RC time constant calculator
Enter a resistance in ohms and a capacitance in farads. The calculator gives the time constant tau = R × C, the cutoff frequency of a first-order RC filter, and the time the capacitor needs to reach 90 and 99 percent of the final voltage. Prefixes work: 10k, 100n, 4.7u.
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How to use it
- Enter the resistance, for example 10k.
- Enter the capacitance, for example 100n or 100nF.
- Read tau, the cutoff frequency and the charge times.
τ = R × C
f = 1 ÷ (2π × R × C)
t = −τ × ln(1 − fraction)
Worked example
With 10 kΩ and 100 nF, τ = 10,000 × 0.0000001 = 1 ms. The cutoff frequency is 1 ÷ (2π × 0.001) = 159.2 Hz. Reaching 90 % takes 2.303 ms and 99 % takes 4.605 ms.
Tips
- Doubling either R or C doubles tau and halves the cutoff frequency.
- Real capacitors have tolerance, often 10 to 20 %, so the actual tau varies.
Frequently asked questions
What is the RC time constant?
It is tau = R × C, in seconds when R is in ohms and C in farads. After one tau a charging capacitor reaches about 63.2 % of the final voltage; a discharging one falls to about 36.8 %. 10 kΩ with 100 nF gives 1 ms.
How do I find the cutoff frequency?
For a first-order RC low-pass or high-pass filter, f = 1 ÷ (2π × R × C). With R = 10 kΩ and C = 100 nF this is about 159.2 Hz, where the output is 3 dB below the passband.
How long does a capacitor take to charge fully?
Never exactly, since it approaches the final value gradually. The time to reach a fraction is t = −τ × ln(1 − fraction): about 2.3 τ for 90 %, 4.6 τ for 99 %. A common rule of thumb is to treat 5 τ as fully charged, which is 99.3 %.
How do I type capacitor values?
Use a prefix: 100n for 100 nF, 4.7u or 4.7µ for 4.7 µF, 22p for 22 pF. An F after the number is allowed, so 100nF works too.
Does this account for the source or load resistance?
No. If the source has its own resistance, or a load draws current from the capacitor, add that resistance to R as an approximation of the real circuit.