Electric Potential Calculator - V = kQ / r Point Solver
Electric potential calculator solves V = kQ / r for a point charge and reads the potential energy U = qV for an optional test charge at the same point.
Electric Potential Calculator
Results
What Is an Electric Potential Calculator?
An electric potential calculator solves the point-charge formula V = kQ / r from a source charge, a distance, and the Coulomb constant k = 1 / (4 pi epsilon_0), so a student can read the potential in volts at any chosen point in space without re-deriving the equation or re-checking the sign convention. The same result panel also reports the potential energy U = qV when an optional test charge is added.
Use the calculator for introductory physics homework, atomic-scale checks (with charge in elementary units and distance in nanometers or angstroms), capacitor and circuit sanity checks, and electrostatics demonstrations. The optional test charge is the bridge to U = qV and to the k q1 q2 / r shortcut for two-charge problems.
The result is a model for an idealized point source. For the force counterpart of the same k = 1 / (4 pi epsilon_0) relationship, the Coulomb's Law Calculator covers F = k q1 q2 / r for the same two-charge setup.
How the Electric Potential Calculator Works
The core calculation uses the point-charge potential formula. The source charge is converted to coulombs, the distance is converted to meters, and the result is reported in volts with an auto-selected prefix.
OpenStax University Physics Volume 2 states V = kQ / r and U = qV. For example, a one microcoulomb point charge at r = 0.01 m gives V = 898.76 kV. A consistent difference from a measured value may point to a wrong unit, a missing factor of 4 pi, or a measurement of V at a point too close to the source.
NIST CODATA gives epsilon_0 = 8.8541878128 x 10^-12 F/m, which sets k = 8.9875517873681764 x 10^9 N*m^2/C^2. The calculator loads that value automatically and prints it in the result panel.
The sign of V tracks the sign of Q, so the source-charge field accepts negative numbers. The auto-prefix moves from V to kV, MV, or pV as the magnitude changes. For the relationship between V and the stored charge on a capacitor, the Capacitance Calculator takes the resulting V along with the plate area and the dielectric to return the stored charge Q = C V.
Key Concepts Explained
An electric potential result is easier to review when the main physical terms stay separate. The Coulomb constant, the relationship between V and E, the sign of V, and the connection between V and U = qV each describe a different part of the same point-charge problem.
Coulomb constant k
k = 1 / (4 pi epsilon_0) ties charge and distance to a force and to a potential. NIST CODATA gives k = 8.9875517873681764 x 10^9 N*m^2/C^2 from epsilon_0 = 8.8541878128 x 10^-12 F/m.
Potential vs electric field
V is a scalar with units of joules per coulomb, so it is a single number at each point in space. The electric field E is a vector, and the two are related by E = -grad V.
Sign of the potential
A positive source charge Q makes V positive everywhere around it. A negative source charge makes V negative everywhere. The sign matters whenever a test charge is added.
Potential energy U = qV
The potential energy of a test charge q at a point is U = qV. The same product also equals k q1 q2 / r for two point charges separated by r, which is the textbook shortcut.
The volt is a derived SI unit equal to one joule per coulomb, so the calculator reports the potential in volts but the potential energy in joules. For the kinetic energy that U = qV converts into when the test charge is released from rest, the Kinetic Energy Calculator takes the same U in joules and returns the speed that the same mass reaches.
How to Use This Calculator
- 1 Enter the source charge. Type the magnitude and sign of the source point charge Q. Use the unit selector for C, mC, µC, nC, pC, or elementary charges e. The sign convention is preserved: a negative Q produces a negative V.
- 2 Enter the distance. Type the straight-line distance r from the source to the evaluation point. Pick m, cm, mm, µm, nm, or angstrom as the unit; the calculator converts to meters before V = kQ / r.
- 3 Optionally enter a test charge. Type a test charge q and pick its unit to add the U = qV row to the result panel. Leaving the test charge at zero suppresses the energy row and keeps the focus on V.
- 4 Read the potential and (if applicable) the energy. The result panel reports V in volts with the auto-selected prefix. When the test charge is non-zero, the U row reports the potential energy in joules with the auto-selected prefix.
