Last updated: 2026-07-01

Electric field of a point charge

A point charge fills the space around it with an electric field — a vector at every location that says how much force a unit charge placed there would feel. For a single point charge the field magnitude is $E = k \cdot \frac{\lvert Q \rvert}{r^2}$, where $Q$ is the source charge, $r$ is the distance from it, and $k \approx 8.99 \times 10^9\ \text{N·m}^2/\text{C}^2$ is Coulomb's constant. The field points straight away from a positive charge and straight toward a negative one, and it falls off with the square of the distance.

This calculator returns the field magnitude in newtons per coulomb (N/C), which is the same unit as volts per metre (V/m), together with the force a positive one-coulomb test charge would feel at that point.

Field points outward or inward

The direction of the field depends only on the sign of the source charge. A positive charge produces a field that radiates outward in all directions, so a second positive charge placed nearby is pushed away. A negative charge produces a field that points inward toward itself, so a positive charge nearby is pulled in. The magnitude is the same for equal amounts of positive or negative charge; only the direction reverses. Because the calculator reports a magnitude, enter the charge with its sign to keep track of direction using the rule above.

Formula

Because the field scales as $1/r^2$, moving twice as far from the charge cuts the field to one-quarter, and three times as far to one-ninth — the same inverse-square behaviour as gravity and light intensity.

Worked example

Suppose a small sphere carries a charge of $Q = 1\ \text{nC}$ ($1 \times 10^{-9}$ C) and you want the field at $r = 0.1$ m (10 cm) away:

Entering 1 nC for the charge and 0.1 m for the distance reproduces this field of about 898.8 N/C. A positive one-coulomb test charge placed there would feel a force of 898.8 N in the outward direction, since $F = qE$ with $q = 1$ C.

Field versus force and potential

It helps to keep three related quantities straight. The electric field $E$ is force per unit charge and exists at a point whether or not anything is there to feel it. The force $F = qE$ is what a specific charge $q$ actually experiences in that field. The electric potential $V = kQ/r$ is energy per unit charge and is a scalar, not a vector. The field is the spatial rate of change of the potential, which is why N/C and V/m describe the same quantity.

Superposition for many charges

Real problems often involve more than one source charge. The electric field obeys superposition: compute the field vector from each charge on its own with $E = k\,\lvert Q \rvert / r^2$, then add those vectors — taking direction into account — to get the net field. This calculator handles one point charge; for a group of charges, evaluate each contribution here and combine them as vectors.