This RC circuit calculator works out a resistor-capacitor circuit’s timing: the time constant τ = RC, the capacitor’s voltage and the circuit current at any moment during charging or discharging, and the energy stored at full charge. RC timing is how electronics measures out delays, filters signals and flashes camera strobes — one resistor, one capacitor, and an exponential that runs a surprising fraction of the modern world.

Time constant τ = RC –
Capacitor voltage at t –
Circuit current at t –
Energy at full charge (½CVs²) –
Practically full / empty by –

Charging: V(t) = Vs(1 − e^(−t/τ)). Discharging: V(t) = Vs·e^(−t/τ). Current follows the resistor’s voltage in both cases. At t = τ the capacitor is 63.2% charged (or 36.8% remaining on discharge); at 5τ the transient is, for all practical purposes, over.

The Time Constant: One Number That Sets the Clock

τ = R × C, in seconds when R is in ohms and C in farads, is the entire personality of an RC circuit. It says how fast the capacitor charges toward the supply (or empties toward zero), and it does so exponentially: each time constant that passes closes 63.2% of the remaining gap. After 1τ you’re at 63.2%, 2τ 86.5%, 3τ 95.0%, 4τ 98.2%, 5τ 99.3% — the familiar asymptotic creep that means “fully charged” is a polite fiction defined as 5τ. The calculator evaluates the exact curve at your chosen instant and reports voltage, current and percentage, so a design question like “how long until the comparator trips at 6 V on a 9 V supply?” becomes one substitution: t = −τ·ln(1 − 6/9) ≈ 1.10τ.

The current tells the complementary story: it starts maximum (the empty capacitor looks like a short circuit: I₀ = Vs/R) and decays with the same exponential as the voltage grows. Energy, meanwhile, accumulates as ½CV² — and hides a famous subtlety: charging a capacitor through a resistor from a fixed supply always dissipates exactly as much energy in the resistor (½CVs²) as ends up stored, whatever the resistance value. R sets only how fast the transfer happens, never the 50% toll. Discharge pays no such toll on paper — the stored ½CV² simply becomes heat in the resistor (or light, in a camera flash — an RC discharge with a very glamorous resistor).

Worked Examples (Verified)

  • 10 kΩ × 100 µF on 9 V (defaults): τ = 1.00 s exactly — the cleanest teaching example in electronics. At t = 1 s (1τ) the capacitor sits at 5.69 V (63.2%), current has fallen to 0.331 mA from its 0.9 mA start, full-charge energy is 4.05 mJ, and by 5 s the show is over.
  • 555-timer heartbeat: the classic timer’s period is set by RC charging between ⅓ and ⅔ of supply — the ln(2)·(R₁+2R₂)C formula is this page’s exponential read at two thresholds. Every blinking LED kit is an RC curve with a comparator watching it.
  • Debounce reality check: a 100 nF capacitor with 10 kΩ gives τ = 1 ms — long enough to swallow a switch’s mechanical chatter, short enough for a human to never notice. The same equation debounces keyboards and delays airbag sensors (longer τ); only the magnitudes move.

Where RC Timing Works for a Living

  • Low-pass filters: the same τ becomes a frequency: fc = 1/(2πRC). Audio tone controls, anti-alias filters and sensor smoothing are RC circuits read in the frequency domain instead of the time domain (our Resonance page’s gentler cousin).
  • Power supplies: reservoir capacitors charge and droop between mains peaks — ripple voltage is an RC (really C·load) discharge curve sampled 100–120 times a second.
  • Wiper delays, porch-light timers, watchdog circuits: a capacitor charging toward a threshold is the cheapest clock in electronics; τ is its gear ratio.
  • Snubbers and soft-starts: an RC across a switch stretches voltage rise time, taming sparks, EMI and inrush — deliberately wasting a little time to save the contacts.
  • Integrators and differentiators: read the resistor’s voltage instead of the capacitor’s, at t ≪ τ, and the same circuit approximates calculus operations — the analog computer’s workhorse.

