What is electron drift velocity?

Drift velocity is the average net velocity of electrons along a conductor due to an applied electric field. Although electrons move randomly at high thermal speeds (~10⁶ m/s), the net drift caused by voltage is very slow — typically fractions of a millimeter per second in copper wire.

What is the drift velocity formula?

v_d = I / (n · q · A), where I is current in amperes, n is the free electron density in m⁻³, q is the elementary charge (1.602 × 10⁻¹⁹ C), and A is the cross-sectional area in m².

What is the free electron density of copper?

Copper has approximately 8.49 × 10²⁸ free electrons per cubic meter. This high carrier density is why copper is an excellent conductor.

Why is drift velocity so small?

Because the carrier density in metals is enormous (~10²⁸ m⁻³), even a large current requires only a tiny drift velocity. For 1 A through 1 mm² copper, drift velocity is roughly 0.074 mm/s.

Does drift velocity equal the speed of electrical signals?

No. Electrical signals (electromagnetic waves) travel close to the speed of light through the field surrounding the wire. Drift velocity of electrons is orders of magnitude slower.

Electron Drift Velocity Calculator

Compute electron drift velocity in a conductor from current, free electron density, and wire cross-section.

Conductor Parameters

Current (I)

Free Electron Density (n)

m⁻³

Copper: 8.49 × 10²⁸ m⁻³ | Aluminum: 6.02 × 10²⁸ m⁻³

Cross-Sectional Area (A)

m²

1 mm² = 1 × 10⁻⁶ m² | 1 cm² = 1 × 10⁻⁴ m²

Quick presets:

Result

Enter parameters and click Calculate

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Summary

The Electron Drift Velocity Calculator applies the formula v_d = I / (n · q · A) to find the average net velocity of charge carriers in a conductor. Enter current, free electron density, and wire cross-sectional area to get drift velocity in meters per second. Results include scientific notation for the very small values typical of metal conductors.

How it works

Enter the current flowing through the conductor in amperes.
Enter the free electron (charge carrier) density in electrons per cubic meter.
Enter the cross-sectional area of the conductor in square meters.
The tool applies v_d = I / (n · q · A) using the elementary charge q = 1.602 × 10⁻¹⁹ C.
Drift velocity is displayed in meters per second with scientific notation for very small values.

Use cases

Verify drift velocity calculations for physics homework or lab reports.
Understand why electron drift in copper wire is much slower than the speed of light.
Explore how wire gauge (cross-sectional area) affects electron drift speed.
Compare drift velocities in different conductor materials with varying carrier densities.
Teach the relationship between macroscopic current and microscopic electron motion.
Estimate drift velocity for custom conductor geometries in circuit design.

Frequently Asked Questions

Last updated: 2026-06-19 · Reviewed by Nham Vu