Electric Potential Calculator (V = kQ/r of a point charge, potential energy qV)

Understanding the electric potential calculator — concept and principle

This calculator gives the electric potential at a distance from a point charge, the field strength there, and the potential energy of a test charge placed at that point. It is a standard tool for electrostatics homework and for quick estimates around charged spheres and small charged objects.

Potential falls as 1/r, the field as 1/r²; a 1 nC test charge there stores 0.45 µJ.

How it is calculated

V = k Q ÷ r; E = k |Q| ÷ r²; U = q V

k = 1 ÷ (4π ε₀) ≈ 8.988 × 10⁹ N·m²/C², with ε₀ = 8.8541878188 × 10⁻¹² F/m.
Q and q are entered in nanocoulombs with their sign; r is in metres.
V is in volts, E in V/m and U in joules (also shown in µJ).

The principle

Potential is the potential energy per unit charge, measured from a reference of zero at infinity. Bringing a positive test charge in from far away towards a positive Q takes work against the repulsion, and that work per coulomb is kQ/r. Potential is a scalar, so it keeps the sign of Q and the potentials of several charges simply add. The field is the slope of the potential, which is why it falls off one power faster, as 1/r². Outside a uniformly charged sphere the same formulas hold with r measured from the centre.

Worked example

Default inputs: Q = 5 nC, r = 0.1 m, test charge q = 1 nC.

k = 1 ÷ (4π × 8.8541878188 × 10⁻¹²) = 8,987,550,000 N·m²/C².
V = 8.98755 × 10⁹ × 5 × 10⁻⁹ ÷ 0.1 = 449.4 V.
E = 8.98755 × 10⁹ × 5 × 10⁻⁹ ÷ 0.1² = 4,494 V/m.
U = 1 × 10⁻⁹ × 449.4 = 4.494 × 10⁻⁷ J = 0.4494 µJ.

Each point is the calculator re-run with only “Distance from the charge r (m)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Distance from the charge r (m)	Electric potential V (V)
0.025	1,798
0.05	898.8
0.075	599.2
0.1	449.4
0.125	359.5
0.15	299.6
0.2	224.7

How to read the result

A positive U means like charges, so energy was stored by pushing them together and will be released if they fly apart. A negative U means opposite charges that attract. Halving the distance doubles V but quadruples E. Small charges give large voltages: a few nanocoulombs at 10 cm already reach hundreds of volts, which is why static electricity can spark although the energy is tiny.

Common mistakes

Dropping the sign of Q, which changes the sign of V and U.
Confusing potential (V) with field (V/m).
Forgetting the nano prefix: 5 nC is 5 × 10⁻⁹ C.
Using the point-charge formula inside a charged conductor or very close to an extended object.

Keep in mind: The formula assumes a point charge or a spherically symmetric charge in vacuum. Dielectrics, nearby conductors and grounded surfaces change the result.

Frequently asked questions

Is electric potential the same as voltage?

Voltage is a difference of potential between two points. Here it is the difference between the point and infinity.

Can potential be zero where the field is not?

Yes. Midway between equal and opposite charges the potential is zero, but the field is not.

How do I handle several charges?

Calculate kQ/r for each charge and add the results with their signs.

Sources: CODATA 2022 recommended values (ε₀), NIST · OpenStax, University Physics Volume 2 (2016), chapter 7 "Electric Potential"

Checked 9 Nov 2026. Electric potential of a point charge V = kQ/r and potential energy U = qV — standard results of electrostatics; ε₀ from CODATA 2022.

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