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Electric potential calculator

This electric potential calculator gives the potential in volts. A 10 nC point charge produces a potential of 299.585 V at a distance of 0.3 m.

Example: What is given: Point charge and distance · Charge q 10 nC · Distance r from the charge 0.3 m → Result: V = 299.585 V (electric potential). Source: NIST CODATA 2022: vacuum electric permittivity ε₀ = 8.8541878188 × 10⁻¹² F/m; Coulomb constant k = 1/(4πε₀) = 8.9875517862 × 10⁹ N m² C⁻². Updated: .

nC
Negative for negative charges. 1 nC = 10⁻⁹ C.
m
Must be greater than 0; the potential is relative to infinity.
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Result

Result
V = 299.585 V (electric potential)
All representations
QuantityValue
Electric potential V299.585 V
Field strength of the point charge E = k·|q|/r²998.617 V/m
Coulomb constant k8,987,551,786.2 N·m²/C²
Calculation steps
  • V = k·q / r = 8,987,551,786.2 N·m²/C² · 10 · 10⁻⁹ C / 0.3 m = 299.585 V.
  • E = k·|q| / r² = 8,987,551,786.2 · 10 · 10⁻⁹ / (0.3)² = 998.617 V/m.
The potential of a point charge is measured against a zero point at infinity. Positive charges give positive potential, negative charges negative potential. Valid in vacuum (in matter k is divided by ε_r).

How it is calculated

Electric potential V tells you how much potential energy a unit charge has at a given location. It is measured in volts (1 V = 1 J/C). The voltage between two points is the difference of their potentials.

Formulas

For a point charge q, V = k·q / r with the Coulomb constant k = 1/(4π·ε₀) = 8,987,551,786.2 N·m²/C² (ε₀ = 8.8541878188 × 10⁻¹² F/m, CODATA 2022). The field strength is E = k·|q| / r². In general V = W / q (work per charge), and in a uniform field V = E·d.

Worked example

A charge of 10 nC creates at r = 0.3 m the potential V = 8,987,551,786.2 · 10 · 10⁻⁹ / 0.3 = 299.585 V; the field strength there is E = 998.617 V/m. For −10 nC the result is -299.585 V. If 3 mJ of work is done on 10 µC, V = 3 · 10⁻³ / (10 · 10⁻⁶) = 300 V. In a uniform field of 1500 V/m over 0.2 m, V = 300 V.

Frequently asked questions

What is the difference between potential and voltage?

Potential belongs to a location (relative to a zero point); voltage is the difference between two potentials.

How do I calculate the potential of a point charge?

Use V = k·q / r. For 10 nC and 0.3 m that gives 299.585 V.

Why can the potential be negative?

Because it carries the sign of the charge: a negative charge creates a negative potential, −10 nC at 0.3 m gives -299.585 V.

Sources and legal basis

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