Electric Potential Calculator

The electric potential at a distance r from a point charge Q is:

V = kQ/r

Where:

• V = Electric potential in volts (V)
• k = Coulomb’s constant = 8.9875 × 10⁹ N·m²/C²
• Q = Charge in coulombs (C)
• r = Distance from the charge in meters (m)

Electric potential vs. electric field:

• Electric potential V is a scalar, just a number at each point
• Electric field E is a vector, carrying both magnitude and direction at each point
• They are related: E = −dV/dr (the field points from high to low potential)

What does electric potential mean?

Electric potential is the potential energy per unit charge. If you place a small test charge q at a point where the potential is V, it has potential energy U = qV.

This is why we measure voltage in volts, because a volt is a joule per coulomb.

Superposition: If multiple charges are present, the total potential is just the sum: V_total = V₁ + V₂ + V₃ + …

This is simpler than adding electric fields (which require vector addition).

Practical reference:

• Near a proton (1.6 × 10⁻¹⁹ C) at the Bohr radius (5.29 × 10⁻¹¹ m): V ≈ 27.2 V
• This is the “Hartree” unit of energy = 27.2 eV, fundamental to atomic physics

Why potential is usually the easier quantity

Field and potential describe the same physics, but potential is a single number at each point while the field is an arrow. For several charges you add the potentials arithmetically and you are done; adding the fields means resolving each into components and summing them as vectors. Physicists nearly always find V first and then differentiate to get E, rather than the other way round.

The sign carries real meaning too. A positive charge creates a positive potential, so bringing another positive charge in from far away costs you work. A negative source creates a negative potential, and the same test charge arrives having released energy. That is the whole reason an electron is bound to a nucleus.

The “zero at infinity” convention

V = kQ/r takes the potential to be zero infinitely far from the charge. That choice is arbitrary but universal, and it is why the formula has no constant term. It also means the number this calculator gives you is a difference: the work per coulomb needed to bring a charge from infinity to that distance. In circuits the same convention is why you can call any node “ground” and measure everything against it.

A caution on getting too close. As r goes to zero the formula sends V to infinity, which is not physics but a sign that the point-charge idealisation has run out. Real charges have finite size, and inside a uniformly charged sphere the potential is finite and flat rather than infinite.