# Alfvén Velocity Calculator

URL: https://speedycalculator.com/calculators/physics/alfven-velocity/
Last updated: 2026-10-30

> The Alfvén velocity calculator finds the speed of Alfvén waves – magnetic waves in a plasma – from the magnetic field strength and the ion density and species.

## Inputs

- Magnetic field B (nT, µT, mT, G, T)
- Ion density n (cm⁻³, m⁻³)
- Ion species

## Results

- Mass density
- Alfvén velocity v_A
- As a fraction of c

## Formula

```
v_A = B / √(μ₀·ρ),  ρ = n·m_i
```

## Explanation

In a magnetised plasma, magnetic field lines behave like plucked strings and carry waves along them. These Alfvén waves heat the solar corona and shape the solar wind and Earth's magnetosphere. Their speed depends only on the field and the plasma density.

### How to use the Alfvén Velocity Calculator

- **Magnetic field B**
- **Ion density n**
- **Ion species**

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

### How it works

Enter the magnetic field, the ion number density and the ion species.

### Inputs explained

FieldWhat to enterMagnetic field BUnits: nT, µT, mT, G, TIon density nUnits: cm⁻³, m⁻³Ion speciesChoose one: Protons (H⁺), Helium (He⁺), Oxygen (O⁺), Electron–positron pairs

### What each result means

- **Mass density** = [Ion density n]×[Ion species]×1.66053906660e-27
- **Alfvén velocity v_A** = [Magnetic field B]÷sqrt(1.25663706212e-6×[Mass density])
- **As a fraction of c** = [Alfvén velocity v_A]÷299792458

### Example values

How the main result changes when **Magnetic field B** changes and everything else stays at the example values above:

Magnetic field B (nT)Alfvén velocity v_A (km/s)2.524.38663.7536.5799548.77326.2560.96657.573.15981097.5464

## Worked example

Inputs — Magnetic field B: 5 nT; Ion density n: 5 cm⁻³; Ion species: Protons (H⁺).

Results — Mass density = 8.3631e-21 kg/m³; **Alfvén velocity v_A = 48.7732 km/s**; As a fraction of c = 0.000163.

## Key terms

- **Plasma**: An ionised gas of free ions and electrons.

## FAQ

**Who was Alfvén?**
Hannes Alfvén, who predicted these waves in 1942 and won the 1970 Nobel Prize.

**Where are Alfvén waves found?**
In the solar wind, corona, magnetospheres and fusion plasmas.

**What is a typical solar-wind value?**
About 50 km/s (B ≈ 5 nT, n ≈ 5 cm⁻³).

**Can v_A exceed light speed?**
The formula can, but relativistic corrections cap the real wave speed below c.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)
- [NASA – Planetary fact sheet](https://nssdc.gsfc.nasa.gov/planetary/factsheet/)