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RC Time Constant Calculator

Find an RC circuit’s time constant and the capacitor voltage at any moment, charging or discharging.

By Nitin Raturi · Last reviewed

Your worksheet

How to use the RC Time Constant Calculator

Find τ = RC and the capacitor voltage at any time.

  1. Enter the resistance in ohms and capacitance in µF.
  2. Enter the supply voltage and the time.
  3. Choose charging or discharging.
  4. Read the voltage, then the milestone times.

Good to know

  • After 5 τ a capacitor is treated as fully charged (99.3%).

τ = R × C. After one τ a capacitor is 63.2% charged; after five, 99.3%.

Resistance (Ω)

The resistor the capacitor charges or discharges through.

How to fill it in

  • Enter ohms: 4.7 kΩ is 4700, 1 MΩ is 1000000.

Example

4.7 kΩ with 220 µF gives τ = 1.0340 s.

Capacitance (µF)

The capacitor’s size in microfarads.

How to fill it in

  • Enter µF: 100 nF is 0.1, 1 F is 1000000.

Supply voltage (V)

The voltage it charges towards, or starts from when discharging.

How to fill it in

  • Enter 0.001 to 10,00,000 V.

Time (s)

How long after switching on (or off) to find the voltage.

How to fill it in

  • Enter seconds: 1 ms is 0.001.

Example

With τ = 1 s and 9 V, it reaches 5.6891 V after 1 s and 8.9394 V after 5 s.

Charging or discharging

Whether the capacitor fills from 0 V or empties from the supply voltage.

How to fill it in

  • Charging: starts empty.
  • Discharging: starts full and drains through the resistor.

Example

Discharging, the same circuit falls to 3.3109 V after 1 s.

Capacitor voltage while charging

5.6891 V

With R = 1,000 Ω and C = 1,000 µF the time constant is 1.0000 s. After 1.0000 s the capacitor is at 5.6891 V, 63.21% of the way up to 9 V.

Time constant τ
1.0000 s
Current now
0.003311 A
Charge stored
0.005689 C
1 τ complete after
1.0000 s
90% complete after
2.3026 s
99% complete after
4.6052 s
5 τ complete after
5.0000 s

Ideal resistor and capacitor, a steady supply, and the capacitor starting empty (charging) or full (discharging). τ = R × C.

ChangelogHow we test this calculatorEmbed this calculator

How this calculator works

  1. Step 1Time constantτ = R × CSets how fast everything happens.
  2. Step 2ChargingVs (1 − e^(−t/τ))Fast at first, then slowing.
  3. Step 3DischargingVs e^(−t/τ)The mirror image.

When a capacitor charges through a resistor, the current starts high and falls as the capacitor fills. The voltage rises quickly at first and then levels off.

The time constant τ = R × C sets the pace. After one τ the capacitor is 63.2% of the way there; after five it is 99.3%.

Worked example: 1 kΩ and 1,000 µF on 9 V

Voltage after 1 second, charging
τ
R × C
V(t)
Vs × (1 − e^(−t/τ))
  1. Time constant1,000 Ω × 0.001 F1.0000 s
  2. Share complete1 − e⁻¹63.21%
  3. Capacitor voltage9 × 63.21%5.6891 V

Read the result

  • After 1 s5.6891 V
  • After 5 s8.9394 V
Capacitor voltage, 9 V supply, τ = 1 s

Discharging is the mirror image: from 9 V the same capacitor falls to 3.3109 V after 1 s.

  • 4.7 kΩ, 220 µF1.0340 sOn 12 V it reaches 10.2656 V after 2 s.
  • Full charge5.1700 sFive time constants: 99.3% of the supply.

Assumptions and limits

  • Ideal partsNo leakage or internal resistance in the source.
  • Steady supplyThe supply voltage does not sag.
  • ToleranceReal capacitors are often ±10–20%.
  • No inductanceRL and RLC circuits behave differently.

An RC circuit charges along an exponential curve set by resistance and capacitance.

To combine resistors first, use the series and parallel resistor calculator. The Ohm’s law calculator relates voltage and current, and the half-life calculator uses the same exponential decay.

Common mistakes

  • Mistake: Using µF as farads in τ = RC.

    Instead: Multiply µF by 10⁻⁶; this tool does it for you.

  • Mistake: Expecting a full charge after one τ.

    Instead: One τ is 63.2%; allow about 5 τ.

Checking the method

A separate script steps the circuit equation forward numerically, without the exponential formula, and matches every golden voltage.

Read how we test our calculators, or browse more maths calculators.

Frequently asked questions

What is the time constant of 1 kΩ and 1,000 µF?

τ = R × C = 1.0000 s. On 9 V the capacitor reaches 5.6891 V after that time.

How long does a capacitor take to charge fully?

About five time constants (99.3%). With τ = 1 s, 9 V gives 8.9394 V after 5 s.

What happens when it discharges?

The voltage falls by the same curve: from 9 V to 3.3109 V after one τ.

What is τ for 4.7 kΩ and 220 µF?

τ = 4,700 × 220 × 10⁻⁶ = 1.0340 s.

Why 63.2%?

After one τ the remaining gap shrinks by a factor e, so 1 − 1/e ≈ 63.2% is done.

Sources and methodology

The formulas are standard time-value-of-money results. We check every figure against golden values worked out independently, by closed form and by month-by-month simulation; see the methodology.

Written and maintained by Nitin Raturi, a software engineer (about the author). Last reviewed 4 Nov 2026; next review due by . Found an error? Tell us.

Changelog

  • : Initial release.