# RC Time Constant Calculator

> Find the time constant τ = R × C of a resistor–capacitor circuit, the capacitor voltage at any time while charging or discharging, and the RC cut-off frequency.

Category: Science & engineering · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/rc-time-constant-calculator

A capacitor charging through a resistor reaches about 63% of the supply voltage after one time constant, τ = R × C, and is treated as fully charged after about 5τ.

Also called: Capacitor charge time calculator.

## Inputs
- Resistance (default 10)
- Resistance unit (options: Ω, kΩ, MΩ; default kohm)
- Capacitance (default 100)
- Capacitance unit (options: pF, nF, µF, mF, F; default uF)
- Capacitor is (options: Charging, Discharging; default charge)
- Supply (or starting) voltage (unit V; default 5; optional)
- Time after switching (default 1; optional)
- Time unit (options: ns, µs, ms, s; default s)

## Results
- Time constant τ
- τ in seconds
- 5τ (≈ 99.3% settled)
- Capacitor voltage at that time
- Share of the final change
- Cut-off frequency 1/(2πRC)

## Formula

```
τ = R × C;  charging: V(t) = V × (1 − e^(−t/τ));  discharging: V(t) = V × e^(−t/τ);  f_c = 1 ÷ (2πRC)
```

Where:
- R: resistance in ohms
- C: capacitance in farads
- τ: time constant in seconds
- V: supply voltage (charging) or starting voltage (discharging)
- t: time since the switch

## Worked example
1. τ = 10,000 Ω × 0.0001 F = 1 s.
2. After t = 1 s = 1τ: V = 5 × (1 − e⁻¹) = 5 × 0.63212 = 3.1606 V.
3. f_c = 1 ÷ (2π × 1) ≈ 0.1592 Hz.

**Result:** A 10 kΩ resistor with a 100 µF capacitor has τ = 1 s; after one second the capacitor has charged to 3.16 V of 5 V.

## What the result means

After 1τ the capacitor has covered 63.2% of the change, after 3τ 95%, and after 5τ 99.3%, which is the usual “fully charged” rule. The same τ sets the −3 dB corner of a first-order RC filter.

## Assumptions and limits
- Ideal resistor and capacitor driven by a step from a stiff voltage source.
- Discharging starts from the voltage entered and decays towards zero.
- Capacitor leakage, ESR, source resistance and tolerance (often ±10–20% for electrolytics) change the real timing.

## Questions

### Why 63%?

After one time constant the remaining gap is e⁻¹ ≈ 36.8% of the original, so 63.2% of the change has happened.

### How long until the capacitor is fully charged?

Mathematically never, but after 5τ it is within 0.7% of the final voltage, which is treated as complete in practice.

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- [RL Time Constant Calculator](https://calculators.geekmidst.com/calculators/rl-time-constant-calculator)
- [Ohm’s Law Calculator](https://calculators.geekmidst.com/calculators/ohms-law-calculator)
- [Resistor Calculator](https://calculators.geekmidst.com/calculators/resistor-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/rc-time-constant-calculator