- 5 Audit the inputs. The supporting rows show the Coulomb constant k, the source charge in coulombs, the distance in meters, and the source charge in elementary charges. These are the same numbers the formula uses, so a manual V = kQ / r check matches the printed result.
The calculator updates as values change and also responds to the Calculate button. Reset restores the one microcoulomb source at one centimeter with no test charge, giving V near 898.76 kV. For the work and the power dissipated by the same V across a circuit element, the Work Energy Power Calculator pairs the voltage with a current or a resistance.
Benefits and When to Use It
No re-derivation of V = kQ / r: Stops you from retyping the point-charge formula every time the charge or the distance changes. The form takes the inputs and the result panel takes the arithmetic.
Sign-aware source and test charges: Accepts negative Q and negative q, so the calculator returns negative V and negative U when the sign calls for it.
Unit-safe charge and distance: Converts C, mC, µC, nC, pC, and elementary charges e for both the source and the test charge, and converts m, cm, mm, µm, nm, and angstrom for distance.
Auto-selected volt and joule prefixes: Prints V in V, mV, µV, nV, or pV and U in J, mJ, µJ, nJ, or pJ so the displayed value stays in the 0.001 to 999 range.
Traceable result panel: Reports the Coulomb constant k, the source charge in coulombs, and the distance in meters alongside V and U.
The calculator is best for textbook point-charge problems and for atomic-scale checks. It is less appropriate for continuous charge distributions. For the W / q direction of the same identity, the Joules to Volts Calculator handles the energy-to-voltage conversion for battery and capacitor labels.
Factors That Affect Results
Three inputs drive every number in the result panel: the source charge Q, the distance r, and the optional test charge q. The Coulomb constant k sets the overall scale.
Source charge Q
V scales linearly with Q. Doubling the source charge doubles V at the same distance and changes the sign of V when the sign of Q flips.
Distance r
V scales as 1 / r. Doubling the distance halves V, and a 10x larger distance cuts V by a factor of 10 on the same source charge.
Test charge q
U = qV scales linearly with q. Doubling the test charge doubles U at the same V, and the sign of U tracks the sign of both q and V.
Coulomb constant k
k = 1 / (4 pi epsilon_0) sets the overall scale. The NIST CODATA value 8.9875517873681764 x 10^9 N*m^2/C^2 is loaded automatically.
The calculator rejects zero or negative distances because the formula divides by r, and it accepts zero or negative charges because both are physically meaningful: a zero Q gives V = 0, while a negative Q gives a negative V.
NIST CODATA gives the elementary charge e = 1.602176634 x 10^-19 C, which the calculator uses as the SI conversion when the source or test charge is entered in elementary charges. For a different form of the same U = qV identity, the Potential Energy Calculator reports gravitational as well as electric potential energy for comparison.
Frequently Asked Questions
Q: What is electric potential and what unit is it measured in?
Electric potential V is the electric potential energy per unit charge at a point in space, defined as V = U / q. The SI unit is the volt (V), which equals one joule per coulomb. The calculator reports V in volts with an auto-selected prefix.
Q: What is the formula for the electric potential of a point charge?
The electric potential of a point charge Q at a distance r is V = kQ / r, where k = 1 / (4 pi epsilon_0) = 8.9875517873681764 x 10^9 N*m^2/C^2 from NIST CODATA. The sign of Q sets the sign of V.
Q: How do you calculate electric potential energy between two charges?
The potential energy between two point charges q1 and q2 separated by r is U = k q1 q2 / r. Equivalently, U = q2 * V1, where V1 is the potential produced by q1 at the location of q2. The calculator returns U in joules when the test charge is non-zero.
Q: How is electric potential different from electric field?
V is a scalar with units of volts (joules per coulomb), and it gives a single number at each point in space. The electric field E is a vector with units of volts per meter, and the two are linked by E = -grad V.
Q: What is the electric potential of a charged conducting sphere?
For a charged conducting sphere of radius R, the potential outside the sphere (r > R) is V = kQ / r, the same as for a point charge. On and inside the conductor (r <= R), V stays at the surface value kQ / R.
Q: How do you calculate volts from work and charge?
V = W / q, where W is the work done in joules to move a charge q in coulombs between two points, and V is the potential difference in volts. The calculator uses the equivalent V = kQ / r formula in its main mode.