Drift Velocity Calculator
Find how slowly charge carriers really move through a wire, and how long one takes to travel along it.
🔌 What is Drift Velocity?
Drift velocity is the average velocity that charge carriers, usually electrons, pick up in a material when an electric field is applied. Inside a metal the conduction electrons are always moving, with random thermal speeds of about a million metres per second, but those motions point in every direction and cancel. An electric field adds a small, steady push, and the carriers acquire a slow net motion along the wire. That net motion is the drift, and it is what carries the current. The relation is I = n q A v, so v = I/(nqA).
The idea is useful in many places. Electricians and teachers use it to explain why current in a household cable involves millimetres per second of motion. Materials scientists use it to link mobility to conductivity. Semiconductor engineers use it for the speed of carriers in a transistor channel or a detector, where velocity saturation limits switching. Physicists use it for ions in gas detectors and in electrolytes, and it is a standard test of the free electron model of a metal.
Several misconceptions come up. The drift velocity is not the speed of the signal, which is a large fraction of the speed of light, because the field spreads through the wire almost at once. It is also not the thermal speed, which is millions of times bigger. And the formula depends on the cross sectional area but not on the length, so a long wire and a short wire of the same material carry the same drift speed for the same current. For alternating current the carriers only oscillate by a tiny distance.
This calculator covers two views of the same physics. The first mode uses the current and the wire diameter, with a carrier density you can set from a material preset, and gives the drift speed, the current density, the transit time over a length of wire and a chart against diameter. The second mode uses the mobility and an electric field, v = μE, and gives the conductivity and resistivity that go with it.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — 10 A in a Copper Wire
A 2 mm diameter copper wire carries 10 A, and the wire is 1 m long
Example 2 — A Thin Wire
1 A through a 0.5 mm diameter copper wire, 1 m long
Example 3 — Aluminium Cable Over 10 Metres
15 A in a 3 mm diameter aluminium wire, 10 m long (n = 18.1×1028)
Example 4 — Mobility in Copper
Copper with μ = 0.0044 m²/(V s) in a field of 0.1 V/m, over 1 m
Example 5 — Silver and a Stronger Field
Silver (n = 5.86×1028) with μ = 0.0067 m²/(V s) in 0.5 V/m, over 2 m
Example 6 — A Lightly Doped Semiconductor Wire
1 mA through a 0.1 mm wide channel with n = 1023 m−3, length 0.01 m
❓ Frequently Asked Questions
🔗 Related Calculators
What is the drift velocity formula?
The drift velocity is v = I/(nqA), where I is the current, n is the number of charge carriers per cubic metre, q is the charge of each carrier and A is the cross sectional area. Equivalent forms are v = J/(nq) with current density J, and v = μE with mobility μ.
How fast do electrons move in a copper wire?
Very slowly. A 10 A current in a 2 mm diameter copper wire gives a drift velocity of 2.3456e-4 m/s, about 0.23 mm/s. The random thermal speeds are around a million metres per second, but they cancel out and carry no net current.
Why does a light switch work instantly if electrons drift so slowly?
The electrons that carry the current are already in the wire everywhere. Closing the switch changes the electric field, and that change propagates along the wire at a large fraction of the speed of light, so carriers throughout the circuit start to drift almost together.
How long does an electron take to travel along a wire?
The time is the length divided by the drift speed. For 10 A in a 2 mm copper wire, one metre takes 4263 s, about 71 minutes. Ten metres of 3 mm aluminium wire at 15 A takes about 38 hours.
What is the free electron density of copper?
The accepted free electron density of copper is 8.47e28 per cubic metre, about one conduction electron per atom. Silver is 5.86e28 and aluminium is 18.1e28, because each aluminium atom gives three. These values come from the standard free electron model tables.
What is electron mobility and how does it relate to drift speed?
Mobility μ is the drift velocity per unit electric field, so v = μE, in units of m²/(V s). In copper at room temperature μ is about 0.0044 m²/(V s). Conductivity then follows as σ = n e μ, which gives about 5.97e7 S/m.
Does a thinner wire make electrons faster?
Yes. For a fixed current the drift speed scales as 1/A, so it scales as one over the diameter squared. A 1 A current in a 0.5 mm copper wire gives 3.7530e-4 m/s, which is 1.6 times faster than 10 A in a 2 mm wire.
Does drift velocity depend on the length of the wire?
No. The drift speed depends on the current, the cross section and the carrier density, but not on the length. The length only matters for the transit time, which is the length divided by the drift speed.
How does drift velocity differ in a semiconductor?
A semiconductor has many orders of magnitude fewer carriers, so the same current density needs much faster drift. With n = 1e23 per cubic metre, 1 mA in a 0.1 mm wire gives 7.95 m/s, compared with micrometres per second for copper.
Is the drift velocity of alternating current the same?
With AC the carriers oscillate back and forth by a tiny distance instead of drifting along. For 50 Hz current of a few amperes in a copper wire the amplitude is only a fraction of a millimetre, and carriers do not travel along the wire.