What is the RC time constant?

The time constant τ (tau) is the product of resistance (R) and capacitance (C). It represents the time needed for a capacitor to charge to approximately 63.2% of the supply voltage or to discharge to approximately 36.8% of its initial voltage.

How many time constants until the capacitor is fully charged?

After 5τ the capacitor is considered fully charged or discharged (>99.3%). After 3τ it reaches about 95%, and after 2τ about 86.5%.

What units should I use?

Any consistent pair works. This calculator supports ohms/kilohms/megohms for resistance and farads/millifarads/microfarads/nanofarads/picofarads for capacitance. Select the unit from the dropdown and the result is always shown in seconds.

What is the charging voltage formula?

V(t) = V₀ × (1 − e^(−t/τ)), where V₀ is the supply voltage, t is elapsed time, and τ is the time constant.

What is the discharging voltage formula?

V(t) = V₀ × e^(−t/τ), where V₀ is the initial voltage across the capacitor, t is elapsed time, and τ is the time constant.

Why is RC called the time constant?

The product R × C has units of seconds, so it sets the natural time scale of the circuit. One time constant is the time the capacitor needs to charge to 63.2% (or discharge to 36.8%) of its final value, which is why τ = R × C is called the time constant.

How is the RC time constant related to cutoff frequency?

For a first-order RC filter the −3 dB cutoff frequency is f_c = 1 / (2π · R · C) = 1 / (2π · τ). A larger time constant means a lower cutoff frequency.

RC Time Constant Calculator

Calculate the RC time constant (τ = R × C) and find voltage at any time point during capacitor charging or discharging.

RC Circuit Parameters

Resistance (R)

Capacitance (C)

Optional — Voltage at Time t

Initial / Supply Voltage V₀ (V)

Time t

Mode

Charging Discharging

Voltage Milestones

Time	τ multiples	% of V₀

Enter R and C values, then press Calculate.

Summary

An RC circuit consists of a resistor and a capacitor in series. The time constant τ (tau) equals R × C and describes how quickly the capacitor charges or discharges. After one time constant, the capacitor reaches about 63.2% of its final voltage when charging, or drops to about 36.8% when discharging. This calculator computes τ and optionally evaluates the voltage V(t) at any given time.

How it works

Enter the resistance in ohms, kilohms, or megohms.
Enter the capacitance in farads, millifarads, microfarads, nanofarads, or picofarads.
Read the time constant τ = R × C, computed instantly in seconds.
Optionally enter a supply voltage and target time, then pick charging or discharging to get V(t): V₀(1 − e^(−t/τ)) when charging, V₀ · e^(−t/τ) when discharging.
Use the milestone table (0.5τ to 5τ) to read the percent charged or remaining at each step.

Use cases

Design RC filter cutoff frequencies for audio and signal processing circuits.
Determine how long a capacitor takes to reach a target voltage in a timing circuit.
Analyze power-supply decoupling and smoothing capacitor behavior.
Check charge/discharge rates in microcontroller GPIO protection networks.
Teach or study transient circuit analysis in electronics courses.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu