Circuit Analysis & FundamentalsDesign workbench
RC / RL Time Constant Calculator
Time constant τ of an RC or RL circuit, the fraction charged/discharged at any time t, and the time to reach a target percentage — with a live charge/discharge curve.
About this calculator
A first-order RC or RL circuit responds to a step with a single exponential governed by one number: the time constant τ. For a resistor–capacitor circuit τ = RC; for a resistor–inductor circuit τ = L/R. One time constant is the time to move about 63.2% of the way to the final value; after roughly five time constants (5τ) the transient is over — within about 0.7% of steady state.
Enter the circuit type and its component values and the calculator returns τ, the fraction charged or discharged at a time t you choose, and the time needed to reach any target percentage. The plot draws the full exponential from 0 to 5τ with a marker at your chosen time, so the shape and the number stay together as you sweep t.
This is the workhorse behind timing and settling estimates: how long a capacitor takes to charge through a resistor, how quickly an RC snubber or debounce settles, how fast an inductor's current builds when a switch closes. The same τ describes charging (rising toward the final value as 1 − e^(−t/τ)) and discharging (decaying as e^(−t/τ)); only the direction differs. Because the response is exponential, reaching the last few percent takes disproportionately long — getting to 99% needs about 4.6τ, nearly five times as long as the first 63%.
Design notes & common mistakes
- τ = RC for RC, τ = L/R for RL — note the inductor puts R in the DENOMINATOR, so more resistance makes an RL circuit FASTER but an RC circuit slower.
- Rules of thumb: 1τ → 63%, 2τ → 86%, 3τ → 95%, 5τ → 99.3%. Engineers call it 'settled' at 5τ.
- The exponential never truly reaches the final value; specify settling to a percentage (e.g. 99%) rather than 'fully charged'.
- Same τ governs charging and discharging — only the direction (rise vs decay) changes.
Assumptions
- Ideal first-order circuit: a single resistor with a single capacitor (RC) or inductor (RL), stepped from one steady state to another.
- The capacitor/inductor is ideal (no ESR/ESL or leakage) and the source is ideal.
- Fractions are of the final value (charging) or initial value (discharging); the actual voltages/currents scale with your source and initial conditions.
- Second-order effects (any second reactive element) are out of scope — that is an RLC problem.
When to use this calculator
Appropriate for
- Estimating charge/discharge or settling time of an RC or RL circuit
- Sizing an RC delay, debounce, or snubber to a target settling time
- Teaching the exponential first-order response and the 63%/5τ rules
Not suitable for
- Second-order (RLC) circuits with ringing or resonance
- Absolute voltage/current values without specifying the source and initial state
- Circuits where component parasitics (ESR/ESL) dominate the timing
What this calculator does not cover
- First-order (single time constant) only — a second reactive element makes it an RLC (second-order) circuit with oscillation, not covered here.
- Results are fractions of the final/initial value; absolute voltages and currents depend on your source and initial conditions.
- Ideal components — ESR, ESL, dielectric leakage, and inductor winding resistance are not modeled.
- Assumes a clean step input; ramped or repetitive inputs need superposition or a full transient analysis.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
What is the time constant of an RC or RL circuit?
For an RC circuit the time constant is τ = R × C; for an RL circuit it is τ = L / R. It is the time to move about 63.2% of the way to the final value after a step, and the transient is essentially complete after about five time constants (5τ).
How long until a capacitor is 'fully' charged?
Strictly, never — the exponential approaches the final value asymptotically. In practice engineers treat it as settled after 5τ, where it is within about 0.7% of the final value. Reaching 99% takes about 4.6τ, and 99.9% about 6.9τ.
Why does more resistance slow an RC circuit but speed up an RL circuit?
Because R appears differently: τ = RC puts resistance in the numerator, so larger R means a longer time constant; τ = L/R puts resistance in the denominator, so larger R means a shorter time constant. Physically, more resistance limits capacitor charging current but dissipates inductor energy faster.
References
- Nilsson, J. & Riedel, S., Electric Circuits, 11th ed. (first-order RC and RL transients)
- Irwin, J. D., Basic Engineering Circuit Analysis, 11th ed. (natural and step response)
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