RC Time Constant Calculator

RC Time Constant Calculator
τ = RC — Time Constant, Milestones, and Cutoff Frequency
R Resistance
C Capacitance
Optional: Voltage Levels
Vs Supply Voltage (for actual voltage levels)
V
Vt Target Voltage (custom threshold)
V
RC Time Constant Analysis
Time Constant (τ)
—
τ = RC
Cutoff Frequency
—
f = 1/(2πτ)
Full Charge (5τ)
—
99.3%
Resistance
—
Capacitance
—
Time Duration Charge % Charge V Discharge % Discharge V
Charge to Vtarget
—
Discharge to Vtarget
—

RC Circuit — Charge and Discharge

The voltage across the capacitor follows an exponential curve. Charging: Vc(t) = Vs(1 − e−t/τ). Discharging: Vc(t) = Vs · e−t/τ. The time constant τ = RC sets the speed.

Vs + R C τ = R × C Charging 63% 1τ 3τ 5τ Discharging 37% 1τ 3τ

RC Time Constant Calculator

Enter resistance and capacitance to get the time constant τ = RC and the cutoff frequency f = 1/(2πτ). Add a supply voltage to see actual charge/discharge voltages at each milestone. Add a target voltage to find the exact time the capacitor crosses a specific threshold. The tool for timing circuits, filters, debounce networks, and 555 timer design.

Core Formulas

τ = R × C — time constant
f = 1 / (2πτ) — cutoff frequency (−3 dB point)

Vcharge(t) = Vs × (1 − e−t/τ) — charging from 0 V
Vdischarge(t) = Vs × e−t/τ — discharging from Vs

tcharge = −τ × ln(1 − Vt/Vs) — time to charge to target Vt
tdischarge = −τ × ln(Vt/Vs) — time to discharge to target Vt

Charge/Discharge Milestone Table

The same percentages apply to every RC circuit regardless of component values — only the time scale changes.

TimeCharge %Charge V (5 V)Discharge %Discharge V (5 V)
1τ63.2%3.16 V36.8%1.84 V
2τ86.5%4.32 V13.5%0.68 V
3τ95.0%4.75 V5.0%0.25 V
4τ98.2%4.91 V1.8%0.09 V
5τ99.3%4.97 V0.7%0.03 V

At 5τ the capacitor is effectively fully charged (99.3%) or fully discharged (0.7%). Most designs treat 3τ (95%) as “done” and 5τ as the absolute guarantee.

Worked Example — 1 Second Timer (10 kΩ, 100 µF, 5 V)

Target: 3.3 V (logic HIGH threshold for a 3.3 V microcontroller reading a 5 V RC input).

τ = 10000 × 100×10−6 = 1.0 s
f = 1 / (2π × 1.0) = 0.159 Hz

tcharge to 3.3 V = −1.0 × ln(1 − 3.3/5) = −1.0 × ln(0.34) = 1.08 s (1.08τ)
tdischarge to 3.3 V = −1.0 × ln(3.3/5) = −1.0 × ln(0.66) = 0.42 s (0.42τ)

The capacitor charges past 3.3 V in 1.08 seconds. Discharging from 5 V, it drops below 3.3 V in only 0.42 seconds. Charging is slower to cross a high threshold because the exponential curve flattens as it approaches Vs. For total charge and energy stored at 5 V, see the Capacitor Charge Calculator.

Worked Example — 555 Timer (47 kΩ, 10 µF, 5 V)

The 555’s internal comparators trigger at ⅓Vs (1.67 V) and ⅔Vs (3.33 V).

τ = 47000 × 10×10−6 = 0.47 s

tcharge to 3.33 V = −0.47 × ln(1 − 3.33/5) = −0.47 × ln(0.334) = 0.516 s
tcharge to 1.67 V = −0.47 × ln(1 − 1.67/5) = −0.47 × ln(0.666) = 0.191 s

The capacitor charges from 0 V to the upper threshold (3.33 V) in 0.516 seconds. The time from the lower threshold to the upper threshold (the 555’s charge phase in astable mode) is 0.516 − 0.191 = 0.325 s. This is the basis for calculating 555 oscillator frequency: f = 1 / (tcharge + tdischarge).

Worked Example — Low-Pass Filter (10 kΩ, 1 nF)

τ = 10000 × 1×10−9 = 10 µs
f = 1 / (2π × 10×10−6) = 15.9 kHz

The same RC pair is simultaneously a 10 µs timing circuit and a 15.9 kHz low-pass filter. Below 15.9 kHz, signals pass through with less than 3 dB of attenuation. Above 15.9 kHz, the capacitor shunts signal to ground at −20 dB/decade. No voltage inputs needed for filter design — just R, C, τ, and f.

