Coulomb's Law Calculator

Use the Coulomb's law calculator to determine the electrostatic force between two charged particles.

Force between the charges21.5701 Nattractive — the charges have opposite signs

Coulomb constant used8.988e+9 N·m²/C²1 ÷ 4πε₀ in vacuum

Field from the first charge at that distance7.19 MV/mkq ÷ r², pointing away from it

Potential from the first charge359.5021 kVkq ÷ r — a scalar, so potentials from several charges simply add without vectors

Potential energy of the pair-1.0785 Jnegative — work must be done to separate them

Electrons in the first charge1.248e+132 µC — a coulomb is an enormous static charge, which is why these pages work in microcoulombs

Electric flux enclosing the first charge225.8818 kV·mQ ÷ ε — Gauss's law, and it is independent of the shape and size of the surface you draw

Flux enclosing both charges-112.9409 kV·monly the NET enclosed charge matters

At 0.5× the separation86.2805 N400% of the force — inverse square, not inverse

At 2× the separation5.3925 N25% of the force — inverse square, not inverse

At 10× the separation215.7012 mN1% of the force — inverse square, not inverse

Gravity between two 1 g masses at this distance26.6972 fN8.08e+14× weaker than the electric force here — electromagnetism dominates gravity utterly at small scales

Field needed to break down dry air3 MV/myour field EXCEEDS it — the air would ionise and spark

The formula

F = k q₁q₂ ÷ r²; E = kq ÷ r²; V = kq ÷ r

The same inverse square, vastly stronger

Coulomb's law has exactly the form of Newton's law of gravitation — an inverse square in the separation, a product of the two sources — but the constant is some twenty orders of magnitude larger relative to typical masses and charges. Between two protons the electric repulsion exceeds the gravitational attraction by about 10³⁶.

The other difference is sign. Gravity only attracts, so it accumulates over astronomical scales; charge comes in both signs and cancels, which is why gravity governs the cosmos while electromagnetism governs chemistry. Bulk matter is electrically neutral to extraordinary precision precisely because any imbalance produces such enormous forces.

A coulomb is a huge amount of static charge: two 1 C charges a metre apart would repel with about nine giganewtons. Real static electricity involves microcoulombs or less, which is why these fields are entered in µC.

A dielectric medium weakens the force by its relative permittivity. Water's value of about 80 reduces electrostatic forces eightyfold, which is exactly why water dissolves ionic salts — it screens the attraction holding the crystal together.