RC Discipline: The Real-World Deviations

  • Capacitor tolerance is wide: electrolytics are commonly ±20% (some −20/+80%), so τ is a range, not a point — precision timing uses film or C0G ceramics and 1% resistors.
  • Leakage and ESR: real capacitors self-discharge (a parallel leak resistance) and resist fast current (series ESR) — millisecond timing barely notices; hour-long timers fail entirely on leakage.
  • Source resistance counts: the R in τ is the total resistance around the loop, including the supply’s output impedance and switch resistance — on low-R designs they’re part of the plan, not noise.
  • Dielectric absorption: a “discharged” big electrolytic can creep back to a surprising voltage as its dielectric relaxes — why technicians short stored capacitors and don’t trust a single discharge.
  • Voltage rating derating: run electrolytics at ≤80% of rated voltage for longevity; the capacitor in a timing circuit that sees full supply forever ages accordingly.

Related Tools

Frequently Asked Questions

How do you calculate the RC time constant?

Multiply resistance by capacitance: τ = R × C. With R in ohms and C in farads the result is seconds. 10 kΩ × 100 µF = 10,000 × 0.0001 = 1.0 s. The capacitor reaches 63.2% of the supply in one time constant, 95% in three, and is treated as fully charged at five. This calculator evaluates the whole curve — voltage, current and percentage at any time you enter, for both charging and discharging.

Why 63.2% at one time constant?

Because the charging curve is V = Vs(1 − e^(−t/τ)) and at t = τ the exponential term is e⁻¹ = 0.368 — so the capacitor has closed 1 − 0.368 = 63.2% of the gap. The number is just 1 − 1/e wearing a lab coat. Symmetrically, on discharge 36.8% of the voltage remains at t = τ: the exponential’s memoryless property means every τ window removes the same fraction of whatever is left.

How long until an RC circuit is fully charged?

Mathematically, never — the exponential approaches the supply asymptotically. Practically, engineers call it done at 5τ (99.3%), and most threshold circuits trip long before: a logic input sees a valid high around 70% (≈1.2τ); a comparator set at ⅔ supply trips at τ·ln(3) ≈ 1.10τ. Design with the threshold your circuit actually uses, computed as t = −τ·ln(1 − Vtrip/Vs).

What happens to the current in an RC circuit?

It starts at its maximum and decays exponentially with the same τ: charging, I(t) = (Vs/R)·e^(−t/τ) — at the first instant the empty capacitor behaves like a wire, and as it fills, its counter-voltage chokes the current to zero. On discharge the current flows the opposite way (shown negative here) starting at −Vs/R. The current curve is the mirror image of the voltage curve; between them they explain why supplies see a brief gulp at switch-on (inrush) sized by Vs/R.

Does a bigger resistor make charging more efficient?

No — and this surprises everyone once: charging a capacitor to Vs through any resistor from a fixed Vs supply stores ½CVs² in the capacitor and dissipates exactly ½CVs² in the resistor. The resistor’s value changes only the schedule (τ), never the 50/50 split. (Charging with a constant-current source or an inductor can dodge the toll — one reason switch-mode converters exist.) Discharge through the same resistor just turns the stored half into heat.

How is an RC circuit a filter?

Because its response depends on frequency: slow signals (long compared to τ) follow the capacitor’s voltage faithfully, fast ones are averaged away before the capacitor can respond. The corner frequency fc = 1/(2πRC) divides the two regimes — our default parts give fc ≈ 0.16 Hz (a timer, not an audio filter); swap in 1.6 kΩ and 100 nF and fc lands near 1 kHz. Every “tone” knob and sensor-smoothing network is this idea at audio or signal scale.

What τ do I need for a 1-second delay?

τ ≈ 1 s divided by the ln-factor of your trip threshold: if the circuit triggers at 63% of supply, τ = 1.0 s directly (10 kΩ × 100 µF, our defaults); at a 50% threshold, t = 0.693τ so τ = 1.44 s (e.g. 14.4 kΩ × 100 µF or 10 kΩ × 144 µF — use the nearest standard values and accept the tolerance conversation above). Then verify with this calculator at t = your delay to read the exact voltage the threshold will see.

Is this RC circuit calculator free?

Yes — free, instant, no sign-up. Enter R, C, supply and a time to get τ, V(t), I(t), stored energy and the 5τ settle time for charging or discharging.