RL Time Constant Calculator
This RL Time Constant Calculator determines the current response of a series resistor-inductor circuit, including τ, 1τ, 3τ, 5τ, final current, and ideal rise and decay reference values.
Reverse modes solve the inductance or resistance required for a target time constant. The tool supports relay, solenoid, choke, switching, transient, and general magnetic-circuit analysis.
The model assumes constant inductance and resistance. Include coil resistance, source impedance, saturation, core loss, switching behavior, and protection components in a final design.
Engineering tool
RL Time Constant Calculator
Calculate RL time constant and current response, or solve inductance or resistance for a target time constant.
Effective circuit inductance.
Total series resistance in the current path.
Applied DC step used to calculate final current.
Time constant (τ)
100 µs
τ = L / R
Result console
- Time constant (τ)
- 100µs
- Inductance (L)
- 10mH
- Resistance (R)
- 100Ω
- Final current
- 50mA
Current Rise and Decay Reference
Ideal step-response current using the entered supply voltage. Decay values use the final current as the initial current.
| Reference | Time | Rise level | Rising current | Decaying current |
|---|---|---|---|---|
| 1τ | 100 µs | 63.2% | 31.606 mA | 18.394 mA (36.8%) |
| 3τ | 300 µs | 95% | 47.511 mA | 2.489 mA (5%) |
| 5τ | 500 µs | 99.3% | 49.663 mA | 0.337 mA (0.7%) |
RL Circuit and Current Response
A voltage step drives current through R and L in series. Current approaches V/R exponentially rather than changing instantaneously.
Formula reference
RL Time Constant Formulas
Higher inductance slows current change, while higher resistance reduces the time constant and final current. Rise and decay follow complementary exponential functions.
Time constant: τ = L / RFinal current: I_final = V / RCurrent rise: I(t) = I_final × (1 - e^(-t/τ))Current decay: I(t) = I_initial × e^(-t/τ)Reverse: L = τR and R = L / τVariable definitions
- τ
- RL time constant in seconds (s)
- L
- Inductance in henries (H)
- R
- Total series resistance in ohms (Ω)
- V
- Applied voltage in volts (V)
- I_final
- Steady-state current in amperes (A)
How to Use This Calculator
- Select time constant, inductance, or resistance mode.
- Enter the known circuit values and choose their engineering units.
- For current references, enter the applied voltage and calculate τ and V/R.
- Compare ideal timing with coil resistance, source impedance, saturation, and switching protection.
Worked Example
10 mH, 100 Ω, and 5 V
L = 10 mH = 0.01 H
R = 100 Ω and V = 5 V
τ = L / R = 0.01 / 100 = 0.0001 s
τ = 100 µs
I_final = V / R = 5 / 100 = 0.05 A = 50 mA
Engineering Notes
Current response timing
RL time constant describes how quickly current rises or decays in an inductor circuit.
Inductance slows response
Higher inductance increases τ and makes the current change more slowly for the same resistance.
Resistance speeds response
Higher total resistance decreases τ, although it also reduces the final V/R current.
Current cannot jump instantly
Inductors oppose sudden current changes by generating a voltage across their terminals.
Flyback protection matters
Interrupting current can generate a high flyback voltage. Select a diode, clamp, or snubber appropriate for the required release speed and energy.
Common Mistakes
- Ignoring the inductor winding resistance and source output resistance.
- Using mH or µs values directly without SI conversion.
- Assuming the ideal V/R current is reached immediately.
- Applying constant inductance beyond the core saturation current.
- Opening the current path without suitable flyback protection.
Support reference
FAQ
What is an RL time constant?
An RL time constant describes how quickly current changes in a first-order resistor-inductor circuit. After one time constant, rising current reaches about 63.2% of its final value.
How do you calculate RL time constant?
Use τ = L / R, with inductance in henries and total series resistance in ohms. The result is the time constant in seconds.
Why does an inductor current rise slowly?
An inductor generates a voltage that opposes changes in current. This back electromotive force limits the initial rate of current rise until the circuit approaches its DC steady state.
What happens when current through an inductor is interrupted?
The inductor generates whatever voltage is necessary, within physical limits, to keep current flowing. A flyback diode, clamp, or snubber is commonly required to control the resulting voltage spike.
How is RL time constant different from RC time constant?
RL timing describes inductor current with τ = L / R. RC timing describes capacitor voltage with τ = RC. Both produce first-order exponential rise and decay responses.
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Browse the Inductors calculator category or review related material in the Engineering Reference Center.
This calculator models an ideal first-order RL circuit. Verify winding and source resistance, saturation, core loss, temperature, voltage and current ratings, switching transients, and flyback protection before production use.