RL Time Constant
The RL time constant τ = L/R determines how quickly current rises or falls in an inductive circuit. It is the inductor equivalent of the RC time constant. Larger inductance or smaller resistance means a longer time constant.
L — Inductance. More L = more energy storage = slower response.
τ = L/R — Time constant. Current reaches 63.2% of final value in 1τ, 95% in 3τ, 99.3% in 5τ.
fc — Corner frequency. The −3 dB point of an RL filter. fc = 1/(2πτ).
RL Time Constant Calculator
The RL time constant τ = L/R determines how quickly current changes in an inductive circuit. It is the inductor counterpart of the RC time constant used with capacitors. This calculator is a triangle solver: enter any two of resistance, inductance, or time constant and it finds the third, plus the discharge milestones and the corner frequency for filter design.
The RL Time Constant
τ in seconds, L in henries, R in ohms
After 1τ: current at 63.2% of final
After 3τ: current at 95.0%
After 5τ: current at 99.3% (fully settled)
Corner frequency: fc = 1 / (2πτ)
Unlike the RC time constant where τ = RC (increasing R slows the response), in an RL circuit increasing R speeds up the response. More resistance dissipates the stored magnetic energy faster, so the current settles sooner. This is the fundamental difference between capacitive and inductive time constants. For the full current vs time calculation, see the Inductor Current Calculator.
RL vs RC: Key Differences
RL circuit: τ = L / R. Current rises/falls. Increasing R makes it faster. Energy stored in magnetic field (½LI²).
Both use the same exponential math. The roles of voltage and current are swapped. For the RC equivalent, see the RC Time Constant Calculator.
Relay Coil (100Ω / 50mH)
5τ = 2.5 ms to fully energise
fc = 1 / (2π × 0.0005) = 318 Hz
The relay coil reaches full current in 2.5 ms. This is the minimum actuation time assuming the relay's mechanical pull-in happens at ~63% of final current (1τ = 0.5 ms plus mechanical delay). The 318 Hz corner frequency means the coil passes DC and low-frequency signals but attenuates anything above ~300 Hz.
SMPS Inductor (0.1Ω / 47µH)
5τ = 2.35 ms
fc = 1 / (2π × 0.000470) = 339 Hz
At 100 kHz switching frequency, each on-time (~5 µs) is just 1% of the time constant. The inductor current ramps nearly linearly each cycle — this is normal continuous conduction mode (CCM) operation. The very low DCR (0.1 Ω) means the time constant is long, which is exactly what you want for smooth current delivery.
EMI Filter (50Ω / 10mH)
fc = 1 / (2π × 0.0002) = 796 Hz
This RL low-pass filter passes frequencies below ~800 Hz and attenuates higher frequencies at 20 dB/decade. Used as a simple EMI filter on power supply inputs or signal lines. For sharper filtering, combine with a capacitor to make an LC filter.
Reverse Solve: Find L for 1ms τ at 50Ω
fc = 1 / (2π × 0.001) = 159 Hz
If you need a 1 ms time constant with 50 Ω total resistance, you need a 50 mH inductor. The reverse solve mode answers this directly — enter the target τ and the circuit resistance, and the calculator finds the required inductance. For the energy this inductor stores at full current, see the Inductor Energy Calculator.
Corner Frequency and Filters
The corner frequency fc = 1/(2πτ) = R/(2πL) is the −3 dB point of an RL filter. Below fc the inductor passes current freely (low impedance). Above fc the inductor increasingly blocks current (impedance rises with frequency). This makes RL circuits natural low-pass filters for current, analogous to RC low-pass filters for voltage. For the full impedance calculation at any frequency, see the Inductive Reactance Calculator.
Frequently Asked Questions
Last updated: March 2026