Electric Potential Calculator
Enter a point charge and distance to compute the electric potential V = k·q/r.
Input Data
Results
At a glance:Electric potential V at a point is the electric potential energy per unit charge: V = U/q_test = k·q/r for a point charge q at distance r. It is a scalar (volts, V = J/C), unlike the vector electric field. Potential difference (voltage) drives current in circuits. For multiple charges, potentials add algebraically. Equipotential surfaces are perpendicular to electric field lines; E = −∇V.
Formula
V = k·q/r
Potential difference relates to field: E = −ΔV/Δr
$$V = \frac{kQ}{r}$$How to Use
- Enter the charge q (C).
- Enter the distance r (m) and permittivity.
- The calculator returns V.
Case Studies
Potential near a proton
q = 1.6×10⁻¹⁹ C, r = 1×10⁻¹⁰ m (atomic scale).
V ≈ 8.988e9×1.6e-19/1e-10 ≈ 14.4 V.
A nearby electron would have U = −eV.
FAQ
What is the difference between potential and potential energy?
Potential V is per-unit-charge (J/C = V); potential energy U = q_test·V is for a specific test charge placed there.
Why is potential a scalar?
It is energy per charge, a single number at each point, so potentials from multiple charges simply add — easier than vector-adding electric fields.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.