problem.

Coulomb's law

Like charges repel and unlike charges attract. The force is an inverse square law: double the distance and it drops to a quarter. The calculator uses k = 8.98755 × 10⁹. For where the law comes from and how it compares with gravity, see the Coulomb's law guide.

Worked examples you can check in the calculator

Example 1: two equal charges

Two charges of +3 µC are 0.2 m apart. Type 3 and −6 for each charge, and 2 and −1 for the distance.

The answer is positive, so they repel. Move them to 0.4 m apart, twice as far, and the calculator gives 0.506 N: a quarter of the force.

Example 2: opposite charges

+2 µC and −5 µC are 10 cm apart. Type the second charge as −5 and −6, and the distance as 1 and −1 (0.1 m). The calculator gives F = −8.99 N. The minus sign means attraction: each charge is pulled towards the other with 8.99 N.

Example 3: two electrons

Set the charge unit to e (elementary charges) and type −1 for each, then 1 nm for the distance. F = 8.99 × 10⁹ × (1.602 × 10⁻¹⁹)² ÷ (10⁻⁹)² = 2.31 × 10⁻¹⁰ N, positive because two negative charges repel. Tiny, but on an electron's tiny mass it is a huge push.

Example 4: field strength around a charge

Choose Radial Field: a 4 nC charge, 0.3 m away. E = kQ ÷ r² = 8.99 × 10⁹ × 4 × 10⁻⁹ ÷ 0.3² = 399 N/C. A 1 C charge placed there would feel 399 N; a 2 µC charge would feel 399 × 2 × 10⁻⁶ = 7.99 × 10⁻⁴ N.

Example 5: between two plates

Choose Uniform Field: 1,500 V across plates 2 cm apart. E = V ÷ d = 1500 ÷ 0.02 = 75,000 N/C, the same as 75,000 V/m. Between parallel plates the field is the same strength everywhere.

Try a question on charges and fields, then press Mark to check your answer in the Electricity course.

What the calculator doesn't do

• Solve for a charge or the distance. Rearrange by hand: r = √(kQ₁Q₂ ÷ F), or Q₂ = Fr² ÷ (kQ₁).
• More than two charges. Work out each pair's force, then add them as vectors. The Vectors Calculator helps with the adding.
• Charges in a material. It uses k for a vacuum (air is very close). In water or another medium, the force is smaller.
• The direction of the field. It gives the size of E. A field points away from a positive charge and towards a negative one.

Common mistakes

• Forgetting to square r. At 0.2 m, divide by 0.04, not 0.2.
• Leaving µC as whole numbers. 3 µC is 3 × 10⁻⁶ C. Set the unit, or type the power of ten.
• Centimetres in the formula. r must be in metres unless you set the unit.
• Reading a negative force as an error. It means attraction.
• Using the distance between surfaces. For charged spheres, r is between their centres.

Read next

Physics · Fields and gravityCoulomb's law: F = kQ₁Q₂/r² explained, with examplesCoulomb's law F = Q₁Q₂ ÷ 4πε₀r² explained: the constants, attraction and repulsion, the inverse square law, worked examples and a comparison with gravity.