More precisely, the electric potential is the energy per unit charge for a test charge that is so small that the disturbance of the field under consideration is negligible.

The motion across the field is supposed to proceed with negligible acceleration, so as to avoid the test charge acquiring kinetic energy or producing radiation.

By definition, the electric potential at the reference point is zero units.

In classical electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V or occasionally φ,[1] equal to the electric potential energy of any charged particle at any location (measured in joules) divided by the charge of that particle (measured in coulombs).

By dividing out the charge on the particle a quotient is obtained that is a property of the electric field itself.

This value can be calculated in either a static (time-invariant) or a dynamic (time-varying) electric field at a specific time with the unit joules per coulomb (J⋅C−1) or volt (V).

Though electric field is not continuous across an idealized surface charge, it is not infinite at any point.

Therefore, the electric potential is continuous across an idealized surface charge.

Classical mechanics explores concepts such as force, energy, and potential.

A net force acting on any object will cause it to accelerate.

As an object moves in the direction of a force acting on it, its potential energy decreases.

where C is an arbitrary path from some fixed reference point to r; it is uniquely determined up to a constant that is added or subtracted from the integral.

Thus, the line integral above does not depend on the specific path C chosen but only on its endpoints, making

This states that the electric field points "downhill" towards lower voltages.

By Gauss's law, the potential can also be found to satisfy Poisson's equation:

A test charge, q, has an electric potential energy, UE, given by

The electric potential arising from a point charge, Q, at a distance, r, from the location of Q is observed to be

Note that, in contrast to the magnitude of an electric field due to a point charge, the electric potential scales respective to the reciprocal of the radius, rather than the radius squared.

The electric potential at any location, r, in a system of point charges is equal to the sum of the individual electric potentials due to every point charge in the system.

This fact simplifies calculations significantly, because addition of potential (scalar) fields is much easier than addition of the electric (vector) fields.

In some other (less common) systems of units, such as CGS-Gaussian, many of these equations would be altered.

The electrostatic potential could have any constant added to it without affecting the electric field.

In electrodynamics, the electric potential has infinitely many degrees of freedom.

For any (possibly time-varying or space-varying) scalar field, 𝜓, we can perform the following gauge transformation to find a new set of potentials that produce exactly the same electric and magnetic fields:[5]

In the Coulomb gauge, the electric potential is given by Poisson's equation

However, in the Lorenz gauge, the electric potential is a retarded potential that propagates at the speed of light and is the solution to an inhomogeneous wave equation:

The SI derived unit of electric potential is the volt (in honor of Alessandro Volta), denoted as V, which is why the electric potential difference between two points in space is known as a voltage.

Variants of the centimetre–gram–second system of units included a number of different units for electric potential, including the abvolt and the statvolt.

Inside metals (and other solids and liquids), the energy of an electron is affected not only by the electric potential, but also by the specific atomic environment that it is in.

The terms "voltage" and "electric potential" are a bit ambiguous but one may refer to either of these in different contexts.