RL Time Constant Calculator
An RL circuit contains a resistor and an inductor. When voltage is applied, the current cannot change instantaneously because the inductor opposes changes in current. Instead, the current builds up exponentially with a time constant tau = L / R. After one time constant, the current reaches 63.2% of its steady-state value V/R. This behavior is fundamental to understanding relay switching times, motor startup, solenoid actuation, and power converter inductor design. Enter inductance in henries and resistance in ohms; optionally provide supply voltage and elapsed time to see the current at that moment.
RL circuit formulas
Time constant: tau = L / R
Current at time t: I(t) = (V/R) * (1 - e^(-t / tau))
Final current: I_final = V / R
The time constant tau (in seconds) is the ratio of inductance (henries) to resistance (ohms). At t = tau, I = 0.632 * I_final. At t = 5*tau, the circuit is considered steady state.
RL circuit applications
- Relay coils and solenoids are RL circuits. The time constant determines how quickly they actuate when energized.
- DC motor armatures are RL loads. Startup current is limited by back-EMF, but the initial transient depends on L/R.
- Switching power supply inductors store energy during the on-phase and release it during the off-phase; the time constant affects efficiency.
- RL low-pass filters attenuate high frequencies above the cutoff frequency f_c = R / (2 * pi * L).
Frequently asked questions
What is the RL time constant?
The RL time constant (tau) is tau = L / R, where L is inductance in henries and R is resistance in ohms. It represents the time for the current to rise to 63.2% of its final value when the circuit is energized.
What is the current growth formula in an RL circuit?
When connected to a supply voltage V, the current at time t is I(t) = (V/R) * (1 - e^(-t/tau)). The final steady-state current is V/R (limited only by resistance, since an ideal inductor has zero DC resistance).
How long does it take an RL circuit to fully energize?
After 5 time constants (5 * tau), the current has reached 99.3% of its final value and is considered fully established. After 1 tau it is at 63.2%, after 2 tau it is at 86.5%.
What happens when you disconnect an RL circuit?
The inductor opposes the sudden change in current and generates a large voltage spike (flyback). This is why flyback diodes are used across inductive loads like relay coils and motor windings.
What are typical inductance values in electronics?
Inductors range from nanohenries (nH) in high-frequency RF circuits, through microhenries (uH) in switching power supply inductors, to millihenries (mH) and henries (H) in audio transformers and power line chokes.
Official sources
- NIST: NIST SP 811, Guide for SI Units.
- OpenStax University Physics: RL Circuits, Vol. 2 Ch. 14.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.