RL Time Constant

τ = L / R

Quick answer

This calculator solves τ = L / R for Time Constant. With Inductance 10 mH, Resistance 0.47 kΩ, the result is 21.28 µs. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Time Constant (µs)
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Formula

τ = L / R

Description

The RL time constant describes how quickly current builds up or decays in an inductive circuit. After one time constant, the current reaches 63.2% of its final value when energizing, or drops to 36.8% when de-energizing. Notice that unlike the RC circuit where τ = RC, the RL time constant has inductance in the numerator and resistance in the denominator. Higher inductance means slower current changes (more energy stored in the magnetic field), while higher resistance means faster current changes (more energy dissipated per cycle).

Variables

  • τ — Time constant in seconds (s)
  • L — Inductance in henries (H)
  • R — Resistance in ohms (Ω)

Practical Notes

The RL time constant is critical in relay and solenoid driver design. When current through an inductor is suddenly interrupted, the collapsing magnetic field generates a large voltage spike (back-EMF) that can damage switches and transistors. Flyback diodes are used to safely dissipate this stored energy.

Symbols and units

Symbol Meaning Default unit Accepted units
tau Time Constant µs ps, ns, µs, ms, s, min, h
L Inductance mH nH, µH, mH, H
R Resistance Ω mΩ, Ω, kΩ, MΩ

Step by step

  1. 1. What you know: Inductance 10 mH, Resistance 0.47 kΩ
  2. 2. The relation: τ = L / R
  3. 3. Substitute: L = 10 mH, R = 0.47 kΩ
  4. 4. Result: Time Constant = 21.28 µs

Worked examples

Minimum range

Given: Inductance 100 µH, Resistance 1 Ω

Result: Time Constant = 100 µs

Low range

Given: Inductance 1 mH, Resistance 10 Ω

Result: Time Constant = 100 µs

Typical

Given: Inductance 10 mH, Resistance 0.47 kΩ

Result: Time Constant = 21.28 µs

High range

Given: Inductance 100 mH, Resistance 4.7 kΩ

Result: Time Constant = 21.28 µs

Maximum range

Given: Inductance 1 H, Resistance 47 kΩ

Result: Time Constant = 21.28 µs

Solving for each variable

Solve for Time Constant

Inductance 100 µH, Resistance 1 Ω → 100 µs

Solve for Inductance

Time Constant 100 ns, Resistance 1 Ω → 100 nH

Solve for Resistance

Time Constant 100 ns, Inductance 100 µH → 1 kΩ

How Time Constant changes with Inductance

Inductance (input) Time Constant (result)
1 mH 2.128 µs
2.5 mH 5.319 µs
5 mH 10.64 µs
7.5 mH 15.96 µs
10 mH 21.28 µs
15 mH 31.91 µs
20 mH 42.55 µs
40 mH 85.11 µs
70 mH 148.9 µs
100 mH 0.2128 ms

The same result in other units

Unit Value
ns 21280
µs 21.28
ms 0.02128

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Frequently asked questions

How do you calculate RL Time Constant?

Use τ = L / R. With Inductance 10 mH, Resistance 0.47 kΩ, Time Constant works out to 21.28 µs.

What is the formula for RL Time Constant?

The formula is τ = L / R. The RL time constant describes how quickly current builds up or decays in an inductive circuit.

How do you find Inductance when you know the other values?

Rearrange for Inductance: with Time Constant 100 ns, Resistance 1 Ω, Inductance is 100 nH.

How do you find Resistance when you know the other values?

Rearrange for Resistance: with Time Constant 100 ns, Inductance 100 µH, Resistance is 1 kΩ.

What units does RL Time Constant use?

Time Constant is shown in ns, µs, ms. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Inductors formulas →
Inductive Reactance RL Time Constant Inductor Energy Series Inductance Parallel Inductance Inductor Quality Factor Inductor Peak Current Check Mutual Inductance

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