LR Time Constant and Settling Calculator
Calculate LR time constant from inductance and resistance, solve related values, or build a generic first-order settling table from a known time constant.
Input
Calculate an LR time constant or use a known time constant to create a generic first-order settling table.
Inputs accept engineering notation such as 10m for 10 mH, 250u for 250 us, and 4k7 for 4.7 kOhm.
Result
A first-order response is about 63.2% settled after one time constant and about 99.3% settled after five time constants.
First-order settling table
Inductor current does not change instantly
An LR time constant gives a first-pass estimate for relay coils, solenoids, inductive loads, current ramp behaviour, and generic first-order settling checks.
LR current ramp
Use tau equals inductance divided by resistance for simple first-order inductor current settling estimates.
Generic settling
Use a known time constant to generate 1 tau to 5 tau settling percentages without assuming a specific RC or LR circuit.
Complementary RC tools
Use the existing RC and capacitor-discharge calculators when you need voltage at time or time to threshold.
Equations, assumptions, and limits
This calculator models ideal first-order LR behaviour. Real inductive loads can include winding resistance, saturation, core loss, driver resistance, clamp paths, and switching transients.
LR time constant
For an ideal series LR circuit, tau equals L divided by R.
Settling percentage
A first-order response settles by 1 - e^-n after n time constants.
Not a clamp model
Flyback clamps, TVS devices, freewheel diodes, and active drivers change the transient shape and need separate review.
Related calculators and next checks
RC time constant calculator
Use for RC charge and discharge voltage at a selected time.
Capacitor discharge calculator
Use for discharge time to a target voltage through an effective resistance.
Inductor energy calculator
Check the magnetic energy associated with the inductor current.
Engineering reference
Equations, assumptions, and design guidance
Solves ideal LR time-constant relationships and reports first-order settling from one to five time constants.
Equations and variables
tau = L / Ry(t) = 1 - exp(-t / tau)- L
- Inductance (H)
- R
- Total series resistance (ohm)
- tau
- Time constant (s)
Assumptions and limitations
Assumptions
- Inductance and resistance remain constant.
- The source and switching transition are ideal.
Limitations
- Winding resistance, source resistance, saturation, core loss, parasitic capacitance, and switching clamps require separate review.
Worked example and design use
10 mH with 10 ohm series resistance
Inputs: L = 10 mH, R = 10 ohm
Outputs: tau = 1 ms, The rising response reaches about 63.2% after one tau
Design guidance
- Include all effective series resistance when estimating a real circuit time constant.
- Check saturation and switching voltage when interrupting inductor current.