# Acceleration of a Particle in an Electric Field Calculator

URL: https://speedycalculator.com/calculators/physics/acceleration-of-particle-in-electric-field/
Last updated: 2026-10-30

> The acceleration of a particle in an electric field calculator finds the force on and acceleration of an electron, proton, alpha particle or any charged particle in a uniform electric field.

## Inputs

- Particle
- Mass m (kg, u (Da), mₑ)
- Charge q (e, C, nC)
- Electric field E (V/m, kV/m, V/cm, MV/m, N/C)

## Results

- Force F
- Acceleration a
- Direction

## Formula

```
F = q·E,  a = q·E / m
```

## Explanation

Electric fields push charged particles, and because electrons are so light they accelerate enormously – 1.76 × 10¹⁴ m/s² in a field of just 1 kV/m. This is the principle behind cathode-ray tubes, particle accelerators and mass spectrometers.

### How to use the Acceleration of a Particle in an Electric Field Calculator

- **Particle**
- **Mass m**
- **Charge q**
- **Electric field E**

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

### How it works

Choose the particle or enter its mass and charge, then the electric field strength.

### Inputs explained

FieldWhat to enterParticleChoose one: Electron, Proton, Neutron (no charge), Alpha particle …Mass mUnits: kg, u (Da), mₑCharge qUnits: e, C, nCElectric field EUnits: V/m, kV/m, V/cm, MV/m, N/C

### What each result means

- **Force F** = [q]×[Electric field E]
- **Acceleration a** = abs([q]×[Electric field E]÷[m])

### Example values

How the main result changes when **Mass m** changes and everything else stays at the example values above:

Mass m (kg)Acceleration a (m/s²)4.5547e-31175,882,001,077,216.36.8320e-31175,882,001,077,216.39.1094e-31175,882,001,077,216.31.1387e-30175,882,001,077,216.31.3664e-30175,882,001,077,216.31.8219e-30175,882,001,077,216.3

## Worked example

Inputs — Particle: Electron; Electric field E: 1,000 V/m.

Results — Force F = -1.6022e-16 N; **Acceleration a = 175,882,001,077,216.3 m/s²**; Direction = Against the field.

## Key terms

- **Electric field**: Force per unit charge.

## FAQ

**Why do electrons accelerate so much?**
Their charge-to-mass ratio is huge: 1.76 × 10¹¹ C/kg.

**Which way does an electron move?**
Opposite to the field direction, because its charge is negative.

**Is gravity important here?**
No – electric forces on particles are vastly stronger.

**What happens at high speeds?**
Relativity limits the speed below c, so a stops being constant.


## 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)