Carrier Drift Velocity
vd = I / (n · A · q)
Quick answer
This calculator solves vd = I / (n × A × q) for Drift Velocity. With Current 2 A, Carrier Density 1 × 10¹⁷ 1/cm³, Cross Section 10 mm², Carrier Charge 100 mC, the result is 2 × 10⁻¹⁴ mm/s. It solves in 5 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Drift velocity is the average speed at which charge carriers move along a conductor when carrying current. It is surprisingly slow—often well under a millimetre per second—even though the electrical signal itself travels near the speed of light. The huge number of carriers makes a large current possible at this tiny drift speed.
Variables
- vd — Drift velocity (m/s)
- I — Current (A)
- n — Carrier density (1/m³)
- A — Conductor cross-sectional area (m²)
- q — Carrier charge (C)
Practical Notes
In copper carrying a typical current density, vd is on the order of 0.1 mm/s. The current density J = n·q·vd ties drift velocity to ampacity and electromigration limits.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| vd | Drift Velocity | mm/s | mm/s, m/s, km/s |
| I | Current | A | pA, nA, µA, mA, A, kA |
| n | Carrier Density | 1/m³ | 1/m³, 1/cm³ |
| A | Cross Section | mm² | mm², cm², m² |
| q | Carrier Charge | C | pC, nC, µC, mC, C |
Step by step
- 1. What you know: Current 2 A, Carrier Density 1 × 10¹⁷ 1/cm³, Cross Section 10 mm², Carrier Charge 100 mC
- 2. The relation: vd = I / (n × A × q)
- 3. Substitute: I = 2 A, n = 1 × 10¹⁷ 1/cm³, A = 10 mm², q = 100 mC
- 4. Result: Drift Velocity = 2 × 10⁻¹⁴ mm/s
Worked examples
Minimum range
Given: Current 2 mA, Carrier Density 1 × 10¹³ 1/cm³, Cross Section 0.1 mm², Carrier Charge 100 µC
Result: Drift Velocity = 2 × 10⁻⁸ mm/s
Low range
Given: Current 20 mA, Carrier Density 1 × 10¹⁴ 1/cm³, Cross Section 1 mm², Carrier Charge 1 mC
Result: Drift Velocity = 2 × 10⁻¹⁰ mm/s
Typical
Given: Current 2 A, Carrier Density 1 × 10¹⁷ 1/cm³, Cross Section 10 mm², Carrier Charge 100 mC
Result: Drift Velocity = 2 × 10⁻¹⁴ mm/s
High range
Given: Current 100 A, Carrier Density 1 × 10²⁰ 1/cm³, Cross Section 1 cm², Carrier Charge 1 C
Result: Drift Velocity = 1 × 10⁻¹⁷ mm/s
Maximum range
Given: Current 1 kA, Carrier Density 1 × 10²¹ 1/cm³, Cross Section 10 cm², Carrier Charge 10 C
Result: Drift Velocity = 1 × 10⁻¹⁹ mm/s
Solving for each variable
Solve for Drift Velocity
Current 2 mA, Carrier Density 1 × 10¹³ 1/cm³, Cross Section 0.1 mm², Carrier Charge 100 µC → 2 × 10⁻⁸ mm/s
Solve for Current
Drift Velocity 0.1 mm/s, Carrier Density 1 × 10¹³ 1/cm³, Cross Section 0.1 mm², Carrier Charge 100 µC → 10 kA
Solve for Carrier Density
Drift Velocity 0.1 mm/s, Current 2 mA, Cross Section 0.1 mm², Carrier Charge 100 µC → 2 × 10⁶ 1/cm³
Solve for Cross Section
Drift Velocity 0.1 mm/s, Current 2 mA, Carrier Density 1 × 10¹³ 1/cm³, Carrier Charge 100 µC → 2 × 10⁻⁸ mm²
Solve for Carrier Charge
Drift Velocity 0.1 mm/s, Current 2 mA, Carrier Density 1 × 10¹³ 1/cm³, Cross Section 0.1 mm² → 20 pC
How Drift Velocity changes with Current
| Current (input) | Drift Velocity (result) |
|---|---|
| 0.2 A | 2 × 10⁻¹⁵ mm/s |
| 0.5 A | 5 × 10⁻¹⁵ mm/s |
| 1 A | 1 × 10⁻¹⁴ mm/s |
| 1.5 A | 1.5 × 10⁻¹⁴ mm/s |
| 2 A | 2 × 10⁻¹⁴ mm/s |
| 3 A | 3 × 10⁻¹⁴ mm/s |
| 4 A | 4 × 10⁻¹⁴ mm/s |
| 8 A | 8 × 10⁻¹⁴ mm/s |
| 14 A | 1.4 × 10⁻¹³ mm/s |
| 20 A | 2 × 10⁻¹³ mm/s |
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<p><a href="https://vbatpower.com/formulas/drift-velocity/">Carrier Drift Velocity</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Carrier Drift Velocity?
Use vd = I / (n × A × q). With Current 2 A, Carrier Density 1 × 10¹⁷ 1/cm³, Cross Section 10 mm², Carrier Charge 100 mC, Drift Velocity works out to 2 × 10⁻¹⁴ mm/s.
What is the formula for Carrier Drift Velocity?
The formula is vd = I / (n × A × q). Drift velocity is the average speed at which charge carriers move along a conductor when carrying current.
How do you find Current when you know the other values?
Rearrange for Current: with Drift Velocity 0.1 mm/s, Carrier Density 1 × 10¹³ 1/cm³, Cross Section 0.1 mm², Carrier Charge 100 µC, Current is 10 kA.
How do you find Carrier Density when you know the other values?
Rearrange for Carrier Density: with Drift Velocity 0.1 mm/s, Current 2 mA, Cross Section 0.1 mm², Carrier Charge 100 µC, Carrier Density is 2 × 10⁶ 1/cm³.
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