HesapHanem

RL Time Constant Calculator

Find the time constant of an RL circuit.

How it is calculated

In a series RL circuit the time constant is τ = L / R, where L is the inductance in henries and R the resistance in ohms; the result is in seconds. The tool also shows it in milliseconds, τ × 1000. After one τ the current has risen to about 63% of its final value when a voltage is applied, and after about five τ it is practically at its final value. Resistance must be above zero; inductance may be zero or more. The seconds value is shown with six decimals and the milliseconds value with four, so very small constants are not rounded away. R is the total series resistance, including the coil's own winding resistance.

Worked example

A coil of L = 0.05 H (50 mH) is in series with R = 100 Ω. τ = 0.05 / 100 = 0.0005 s. In milliseconds that is 0.0005 × 1000 = 0.5 ms. The time constant is 0.000500 s, or 0.5000 ms. The current needs roughly 5 × 0.5 = 2.5 ms to settle close to its final value.

Try this example →

Common mistakes

  • Entering inductance in millihenries (50) while the field expects henries (0.05), making τ a thousand times too large.
  • Entering resistance in kilohms without converting to ohms.
  • Forgetting the coil's own resistance or the source resistance, which add to R in the circuit.
  • Using this formula for an RC circuit. That one is τ = R × C, not L / R.
  • Expecting the current to reach its final value after exactly one τ; one τ is only about 63%.

About this calculator

The time constant of an RL (resistor-inductor) circuit is τ = L/R, where L is inductance and R is resistance. It defines how quickly current rises or decays in the circuit: after one time constant, current reaches about 63.2% of its final value; after five time constants, it's essentially fully settled (>99%) — the same exponential charging pattern seen in RC circuits, but governed by inductance instead of capacitance.

Electrical engineers use the RL time constant to predict switching behavior in circuits with inductive loads — relays, solenoids, motor windings, and transformer coils — where a sudden current interruption can generate a damaging voltage spike, which is why techniques like flyback diodes are sized with this time constant in mind.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    The time constant helps when choosing a switching rate for an inductive load. If you drive a coil with a PWM signal whose period is much shorter than τ, the current stays close to its average and ripples little. With τ of 0.5 ms, a 20 kHz signal has a 50 µs period, ten times shorter. Waiting 3τ gets you to about 95% of the final current. What load are you driving?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators