RC Time Constant Calculator — τ = R·C, Charge & Discharge Time

Overview

How to Use This Calculator

1. Enter capacitance C — select the unit (pF, nF, μF, mF, or F) and enter the value. Ceramic decoupling cap: 100 nF. Bulk power-supply cap: 100–10,000 μF. Timer/delay: 1–100 μF. Signal coupling: 100 nF–10 μF.

2. Enter resistance R — use the effective charging-path resistance: limiting resistor plus source impedance, switch on-resistance, capacitor ESR, and trace resistance. Omitting these underestimates τ and overestimates peak current.

3. Enter supply voltage V (DC) — common values: 5 V (logic), 12 V (automotive), 24 V (industrial), 48 V (telecom), 325 V (rectified mains). AC sources are out of scope — rectify to DC first.

4. Click Calculate — get τ, final voltage, peak transient current, 5τ settling time, energy stored in the capacitor, first-order RC cutoff frequency, and the combined Track A / Track B status badge.

5. Open advanced parameters (optional) — switch Transient Mode to Discharge for decay from a pre-charged cap. Add Analysis Time for a moment snapshot. Enter the capacitor voltage rating and type for over-voltage and DC-bias warnings. Add a bleed resistor to compute discharge time. Enter cycle frequency to compute average resistor power.

6. Design Verification — enter a Target Time Constant to compare your computed τ against a design goal. Add capacitance and resistance tolerances for a realistic τ band showing component variation.

All calculations use SI base units internally. Unit dropdowns convert your entry to farads and ohms before computing. Supply voltage affects final voltage, stored energy, and peak current — but not τ = R·C.

Inputs & Outputs

Formula

τ = R × C    [seconds]

v_C(t) = V_final + (V_initial − V_final) × e^(−t/τ)    [V]

i(t) = (V_final − V_initial) / R × e^(−t/τ)    [A]

I_peak_charge    = |V_supply − V_initial| / R
I_peak_discharge = V_initial / R

t_settle = 5 × τ    (99.3% of final value)
t_half = τ × ln(2) ≈ 0.6931 × τ    (50% of final value)

W_C = ½ × C × V_final²    [joules stored at steady state]
W_R_pulse = ½ × C × (V_final − V_initial)²    [joules in R per transient event]
P_R_avg = W_R_pulse × f_cycle    [W, when cycle frequency provided]

f_c = 1 / (2π × R × C) = 1 / (2π × τ)    [Hz]

τ_bleed = R_bleed × C
t_to_50V = τ_bleed × ln(V_start / 50)    if V_start > 50 V
P_bleed = V_start² / R_bleed    [continuous dissipation]

deviation = (τ − τ_target) / τ_target × 100    [%]
C_needed = τ_target / R    (keep R fixed)
R_needed = τ_target / C    (keep C fixed)

With tolerances:
τ_min = R × (1 − R_tol%) × C × (1 − C_tol%)
τ_max = R × (1 + R_tol%) × C × (1 + C_tol%)

Key Facts

• The time constant τ = R·C has units of seconds when R is in ohms and C is in farads — ohm × farad = (V/A) × (A·s/V) = s.
• After 1τ, voltage reaches 63.2% of final during charging. After 5τ, 99.3%. These percentages apply identically to both charge and discharge transients.
• The half-voltage time τ·ln(2) ≈ 0.693·τ is when voltage crosses 50% — used for Schmitt trigger threshold calculations and 555 timer timing.
• Energy stored in a capacitor at steady state is W = ½·C·V². A 100 nF cap at 5 V stores 1.25 μJ; a 1000 μF cap at 400 V stores 80 J.
• During full charging from zero, exactly half the source energy is stored in the capacitor and half is dissipated in R, regardless of the value of R.
• Capacitors retain charge long after power-off unless a discharge path is provided. A film capacitor at 400 V can remain hazardous for many minutes.
• τ and the −3 dB cutoff frequency are reciprocal: f_c = 1/(2π·τ). A 1 ms time constant corresponds to a 159 Hz cutoff.
• Supply voltage V does not affect τ. Doubling V doubles I_peak, quadruples stored energy, and doubles V_final — but τ = R·C is unchanged.
• Class II ceramic dielectrics (X5R, X7R, Y5V) lose 30 to 80 percent of capacitance near their rated voltage under DC bias — effective τ may be much lower than nominal.
• Polar capacitors (electrolytic, tantalum) fail catastrophically if reverse-biased even briefly — verify circuit polarity before energizing.

Applications

• Power-supply bulk filter capacitors — settling time, inrush current, and stored energy screening for safety and component sizing.
• Decoupling and bypass capacitors — charge recovery speed for IC switching current demands; first-order τ provides intuition for energy availability.
• Timer and delay circuits — RC delay for Schmitt triggers, 555 timers, and MCU debouncing; half-voltage time τ·ln(2) gives threshold crossing for 50% V threshold.
• Coupling capacitors — AC signal blocking of DC with first-order high-pass cutoff f_c = 1/(2π·R·C).
• Snubber networks — RC time constant reference for switch-ringing damping and dV/dt control.
• Audio and instrumentation filters — first-order RC rolloff at f_c for tone controls, anti-aliasing prefilters, and post-DAC smoothing.
• Sample-and-hold circuits — 5τ acquisition time estimation for hold capacitor charge recovery from source impedance.
• Design Verification — checking whether a chosen R and C combination meets a target time constant within component tolerance.
• Bleed resistor sizing — computing safe-discharge time and continuous power for high-voltage bulk capacitors per IEC 61010-1 requirements.
• X-cap and Y-cap mains EMI suppression — discharge time verification for IEC 60384-14 safety capacitor requirements.

Standards & References

• IEC 60050-131:2002 — International Electrotechnical Vocabulary, Part 131: Circuit theory. Defines time constant, transient response, RC circuit, and related foundational terminology.
• IEC 60384-1:2021 — Fixed capacitors for use in electronic equipment, Part 1: Generic specification. Establishes voltage ratings, tolerance classes, marking, and derating practice.
• IEC 60384-14:2023 — Fixed capacitors for electromagnetic interference suppression and connection to the supply mains. Defines X and Y safety capacitor classes with discharge requirements.
• IEC 61010-1:2010 (with Amendment 1:2016) — Safety requirements for electrical equipment for measurement, control, and laboratory use. Covers capacitor discharge requirements after power-off.
• IPC-2221C — Generic Standard on Printed Board Design — Establishes PCB design requirements including component derating guidance.
• MIT OCW — Transient Analysis of First Order RC and RL Circuits — Standard derivation of the RC transient solution to Kirchhoff's voltage law with worked examples.
• BIPM SI Brochure — The farad (F) SI derived unit of capacitance: 1 C/V (coulomb per volt).

Common Mistakes to Avoid

• Entering R as the external resistor alone, ignoring source impedance, switch on-resistance, capacitor ESR, and trace resistance. All are in series with the capacitor and must be included in the effective R.
• Entering capacitance in F when μF was intended, or μF when nF was intended. A 100 μF capacitor is 0.0001 F or 100,000 nF — verify the unit dropdown matches the value.
• Using RMS voltage from an AC source. A 120 V RMS AC supply rectified produces about 170 V peak. Use the actual DC value at the capacitor terminals.
• Forgetting that capacitors retain charge after power-off. A bulk filter cap at 400 V remains a shock hazard for minutes — always include a bleed path for high-voltage circuits.
• Reverse-biasing an electrolytic or tantalum capacitor. Even brief reverse voltage causes catastrophic failure. Verify polarity before energizing.
• Assuming Class II ceramic capacitance is stable under DC bias. A 10 μF X7R MLCC at 8 V on a 10 V rated cap can drop to 4 μF — use Class I (C0G/NP0) for stable timing.
• Treating f_c as the operating frequency limit. The first-order RC cutoff is the −3 dB point, not a hard cutoff — signals above f_c are attenuated, not blocked.
• Sizing a bleed resistor by discharge time only. Faster discharge means lower R_bleed and higher continuous power V²/R_bleed while the supply is on — verify the resistor's power rating.
• Confusing single-pulse energy with continuous dissipation. Resistor Pulse Energy is the energy per transient. For repeated cycles, multiply by cycle frequency to get average power.
• Assuming supply voltage changes τ. τ = R·C depends only on R and C. Voltage changes the final state, stored energy, and inrush current — not the timing.

Frequently Asked Questions