RL Time Constant

\tau = \frac{L}{R}

Time constant for RL circuit current growth or decay.

Variables

Time constant

Characteristic time

Allowed values: greater than 0

Inductance

Circuit inductance

In SI units: kg·m²/(A²·s²)

Allowed values: greater than 0

Resistance

Circuit resistance

In SI units: kg·m²/(A²·s³)

Allowed values: 0 or more

Derivation

From differential equation: I(t) = I₀(1 - e^(-Rt/L)) for growth.

Your notes

0/5000

Check value

Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

L = 2 H (Inductance)
R = 3 Ω (Resistance)

Result: τ = 0.66666667 s

Other electricity & magnetism formulas with the same quantities

Inductor Energy (Electromagnetic Induction) shares Inductance
Ohm's Law (Electric Circuits) shares Resistance
Electric Power (Electric Circuits) shares Resistance
Resistance (Electric Circuits) shares Resistance
Inductive Reactance (AC Circuits) shares Inductance
Impedance (RLC Series) (AC Circuits) shares Resistance

Where this formula is listed

Electricity & Magnetism formulas, under Electromagnetic Induction, alongside Faraday's Law, Magnetic Flux, Motional EMF, Mutual Inductance EMF and Transformer Equation.
In the electricity & magnetism list it comes after Inductor Energy and before Mutual Inductance EMF.
Electricity & Magnetism formula sheet, one of 48 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the RL Time Constant formula?

RL Time Constant is written τ = L/R. Time constant for RL circuit current growth or decay. It belongs to Electricity & Magnetism, under Electromagnetic Induction.

What are the units in τ = L/R?

In SI units, τ is time constant, measured in s; L is inductance, measured in kg·m²/(A²·s²); R is resistance, measured in kg·m²/(A²·s³).

How is the RL Time Constant formula derived?

From differential equation: I(t) = I₀(1 - e^(-Rt/L)) for growth. The result is τ = L/R.