Hong Life CalculatorsUnderstanding the drift velocity calculator — concept and principle
When current flows in a wire, the free electrons move along it surprisingly slowly. This calculator finds that average drift velocity from the current, wire diameter and free-electron density, and also gives the current density and how long an electron takes to drift one metre.
How it is calculated
- Current I = n q A vd, so drift velocity vd = I ÷ (n q A).
- n: free charge carriers per m³; q = e = 1.602 × 10⁻¹⁹ C; A = π d² ÷ 4.
- For copper, one free electron per atom gives n ≈ 8.34 × 10²⁸ per m³ (from density 8.80 g/cm³ and molar mass 63.54 g/mol, as in the OpenStax example).
- Current density J = I ÷ A; time to drift 1 m = 1 ÷ vd.
The principle
Current is the charge passing a cross-section each second. That charge is carried by enormous numbers of electrons, so each one need only move slowly. Electrons actually move randomly at high speed, bouncing off the lattice; the field adds a tiny average drift on top. A lamp lights at once because the electric field travels along the wire at nearly the speed of light, pushing all electrons at the same time.
Worked example
Default inputs: 20 A, diameter 2.053 mm (12-gauge wire), n = 8.34 × 10²⁸ per m³.
- A = π ÷ 4 × 2.053² ≈ 3.3103 mm² = 3.3103 × 10⁻⁶ m².
- vd = 20 ÷ (8.34 × 10²⁸ × 1.602 × 10⁻¹⁹ × 3.3103 × 10⁻⁶) ≈ 4.522 × 10⁻⁴ m/s = 0.4522 mm/s.
- Current density = 20 ÷ 3.3103 ≈ 6.042 A/mm².
- Time to drift 1 m = 1 ÷ 0.0004522 ≈ 2,211 s ≈ 0.61 hours.
| Wire diameter (mm) | Drift speed (mm/s) |
|---|---|
| 0.513 | 7.2345 |
| 1.03 | 1.8086 |
| 1.54 | 0.8038 |
| 2.05 | 0.4522 |
| 2.57 | 0.2894 |
| 3.08 | 0.201 |
| 4.11 | 0.113 |
How to read the result
Drift speeds in household wiring are typically well under a millimetre per second. Thinner wires or higher currents raise the drift speed and current density, which also raises heating; wire sizing rules limit current for that reason. In semiconductors, with far fewer carriers, drift speeds are much higher for the same current density.
Common mistakes
- Using the electrons' random thermal speed instead of drift speed.
- Using diameter as radius in the area formula.
- Using n per cm³ instead of per m³.
- Thinking the drift speed is how fast signals travel.
Frequently asked questions
How fast do electrons move in a wire?
Their average drift is typically a fraction of a millimetre per second, even at high currents.
Why does a light turn on instantly?
The electric field propagates at nearly the speed of light, moving all the electrons together.
What is n for copper?
About 8.5 × 10²⁸ free electrons per m³; the OpenStax example uses 8.34 × 10²⁸.
Sources: OpenStax, University Physics Volume 2, Section 9.1 Electrical Current (drift velocity example) · Halliday, Resnick & Walker, Fundamentals of Physics (current and drift speed)