E = k·Q / r²Q = E·r² / k  ·  r = √(k·Q / E)

Electric field: the electric field (E) of a point charge is the force it exerts per unit of charge at a distance, defined by E = kQ/r². This free calculator solves for field strength, source charge or distance — in any unit — and shows every step of the working.

How to calculate the electric field

The electric field describes the influence a charge spreads through the space around it. For a single point charge, the field strength a distance r away is given by E = k·Q / r², where Q is the source charge and k = 8.9875×10⁹ N·m²/C² is Coulomb’s constant. The result comes out in newtons per coulomb (N/C), which is identical to volts per metre (V/m).

There are three steps. First, decide which quantity you want — field strength, charge or distance — and select it in the calculator’s Solve for menu. Second, enter the two values you already know and pick their units; the calculator converts everything to SI base units (coulombs and metres) behind the scenes, so you never have to convert by hand. Third, read the answer together with the worked steps, which show the formula, your numbers substituted in, and the final value with its units.

The equation rearranges easily. If you measure the field and know the distance, the source charge is Q = E·r² / k. If you know the charge that produces a given field, the distance is r = √(k·Q / E). Notice the inverse-square term: the field drops with the square of the distance, so moving twice as far away leaves you with only a quarter of the field strength.

The field is closely tied to force. Because the field is the force felt per unit charge, E = F/q, a test charge q placed in the field experiences F = qE. To work directly with the force between two charges instead, use the Coulomb’s law calculator, which shares the same constant and the same 1/r² dependence. For the physics behind that constant and how the field of a point charge is derived from it, see our guide to Coulomb’s law and the electric field.

Worked example

Find the electric field 10 cm from a point charge of 1 µC. Convert first: Q = 1×10⁻⁶ C and r = 0.10 m. Then E = k·Q / r² = (8.9875×10⁹)(1×10⁻⁶) / (0.10)² = 8987.5 / 0.01 ≈ 8.99×10⁵ N/C. So the field is about 900 kV/m pointing radially outward from the (positive) charge. Doubling the distance to 0.20 m would quarter this to roughly 2.25×10⁵ N/C.

Why the electric field matters

The electric field is the bridge between a charge and the forces other charges feel, so it underpins everything from capacitors and circuit design to the behaviour of insulators near their breakdown voltage, the deflection of beams in old display tubes, and the way charged particles move in accelerators and the atmosphere.

Frequently asked questions

What is the formula for the electric field of a point charge?

The electric field strength a distance r from a point charge Q is E = kQ/r², where k = 8.9875×10⁹ N·m²/C² is Coulomb’s constant. The field points away from a positive charge and toward a negative one, and it falls off with the square of the distance.

What are the units of electric field strength?

Electric field is measured in newtons per coulomb (N/C), which is exactly equivalent to volts per metre (V/m). Both express the force a field exerts on each coulomb of charge, or equivalently the rate at which the electric potential changes with distance.

How is electric field related to force?

The electric field is the force per unit charge: E = F/q. So a charge q placed in a field E feels a force F = qE. Combining this with Coulomb’s law for two point charges gives the field of a single source charge, E = kQ/r².

Does the sign of the charge change the field strength?

The magnitude E = kQ/r² depends only on the size of the source charge, not its sign. The sign sets the direction: field lines point outward from a positive charge and inward toward a negative one. This calculator returns the magnitude, so enter the size of the charge.

How does the electric field change with distance?

It follows an inverse-square law: doubling the distance r quarters the field strength, and tripling it cuts the field to one ninth. Halving the distance multiplies the field by four. This is the same 1/r² behaviour seen in Coulomb’s law and gravitation.

References & formula source

  • Halliday, Resnick & Walker — Fundamentals of Physics, Chapter 22 (Electric Fields).
  • Young & Freedman — University Physics with Modern Physics, §21.4 (Electric Field and Electric Forces).
  • NIST — CODATA recommended value of the Coulomb constant and the vacuum permittivity.

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