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RL Time Constant Calculator

Estimate how current rises after a constant-voltage step in an ideal series resistor-inductor circuit. Enter total series resistance, including any resistance you intentionally include in the model. Inductance is entered in millihenries. The current starts at zero and approaches the stated steady-state value. A larger inductance slows the response; a larger resistance reduces the time constant as well as the final current at a fixed supply voltage.

Enter every field, including explicit zeros when permitted. Decimal and scientific notation are accepted; commas, fractions and blanks are rejected. Each input must be finite and no larger than 1 billion in absolute value. Observe the units and positive-value requirements below.

Time constant τ (s)0.01
Five time constants (s)0.05
Steady-state current (A)1.2
Current at time t (A)0.7585446706

How to use this calculator

  1. Match your inputs to the stated circuit model and field labels.
  2. Convert your quantities to the units printed next to each field.
  3. Select Calculate, or press Enter, and read the labeled results.

Formula and method

τ = L/R; I∞ = V/R; current from zero after a voltage step: I(t) = I∞(1 − e⁻ᵗ/τ).

The calculation runs in your browser. After changing an input, select Calculate again. Invalid inputs or undefined mathematical conditions hide the previous result so it cannot be mistaken for an answer to the new values.

Worked example

For 100 mH, 10 Ω and 12 V, τ = 0.01 s and I∞ = 1.2 A. At t = 0.01 s, current is approximately 0.7585446706 A.

Limitations and safety

Ideal-component calculation only. Component tolerance, heating, parasitic effects and frequency limits are not modeled. This output does not establish component ratings, wiring compliance or a safe circuit design. Have consequential designs checked by a qualified professional; do not use this tool as instructions for working on energized equipment. The model assumes zero initial current, constant components and no magnetic saturation. It does not model switching spikes or protective devices.

The fields accept signed numerical input, but positive-only component values and nonnegative time or frequency requirements are enforced by the calculation. Read each error message before changing a value. Results use floating-point arithmetic and are shown to approximately 10 significant digits; component tolerances generally do not justify using all those digits in a physical design.

Frequently asked questions

Does the resistance include the coil winding?

Enter the total series resistance for your chosen ideal model. The calculator does not infer winding or source resistance automatically.

Why are my units important?

The calculator uses exactly the units printed in the input labels. For example, a micro-unit is one millionth of a base unit, and a milli-unit is one thousandth. Entering a base-unit value into a prefixed-unit field changes the meaning of the input.

Does the answer establish a safe component rating?

No. The formula evaluates an ideal model. Ratings, tolerances, transients, installation requirements and environmental limits need a separate design assessment.

Review notes and reference

Reviewed October 3, 2026. The default worked example and an additional boundary or scaling check were tested against expected values. Validation checks included blanks, nonnumeric text and inputs outside the supported range. OpenStax University Physics formula reference provides the circuit theory behind this model. The text and worked example on this page are original.

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