Electric Potential Energy Calculator
The electric potential energy between two point charges q1 and q2 separated by distance r is U = k * q1 * q2 / r, where k = 8.9875 * 10^9 N m^2/C^2 is Coulomb's constant. A positive U indicates repulsion (same-sign charges), and a negative U indicates attraction (opposite-sign charges). This formula is the basis for understanding ionic bonding, capacitor energy storage, and atomic physics. Enter charges in coulombs (use negative values for negative charges) and separation in meters. For microcoulombs, enter the value multiplied by 10^-6.
Electric potential energy formula
U = k * q1 * q2 / r
k = 8.9875 * 10^9 N m^2/C^2
U is in joules (J), charges q1 and q2 are in coulombs (C), and separation r is in meters (m). Example: q1 = +2 uC (2e-6 C), q2 = -3 uC (-3e-6 C), r = 0.1 m. U = 8.9875e9 * 2e-6 * (-3e-6) / 0.1 = -0.5393 J.
Electric potential energy in context
- Work done moving a charge from infinity to distance r equals U (the potential energy stored).
- In capacitors, energy stored is U = 0.5 * C * V^2, derived from the electric potential energy of the charge distribution on the plates.
- Atomic energy levels are quantized versions of the electron-nucleus potential energy U = k * e * (-e) / r, modified by quantum mechanics.
- NIST CODATA value for Coulomb's constant: k = 8.9875517923 * 10^9 N m^2/C^2 (exact in SI since 2019 redefinition).
Frequently asked questions
What is electric potential energy?
Electric potential energy (U) is the energy stored in the configuration of charged particles. For two point charges q1 and q2 separated by distance r, U = k * q1 * q2 / r, where k is Coulomb's constant (8.9875 * 10^9 N m^2/C^2).
What does a negative electric potential energy mean?
Negative potential energy means the charges attract each other (opposite signs). Work must be done to separate them. Positive potential energy means the charges repel (same sign) and work is needed to push them together.
What is Coulomb's constant?
Coulomb's constant k = 1/(4*pi*epsilon_0) = 8.9875 * 10^9 N m^2/C^2, where epsilon_0 is the permittivity of free space (8.854 * 10^-12 C^2/(N m^2)). This constant appears in both the force and potential energy formulas for point charges.
How is electric potential energy related to electric potential?
Electric potential V at a point is U/q for a test charge q. Potential energy U = q * V. The potential due to a point charge q1 at distance r is V = k * q1 / r. The potential energy of charge q2 in this potential is U = q2 * V = k * q1 * q2 / r.
What are typical charge magnitudes in physics problems?
Elementary charge e = 1.602 * 10^-19 C (proton or electron). Typical static electricity charges are microcoulombs (10^-6 C) to millicoulombs (10^-3 C). Lightning discharges involve coulombs of charge. The formula accepts any unit-consistent charge in coulombs.
Official sources
- NIST CODATA: NIST Value of Permittivity of Free Space.
- OpenStax University Physics: Electric Potential Energy, Vol. 2 Ch. 7.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.