About this calculator
A resistor and a capacitor together control how quickly a voltage changes. The time constant τ = R × C is the time for the capacitor to charge to 63% of the supply, and it sets the cut-off frequency of an RC filter.
Enter the resistance in ohms (you can write 4.7k or 1M) and the capacitance in microfarads.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
10 kΩ and 1 µF
- Time constant τ = RC
- 10 ms
- Cut-off frequency
- 15.9155 Hz
- Charged to 63.2% after
- 10 ms
- Charged to 95% after (3τ)
- 30 ms
- Charged to 99.3% after (5τ)
- 50 ms
A 10 kΩ resistor with a 1 µF capacitor has a time constant of 10 ms and a cut-off frequency of 15.9155 Hz.
Show the working
- Time constant τ = R × C = 10,000 Ω × 1e-6 F = 0.01 s.
- Cut-off (−3 dB) frequency fc = 1 ÷ (2π R C) = 1 ÷ (2π × 0.01) = 15.915494 Hz.
- After one time constant a charging capacitor reaches 63.2% of the supply voltage; after five it is within 1% of full. Resistance accepts k and M suffixes, such as 4.7k.
1 MΩ and 10 µF
- Time constant τ = RC
- 10 s
- Cut-off frequency
- 15.9155 mHz
- Charged to 63.2% after
- 10 s
- Charged to 95% after (3τ)
- 30 s
- Charged to 99.3% after (5τ)
- 50 s
A 1 MΩ resistor with a 10 µF capacitor has a time constant of 10 s and a cut-off frequency of 15.9155 mHz.
Show the working
- Time constant τ = R × C = 1,000,000 Ω × 1e-5 F = 10 s.
- Cut-off (−3 dB) frequency fc = 1 ÷ (2π R C) = 1 ÷ (2π × 10) = 0.015915 Hz.
- After one time constant a charging capacitor reaches 63.2% of the supply voltage; after five it is within 1% of full. Resistance accepts k and M suffixes, such as 4.7k.
100 Ω and 0.1 µF
- Time constant τ = RC
- 10 µs
- Cut-off frequency
- 15.9155 kHz
- Charged to 63.2% after
- 10 µs
- Charged to 95% after (3τ)
- 30 µs
- Charged to 99.3% after (5τ)
- 50 µs
A 100 Ω resistor with a 0.1 µF capacitor has a time constant of 10 µs and a cut-off frequency of 15.9155 kHz.
Show the working
- Time constant τ = R × C = 100 Ω × 1e-7 F = 1e-5 s.
- Cut-off (−3 dB) frequency fc = 1 ÷ (2π R C) = 1 ÷ (2π × 1e-5) = 15,915.494309 Hz.
- After one time constant a charging capacitor reaches 63.2% of the supply voltage; after five it is within 1% of full. Resistance accepts k and M suffixes, such as 4.7k.
The formulas
- Time constant: τ = R × C
- Cut-off frequency: fc = 1 ÷ (2π R C)
- Charging: V = Vsupply × (1 − e^(−t ÷ τ))
Charge time table
- After 1τ: 63.2% charged
- After 2τ: 86.5%
- After 3τ: 95.0%
- After 5τ: 99.3% (treated as fully charged)
As a filter
Used as a low-pass filter, the circuit lets frequencies below fc through and reduces higher ones by 6 dB per octave. Swap the positions of the resistor and capacitor and you get a high-pass filter with the same cut-off frequency.
Frequently asked questions
What is the RC time constant?
R × C in seconds: the time to charge to 63.2% of the final voltage.
How long does a capacitor take to charge fully?
About five time constants.
What is the cut-off frequency?
The frequency where the output is 3 dB (about 70.7%) of the input: fc = 1 ÷ 2πRC.
What unit is the capacitance in?
Microfarads. Write 0.1 for a 100 nF capacitor.
Can I type 4.7k?
Yes, k means thousand and M means million for the resistance.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.