What this calculator does
Electrons in a current-carrying wire move astonishingly slowly. A 10 amp current in a millimetre-square copper wire corresponds to a drift velocity under a millimetre per second, which means an individual electron takes hours to travel a metre.
This surprises people because switching on a light is instantaneous. The resolution is that the electric field propagates at close to light speed and sets every electron in the circuit moving almost at once, even though each one crawls.
The formula
Divide the current by the product of carrier density, cross-sectional area and the elementary charge. Area is converted from square millimetres to square metres first.
| Term | Meaning |
|---|---|
| Drift velocity | The average net velocity of charge carriers along the wire, superimposed on their much faster random motion. |
| Carrier density (n) | The number of free charge carriers per cubic metre. Copper has about 8.5 × 10²⁸. |
| Current density (J) | Current per unit cross-sectional area, in amps per square metre. |
The inputs explained
| Field | What to enter |
|---|---|
| Current (A) | The current in amps. |
| Charge carrier density (copper ≈ 8.5×10²⁸) (/m³) | The free charge carrier density in carriers per cubic metre. Copper is about 8.5 × 10²⁸. |
| Wire cross-section area (mm²) | The wire's cross-sectional area in square millimetres. |
When to use it
Understanding why a light comes on instantly
Comparing the drift velocity with the signal speed resolves an apparent paradox that puzzles most people first meeting it.
Relating current to conductor size
The same current in a thicker wire means a lower drift velocity and current density, which is why thicker cable runs cooler.
Working through a conduction problem
Drift velocity is the usual bridge between the microscopic picture of charge carriers and the macroscopic current.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does conductor size change the drift velocity?
The same current in wires of increasing cross-section.
| Cross-section | Drift velocity (mm/s) | Current density |
|---|---|---|
| 1 mm² | 0.734 mm/s | 1.0000e+7 A/m² |
| 2 mm² | 0.367 mm/s | 5.0000e+6 A/m² |
| 5 mm² | 0.147 mm/s | 2.0000e+6 A/m² |
Questions
If electrons move so slowly, why does a light come on immediately?
Because the electric field that pushes them travels at close to the speed of light. Every electron in the circuit starts moving almost simultaneously, so current flows everywhere at once even though each electron barely creeps.
Is drift velocity the actual speed of electrons?
No, it is the net drift superimposed on random thermal motion. Individual electrons move at hundreds of kilometres per second in random directions; the drift is a tiny systematic bias on top of that.
Why does a thicker wire have a lower drift velocity?
Because the same current is shared among more carriers. More cross-section means more electrons available, so each needs to drift more slowly to carry the same total.
Does drift velocity explain resistance?
Indirectly. Resistance arises because drifting electrons scatter off the lattice, and that scattering is what limits the drift velocity for a given field. The two ideas are closely linked.
For the current, voltage and resistance relationship, see the Ohm's law calculator. For the wire size a current needs, see the wire size calculator.