Electrical

RC Time Constant Calculator

Solve RC time constant, required resistance, required capacitance, charging/discharging voltage, 5τ settling time, and cutoff frequency.

Formula τ = R × CReviewed Sep 1, 2026

An RC circuit does not jump instantly to its final voltage. A resistor and capacitor respond exponentially, and the time constant τ = RC tells you the scale of that response. This calculator solves any one of R, C, or τ from the other two, then adds the practical timing details users usually need: 1τ to 5τ milestones, voltage at a selected time, time to a target threshold, half-life, and the matching first-order cutoff frequency.

Calculation Bench

Solve For

01Resistance

R · Series resistance that limits capacitor charge or discharge current.

02Capacitance

C · Capacitor value in the RC network.

Transient Mode

Optional Voltage Timing

03Source Voltage

Vs · Required only when calculating voltage at time or time to target voltage.

04Elapsed Time (optional)

t · Add this to calculate the capacitor voltage at a specific time.

05Target Voltage (optional)

Vtarget · Add this to calculate time to reach a threshold. It must be below the final/initial voltage.

1τ is 63.2% charged or 36.8% remaining on discharge; 5τ is a practical settling estimate, not true 100%.

Solution

Enter any two of resistance, capacitance, and time constant. Optional voltage fields add charge/discharge timing.

τ = R × C

Formula Sheet

\tau = RC

R = \dfrac{\tau}{C}

C = \dfrac{\tau}{R}

V_C(t)=V_s(1-e^{-t/\tau})

V_C(t)=V_0e^{-t/\tau}

f_c=\dfrac{1}{2\pi RC}

τTime Constant
RResistance
CCapacitance
Vc(t)Capacitor Voltage
fcCutoff Frequency

Variables & Units

Symbol	Variable	Description	Common Units
τ	Time Constant	Characteristic RC response time; one τ reaches 63.2% of a charge step or leaves 36.8% during discharge.	µs, ms, s, min
R	Resistance	Series resistance that limits capacitor charge or discharge current.	Ω, kΩ, MΩ
C	Capacitance	Capacitor value in the RC network.	pF, nF, µF, mF, F
Vc(t)	Capacitor Voltage	Voltage across the capacitor at elapsed time t.	mV, V
fc	Cutoff Frequency	The -3 dB corner frequency of the equivalent first-order RC filter.	Hz, kHz

How to Use This Calculator

01Choose what you want to solve: time constant, resistance, or capacitance.
02Enter the other two values. Common real-world units are kΩ for resistance, µF or nF for capacitance, and ms for timing.
03Choose Charging when the capacitor starts low and rises toward a source voltage. Choose Discharging when it starts charged and decays toward zero.
04Leave the optional voltage fields blank if you only need τ, 5τ, and cutoff frequency.
05Enter elapsed time to calculate capacitor voltage at that instant. Enter target voltage to calculate the time required to reach that threshold.
06Remember that an ideal RC curve never reaches 100% exactly. The common 5τ rule means about 99.3% charged or 0.7% remaining.

How the Formula Works

The time constant is the product of resistance and capacitance: τ = R × C. With R in ohms and C in farads, τ is in seconds.

During charging from zero, capacitor voltage follows Vc(t) = Vs(1 - e^(-t/τ)). During discharge from an initial voltage, it follows Vc(t) = V0 e^(-t/τ).

The same R-C pair also sets a first-order filter corner: fc = 1/(2πRC). A timing circuit and a simple low-pass filter are different applications of the same time constant.

Worked Example 01

10 kΩ and 100 µF timing capacitor

Known

Resistance (R): 10 kΩ
Capacitance (C): 100 µF

Formula

τ = R × C

Substitution

τ = 10,000 × 0.000100

Result

τ = 1.0 s; 5τ ≈ 5.0 s; fc ≈ 0.159 Hz

This is a slow visible delay. After 1 second a charging capacitor is about 63.2% of the way to its final voltage; after 5 seconds it is about 99.3% settled.

Worked Example 02

Required resistor for a 10 ms debounce network

Known

Target time constant (τ): 10 ms
Capacitance (C): 1 µF

Formula

R = τ / C

Substitution

R = 0.010 / 0.000001

Result

R = 10 kΩ

A 1 µF capacitor with a 10 kΩ resistor gives a 10 ms time constant, a common starting point for hardware debounce filtering.

Worked Example 03

Charging voltage after one time constant

Known

Source voltage (Vs): 5 V
Time: 1τ

Formula

Vc(t) = Vs(1 - e^(-t/τ))

Substitution

Vc = 5 × (1 - e^-1)

Result

Vc ≈ 3.16 V

One time constant reaches 63.2% of the final voltage, so a 5 V step charges the capacitor to about 3.16 V at t = τ.

Applications

01Sizing a simple power-on delay or reset timing network
02Checking pushbutton debounce timing before firmware filtering
03Estimating RC low-pass or high-pass cutoff frequency
04Calculating capacitor charge/discharge voltage at a known elapsed time

Assumptions

01The circuit is a first-order, single-resistor/single-capacitor RC network.
02The capacitor starts at 0 V for charging mode and decays toward 0 V in discharging mode.
03Resistance and capacitance are ideal nominal values unless the user manually includes tolerance effects.

Where This Model Stops

01Does not model ESR, leakage, dielectric absorption, source resistance, switch resistance, PCB parasitics, op-amp input bias current, or comparator thresholds with hysteresis.
02Does not replace a 555 timer calculator, SPICE simulation, or datasheet timing model for production electronics.
03Large electrolytic capacitors and very high-value resistors can deviate strongly from ideal timing because leakage current becomes significant.

References

[1]
RC Charging Circuit
All About Circuits
Reference for RC charging/discharging exponential behavior and time-constant interpretation.
[2]
RC Time Constant Calculator
All About Circuits
Shows the practical solve-any-two workflow and common 1τ to 5τ charge percentage table.

Frequently Asked Questions

What does one RC time constant mean?

After one time constant, a charging capacitor reaches about 63.2% of its final voltage. During discharge, about 36.8% of the initial voltage remains.

Why is 5τ considered fully charged?

An ideal exponential never reaches the final value exactly, but after 5τ it is about 99.3% complete. For many timing and filter checks that is close enough to call settled.

How is this different from the Capacitor Energy Calculator?

The Capacitor Energy Calculator answers how much energy is stored at a voltage. This RC Time Constant Calculator answers how fast the voltage changes through a resistor and what voltage exists at a given time.

Does this calculate a 555 timer delay?

No. A 555 timer uses comparator thresholds and separate charge/discharge paths depending on the circuit. This page gives the basic RC exponential, which is the starting point but not the full 555 timing model.

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