RC / RL Time Constant Calculator

Frequently Asked Questions

What is the RC time constant?

τ = R·C, the time for a charging capacitor to reach about 63% of the supply voltage (or discharge to 37%).

When is a capacitor "fully" charged?

Practically after 5τ it is at over 99% of the final voltage, the usual rule of thumb for settling time.

What does the calculator output?

The time constant and the capacitor voltage at any chosen time during charge or discharge.

Where does this apply?

Timing circuits, debounce filters, RC low/high-pass filters, and oscillator design.

Why does a bigger resistor make an RL circuit faster but an RC circuit slower?

The two formulas place R on opposite sides. For RC, τ = R×C, so more resistance limits the charging current and the capacitor takes longer to reach its final voltage. For RL, τ = L÷R, so more resistance forces the inductor current to settle sooner, shrinking τ. In short, resistance slows charge building up on a capacitor but speeds the decay of current in an inductor.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

The time constant τ sets how fast a first-order circuit charges or decays. For a resistor-capacitor circuit τ = R × C; for a resistor-inductor circuit τ = L ÷ R. After one τ a charging capacitor reaches 63.2% of its final voltage; the general charging curve is V(t) = V₀(1 − e^(−t/τ)) and the decay curve is V(t) = V₀·e^(−t/τ). Solving for the time to reach a fraction f gives t = τ·ln(1 ÷ (1 − f)). This calculator reports τ, the times to reach 50%, 63.2%, 95%, and 99%, a practical 5τ settling time, and the value at any time t you enter. Capacitance is entered in µF and inductance in henries.

Worked Example: An RC Low-Pass Filter

Take R = 10 kΩ and C = 100 µF. Then τ = 10,000 × (100 × 10⁻⁶) = 1.0 s. The capacitor reaches 50% of supply in τ·ln 2 ≈ 0.69 s, 63.2% at exactly 1.0 s, 95% in τ·ln 20 ≈ 3.0 s, and 99% in τ·ln 100 ≈ 4.6 s. Engineers use 5τ (≈ 5 s here, >99.3%) as the rule-of-thumb "fully settled" time. With a 5 V supply, at t = 0.5 s the capacitor has charged to 5×(1 − e^(−0.5)) ≈ 1.97 V.

Real-World Uses

Filters: the -3 dB cutoff frequency of a single-pole filter is fᶜ = 1 ÷ (2πτ), using that stage's own τ - for an RC filter τ = R×C, and for an RL filter τ = L÷R.

Timing & debounce: 555-timer intervals and switch-debounce delays.

Power-on reset: hold a reset line until the supply stabilizes.

Snubbers & flyback: RL time constants govern relay and motor turn-off transients.

Common Mistakes

For RL circuits τ is L ÷ R, not L × R - a larger resistor makes an RL circuit respond faster, the opposite of RC. Forgetting to convert µF to farads (or mH to H) shifts τ by a factor of a million (or a thousand). Assuming the capacitor is "fully charged" after one τ is wrong - it is only 63.2%; allow 5τ for >99%. The charge/decay equations also assume the capacitor starts fully discharged (or charged); a nonzero initial condition needs an offset term.

Limitations & Related

These formulas apply to ideal, linear, first-order circuits with a single R and a single C or L driven by a step input. Real components have tolerance (electrolytic capacitors often ±20%), parasitic resistance and inductance, and temperature drift, so the actual τ varies. Second-order RLC circuits can oscillate and need a different (damped-resonance) treatment entirely. Source and load resistances combine with R and must be included. Related tools include the capacitor-energy and reactance/impedance calculators for AC behavior.

RC / RL Time Constant Calculator

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