ConverterHub

Drift Velocity Calculator

Find how slowly electrons drift in a wire.

Result

3.6715e-4 m/s
3.6715e-1 mm/s

How it is calculated

The tool solves the current equation I = n × A × q × vd for the drift speed: vd = I ÷ (n × A × q). Inputs: I the current in amperes; n the charge-carrier density in carriers per cubic metre (m⁻³); A the cross-sectional area of the conductor in square metres; and q the charge per carrier in coulombs. If q is empty, zero or negative, the elementary charge 1.602176634 × 10⁻¹⁹ C is used. Density and area must be greater than zero. The answer is printed in scientific notation, in m/s and in mm/s, so 3.6715e-4 means 3.6715 × 10⁻⁴. A negative current gives a negative speed, which only indicates the opposite direction. Use SI units throughout: an area of 1 mm² must be typed as 1e-6.

Worked example

A wire carries I = 5 A. Its carrier density is n = 8.5e28 per m³ and its cross-section is 1 mm², typed as A = 1e-6 m². The charge is the default 1.602e-19 C. Step 1: n × A × q = 8.5e28 × 1e-6 × 1.602e-19 = 1.3618e4. Step 2: vd = 5 ÷ 13,618 = 3.6715e-4 m/s, which the tool also gives as 3.6715e-1 mm/s. The carriers therefore drift at about a third of a millimetre per second, which is far slower than the signal in a circuit.

Try this example →

Common mistakes

  • Typing the area in mm² or cm². The formula needs m², so 1 mm² is 1e-6, not 1.
  • Entering the density per cm³ instead of per m³. A value in cm⁻³ must be multiplied by 1,000,000 first.
  • Confusing drift speed with signal speed. Drift speed is the slow average motion of the carriers, not how fast a change in the circuit travels.
  • Reading 3.6715e-4 as 3.6715 or 0.36715. The e-4 means multiply by 10⁻⁴, so the value is 0.00036715 m/s.

About this calculator

The drift velocity is the average speed at which charge carriers (typically free electrons) move through a conductor due to an electric field, given by vd = I / (n·A·q), where I is the current, n is the charge-carrier density (carriers per unit volume), A is the conductor's cross-sectional area, and q is the charge per carrier. It's usually startlingly slow — often on the order of millimetres per second in a copper wire — because electrons zigzag between collisions with the metal's lattice ions far more than they move net distance.

Electrical engineers and physics students use this calculation to distinguish drift velocity from the much faster signal propagation speed (close to the speed of light) — a light bulb turns on almost instantly not because individual electrons race down the wire, but because the electric field that pushes them propagates near light-speed through the whole circuit. It's also used to size conductors and understand current density limits in wiring design.

Was this helpful?

You can pick up to 3 reactions.

Comments

  • Be the first to comment.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators