Electronics / Circuits
RC Time Constant Calculator (τ, Charge Curve, Cut-off)
Work out the time constant of a resistor and capacitor, how far the capacitor charges or discharges after each time constant, the voltages it reaches, and the cut-off frequency of an RC filter.
RC Time Constant Calculator (τ, Charge Curve, Cut-off): The time constant τ = R × C is the time a capacitor charging through a resistor takes to reach 63.2% of the supply; after 2, 3, 4, and 5 τ it reaches 86.5%, 95.0%, 98.2%, and 99.3%, following 1 − e^(−t/τ). Discharging follows the mirror image. Used as a filter, the same pair has its −3 dB cut-off at 1 ÷ (2π × R × C). Runs 100% locally in your browser with zero server file uploads.
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| Time | Charging: share of supply | Voltage | Discharging: share left |
|---|---|---|---|
| 1 τ = 1 s | 63.2% | 3.161 V | 36.8% |
| 2 τ = 2 s | 86.5% | 4.323 V | 13.5% |
| 3 τ = 3 s | 95% | 4.751 V | 5% |
| 4 τ = 4 s | 98.2% | 4.908 V | 1.8% |
| 5 τ = 5 s | 99.3% | 4.966 V | 0.7% |
τ = R × C. Charging through the resistor, the capacitor reaches 63.2% of the supply after one τ, 86.5% after two, and 99.3% after five, usually taken as full. Discharging follows the same curve downwards. As a low-pass or high-pass filter, the same R and C have their −3 dB cut-off at 1 ÷ (2π × R × C).
Worked examples
1 kΩ and 1 µF: τ = 1 ms and the cut-off is 159 Hz. 10 kΩ and 100 nF: τ = 1 ms as well. 100 kΩ and 10 µF: τ = 1 s, a slow fade suitable for a light that dims when switched off.
To read the capacitor's printed value, use the capacitor code converter.
Debouncing a switch
An RC network on a button input smooths its contact bounce: with τ around 5 to 10 ms the voltage changes too slowly for the bounces to register as separate presses. Many designs debounce in software instead.
The 555 timer calculator uses the same charging curve to set its timing.
How to use it
- Enter the resistance in kilohms and the capacitance in microfarads.
- Optionally enter the supply voltage.
- Read τ, the cut-off frequency, and the charging table and curve.
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Frequently asked questions
How long until the capacitor is fully charged?
In theory never, but after 5 τ it is within 1%, which is the usual working answer.
What is 10 kΩ and 100 µF?
τ = 10,000 × 0.0001 = 1 second.
How does this relate to a filter?
An RC low-pass filter passes frequencies below 1 ÷ (2πRC) and cuts higher ones by 20 dB per decade; swapping R and C makes a high-pass filter with the same cut-off.
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