Worked Example — Switch Debounce (10 kΩ, 100 nF, 3.3 V)

τ = 10000 × 100×10−9 = 1 ms
f = 159 kHz

Target: 1.65 V (midpoint, Schmitt trigger threshold)
tcharge to 1.65 V = −0.001 × ln(1 − 1.65/3.3) = −0.001 × ln(0.5) = 0.693 ms

The capacitor crosses the midpoint in 0.693 ms. Mechanical switch bounce typically lasts 1–10 ms. A 1 ms time constant means the capacitor voltage changes slowly enough that short bounce transients cannot flip the logic state, but fast enough that a genuine press registers within a few milliseconds. Increase C to 1 µF (τ = 10 ms) for particularly noisy switches.

Time Constant and Cutoff Frequency — Two Views of the Same Circuit

τ = RC describes the circuit in the time domain — how fast things charge and discharge. f = 1/(2πτ) describes the same circuit in the frequency domain — what frequencies pass through and what frequencies are blocked. They are mathematically linked and always move together:

τ = 1 µs → f = 159 kHz
τ = 10 µs → f = 15.9 kHz
τ = 100 µs → f = 1.59 kHz
τ = 1 ms → f = 159 Hz
τ = 10 ms → f = 15.9 Hz
τ = 1 s → f = 0.159 Hz

Use whichever view suits your application. Timing circuits think in τ. Filter design thinks in f. The calculator shows both. The underlying V = IR relationship behind both is covered by our Ohm’s Law Calculator.

How to Choose R and C

Start with τ

Decide the time constant you need from the application requirements (delay time, filter frequency, debounce duration). Then pick R and C whose product equals τ. There are infinite R×C combinations for any given τ — the choice between them depends on other constraints.

Practical Constraints

R too low — high peak current (I = V/R) at t = 0. May exceed the source’s drive capability. Below ~100 Ω, the source impedance and wire resistance start affecting the actual τ.

R too high — the circuit becomes sensitive to leakage currents and noise pickup. Above ~10 MΩ, stray capacitance on the PCB and input bias currents of connected ICs can distort the timing.

C too small — parasitic capacitance (a few pF on a typical PCB) becomes a significant fraction of C, making the actual τ larger than calculated. Keep C at least 10× the estimated parasitic capacitance.

C too large — physical size, cost, and leakage current increase. Electrolytic capacitors above ~1000 µF have significant leakage that affects long timing intervals.

For most timing and debounce circuits, R in the 1 kΩ to 100 kΩ range and C in the 1 nF to 100 µF range gives reliable, predictable results.

Frequently Asked Questions

How long to fully charge a capacitor?
5τ reaches 99.3%. Multiply R × C × 5. For 10 kΩ and 100 µF: 5 × 1.0 s = 5 seconds. There is no exact “full” time — the exponential curve never quite reaches Vs.
How do I find the time to reach a specific voltage?
Enter R, C, Vs, and Vt in the calculator. The formula is t = −τ × ln(1 − Vt/Vs) for charging. For example, to reach 3.3 V from a 5 V supply with τ = 1 s: t = −1 × ln(1 − 0.66) = 1.08 s.
What is the relationship between time constant and filter frequency?
f = 1/(2πτ). A 1 ms time constant gives a 159 Hz cutoff frequency. They describe the same RC behaviour in different domains — time vs. frequency.
Why does discharge cross a threshold faster than charge?
It depends on the threshold relative to Vs. For thresholds above 50% of Vs, charging takes longer because the exponential flattens near Vs. For thresholds below 50%, discharge takes longer because the exponential flattens near 0 V. At exactly 50% (Vs/2), both take the same time: 0.693τ.
Does this calculator account for capacitor ESR?
No. The formulas assume an ideal capacitor. In practice, ESR adds a small resistance to R, slightly reducing the effective τ. For timing circuits this effect is negligible unless ESR is a significant fraction of R. For ESR-specific analysis, use the ESR Capacitor Calculator.
Can I use this for discharge safety timing?
Yes. Enter R (bleeder resistor), C (capacitor), Vs (initial voltage), and Vt (safe voltage threshold). The discharge time tells you how long to wait. For dedicated safety discharge design with power rating checks, use the Bleeder Resistor Calculator.

Last updated: March 2026