What is the RC time constant?

The time constant τ = R × C (in seconds) is the time it takes for the capacitor voltage to reach approximately 63.2% of the supply voltage during charging (or fall to 36.8% of its initial voltage during discharging). After 5τ the capacitor is considered fully charged or discharged (>99%).

How is impedance different from resistance in an RC circuit?

Resistance R opposes current at all frequencies equally. Capacitive reactance X_C = 1/(2πfC) opposes only AC current and decreases as frequency increases. Total impedance Z = √(R² + X_C²) combines both effects and determines the overall opposition to AC current flow.

Why does current lead voltage in a capacitor?

A capacitor charges up in response to voltage. At the instant voltage is applied, current flows freely before any charge has built up, so the current peaks before the voltage does. This results in current leading the voltage by a phase angle up to 90° (pure capacitor).

What is the cutoff frequency of an RC circuit?

The −3 dB cutoff frequency is f_c = 1 / (2πRC) = 1 / (2πτ). For a low-pass filter (output across C), frequencies below f_c pass with minimal attenuation; above f_c they are attenuated. For a high-pass filter (output across R), the roles are reversed.

What units should I use?

Use consistent SI units: ohms (Ω) for resistance and farads (F) for capacitance. The calculator accepts kΩ, MΩ, μF, nF, and pF via the unit selectors and converts automatically before computing.

How many time constants to fully charge a capacitor?

Practically, 5τ is used: at 5τ the capacitor is 99.3% charged. For precision work, 7τ gives 99.9%. The exact percentage at any time t is (1 − e^(−t/τ)) × 100%.

RC Circuit Calculator

Name: RC Circuit Calculator
Availability: InStock
Author: Nham Vu

Enter resistance and capacitance to compute the RC time constant, cutoff frequency, impedance, phase angle, and transient charge/discharge response.

Circuit Parameters

Resistance (R)

Capacitance (C)

Supply Voltage (V_s) — for transient chart

AC Frequency (f) — for impedance

Transient Mode

Results

Time Constant (τ)

—

Cutoff Freq (f_c)

—

Impedance (Z)

—

Phase Angle (φ)

—

Reactance (X_C)

—

V at 1τ

—

Voltage at Time t

Time (multiples of τ)

× τ

—

Charge/Discharge Curve

Summary

Enter resistance and capacitance to compute the RC time constant, cutoff frequency, impedance, phase angle, and transient charge/discharge response.

How it works

Enter the resistance R in ohms and capacitance C in farads (or use the unit selectors for kΩ, μF, nF, pF).
Optionally enter a supply voltage and an AC frequency to compute impedance and cutoff frequency.
The calculator derives the time constant τ = R × C — the time for voltage to reach ~63.2% of its final value.
Capacitive reactance X_C = 1 / (2πfC) and total impedance Z = √(R² + X_C²) are computed from the frequency.
Phase angle φ = −arctan(X_C / R) shows how much the current leads the voltage.
The charge/discharge chart plots V(t) = V_s × (1 − e^(−t/τ)) for charging and V(t) = V_0 × e^(−t/τ) for discharging.

Use cases

Design RC low-pass or high-pass filters and verify the −3 dB cutoff frequency.
Estimate capacitor charge time in power-supply hold-up and debounce circuits.
Analyze transient behavior in signal coupling and bypass networks.
Verify capacitor selection for a given settling time requirement.
Calculate AC impedance for audio tone-control and crossover networks.
Teach or learn RC circuit theory with an interactive visual aid.
Compute discharge time for camera flash capacitors and energy storage circuits.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu