Electric Potential Calculator: Voltage V = kq/r from One or Several Point Charges
Find the electric potential (voltage) at a point from one point charge or several charges by superposition, with field strength and potential energy.
How it works
V = k·q ÷ r · several charges: V = k·Σ(qᵢ ÷ rᵢ) · k = 1 ÷ (4π ε₀) = 8.9876 × 10⁹ N·m²/C² (divided by εr in a medium) · rᵢ = √((x − xᵢ)² + (y − yᵢ)²) · E = k·|q| ÷ r² · U = q_test × V
Electric potential is the potential energy per coulomb that a charge would have at a point, measured from zero at infinity. For one point charge it is V = kq/r: it falls off as 1/r (more slowly than the field, which falls as 1/r²) and takes the sign of the charge, so a negative charge creates a negative potential. Its unit is the volt, one joule per coulomb. Because potential is a scalar, several charges combine by simple addition: work out kq/r for each charge using its distance to the point and add the results with their signs. This is easier than adding fields or forces, which need components. In "Several charges" mode, type each charge with its x and y position (or just its distance to the point), and the calculator gives each contribution and the total. The relative permittivity under More options models a uniform medium such as oil or water, which reduces the potential by εr. The same formula gives the potential outside a uniformly charged sphere, measured from its center. This calculator gives the voltage; for the force between two charges use the Coulomb’s law calculator, and for the field vector use the electric field calculator.
Worked example
A +0.4 µC charge (4 × 10⁻⁷ C) is 10 cm (0.1 m) from a point. V = 8.988 × 10⁹ × 4 × 10⁻⁷ ÷ 0.1 = 35,950 V, or 35.95 kV. The field there is k·q ÷ r² = 359,500 V/m, pointing away from the charge. At 20 cm the potential halves to 17,975 V while the field drops to a quarter. In the "Several charges" default, a −0.2 µC charge 10 cm on the other side adds −17,975 V, so the total at the point is 17,975 V.
Sources: OpenStax University Physics Vol. 2, 7.3 Calculations of Electric Potential (Examples 7.10 and 7.12) · Omni Calculator: Electric potential (0.4 µC at 10 cm example)
Frequently asked questions
What is the formula for electric potential?
For a point charge V = kq/r, where k = 8.99 × 10⁹ N·m²/C², q is the charge in coulombs and r the distance in meters. For several charges, add kq/r for each one with its sign.
What is the difference between electric potential and electric field?
Potential is a scalar energy per charge in volts and falls as 1/r. The field is a vector force per charge in volts per meter (N/C) and falls as 1/r². The field points from high to low potential, and for a point charge E = V/r.
Can electric potential be negative?
Yes. A negative charge creates a negative potential around it, and a positive test charge placed there has negative potential energy, meaning it is attracted. Only differences in potential are physically measurable; the zero is set at infinity by convention.
What is the potential 5 cm from a −3 nC charge?
V = 8.99 × 10⁹ × (−3 × 10⁻⁹) ÷ 0.05 = −539 V. Choose nC and cm as units and enter −3 and 5.
How do I find the potential of a dipole?
Choose "Several charges" and enter both charges with positions, e.g. "3, 0, 2" and "-3, 0, -2" in nC and cm. At (0, 1 cm) the potential is about 1,798 V: the near +3 nC charge contributes 2,696 V and the far −3 nC charge −899 V.
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This calculator is for educational purposes. Double-check important results before acting on them.