# Electric Potential Calculator

URL: https://speedycalculator.com/calculators/physics/electric-potential/
Last updated: 2026-10-30

> The electric potential calculator finds the electric potential (voltage) at a point due to a single point charge or a system of up to five point charges.

## Inputs

- Configuration
- Relative permittivity ε_r
- Charge q₁ (nC, µC, C, pC, e)
- Distance r₁ (cm, mm, m, in, ft)
- Charge q2 (nC, µC, C, pC, e)
- Distance r2 (cm, mm, m, in, ft)
- Charge q3 (nC, µC, C, pC, e)
- Distance r3 (cm, mm, m, in, ft)
- Charge q4 (nC, µC, C, pC, e)
- Distance r4 (cm, mm, m, in, ft)
- Charge q5 (nC, µC, C, pC, e)
- Distance r5 (cm, mm, m, in, ft)

## Results

- Electric potential V
- Energy of a +1 µC test charge there

## Formula

```
V = k·q / (ε_r·r),  V_total = Σ k·qᵢ/(ε_r·rᵢ)
```

## Explanation

Electric potential is the potential energy per unit charge at a point. Unlike the electric field, it is a scalar – potentials from several charges simply add up, with signs.

### How to use the Electric Potential Calculator

- **Configuration**
- **Relative permittivity ε_r**
- **Charge q₁**
- **Distance r₁**
- **Charge q2**
- **Distance r2**
- **Charge q3**
- **Distance r3**
- **Charge q4**
- **Distance r4**
- **Charge q5**
- **Distance r5**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose single charge or system and enter each charge (with sign) and its distance from the point.

### Inputs explained

FieldWhat to enterConfigurationChoose one: Single point charge, System of point chargesRelative permittivity ε_rA numberCharge q₁Units: nC, µC, C, pC, eDistance r₁Units: cm, mm, m, in, ftCharge q2Units: nC, µC, C, pC, eDistance r2Units: cm, mm, m, in, ftCharge q3Units: nC, µC, C, pC, eDistance r3Units: cm, mm, m, in, ftCharge q4Units: nC, µC, C, pC, eDistance r4Units: cm, mm, m, in, ftCharge q5Units: nC, µC, C, pC, eDistance r5Units: cm, mm, m, in, ft

### Example values

How the main result changes when **Relative permittivity ε_r** changes and everything else stays at the example values above:

Relative permittivity ε_rElectric potential V (V)1179.7511.25143.80081.5119.834289.8755

## Worked example

Inputs — Configuration: Single point charge; Relative permittivity ε_r: 1; Charge q₁: 2 nC; Distance r₁: 10 cm.

Results — **Electric potential V = 179.751036 V**; Energy of a +1 µC test charge there = 0.17975 mJ.

## Key terms

- **Electric potential**: Potential energy per unit charge.

## FAQ

**Is potential a vector?**
No – it is a scalar, so contributions add algebraically.

**Where is the potential zero?**
By convention, infinitely far away.

**What is the relation to the field?**
The field is the negative gradient of potential.

**How is potential related to voltage?**
Voltage is the difference in potential between two points.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)