# Electric Potential Calculator

V = k·Q/r with the sign preserved, plus the electron potential energy U = −e·V in eV — at the Bohr radius this reproduces 27.2114 V, twice hydrogen's ionization energy.

> Canonical page: https://elysiatools.com/en/tools/electric-potential-calculator

- **Category:** Science & Education

- **Keywords:** electric potential, voltage, point charge, potential energy, electron volt, electromagnetism

## Overview

The Electric Potential Calculator computes the electrostatic potential (V = k·Q/r) around a point charge and determines the resulting potential energy (U = −e·V) for an electron in electronvolts (eV).

## Inputs

- **Charge Q** (number): e.g. 1
- **Charge unit** (select)
- **Distance r** (number): e.g. 1
- **Distance unit** (select)

## When to use

- Calculating the electric potential created by point charges across metric and microscopic scales.
- Finding the potential energy of an electron at a specific distance from an atomic nucleus or charged particle.
- Verifying electrostatics homework problems and laboratory benchmark values.

## How it works

- Enter the source charge magnitude Q and select its unit (C, mC, µC, nC, or pC).
- Enter the radial distance r and choose the distance unit (m, cm, mm, µm, or nm).
- The tool applies Coulomb's constant (k ≈ 8.98755 × 10⁹ N·m²/C²) to compute V = k·Q/r while preserving charge sign.
- It converts the result into electron potential energy U = −e·V expressed in eV, detailing particle polarity and interaction behavior.

## Use cases

- Physics students solving electromagnetism problems involving point charge potentials and field distributions.
- Educators demonstrating atomic scale binding energy and virial theorem relationships in hydrogen-like systems.
- Engineers evaluating electrostatic voltage levels generated by static charges at varying distances.

## Frequently asked questions

### What formula is used to calculate electric potential?

It uses V = k·Q/r, where k is Coulomb's constant (8.98755 × 10⁹ N·m²/C²), Q is the source charge, and r is the distance.

### How is the electron potential energy U determined?

The electron potential energy is calculated as U = −e·V, directly yielding electronvolts (eV) from the potential in volts.

### Does the calculator support negative charges?

Yes, entering a negative charge value preserves the sign, resulting in a negative potential and a positive electron potential energy.

### What charge units are supported?

You can select Coulombs (C), millicoulombs (mC), microcoulombs (µC), nanocoulombs (nC), or picocoulombs (pC).

### What distance units can be selected?

Supported units include metres (m), centimetres (cm), millimetres (mm), micrometres (µm), and nanometres (nm).

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