Electronics · Timing
RC time constant calculator.
Enter a resistor and a capacitor to see how long the capacitor takes to charge, and the cutoff frequency of the same pair as a filter.
Inputs
Result
Enter R and C.
RC time constant formulas
The time constant is tau = R × C, in seconds when R is in ohms and C is in farads. Charging through the resistor from zero, the capacitor reaches about 63.2% of the applied voltage after one tau, 86.5% after two, 95.0% after three, 98.2% after four and 99.3% after five. Discharging, it falls to about 36.8% after one tau.
Worked example. 10 kΩ and 100 µF: tau = 10,000 × 0.0001 = 1 s. Five tau is 5 s. The time to reach 90% is −tau × ln(1 − 0.90) = 2.303 s.
Cutoff frequency. The same R and C form a first-order low-pass or high-pass filter with fc = 1 ÷ (2πRC) = 0.159 Hz here.
Electrolytic capacitors often have wide tolerances and leakage, so real timing drifts from the calculated figure. For precise timing use a film or C0G part and check the datasheet.
Frequently asked questions
What is the time constant of an RC circuit?
tau = R × C. For 10 kΩ and 100 µF it is 1 second.
How long does a capacitor take to fully charge?
In theory never, but about 99.3% after five time constants is usually treated as fully charged. Here that is 5 seconds for tau = 1 s.
How do I find the time to reach a given voltage?
t = −tau × ln(1 − fraction). For 90% this is about 2.303 tau.
How is the cutoff frequency related to tau?
fc = 1 ÷ (2πτ), about 0.159 ÷ τ. A 1 s time constant gives roughly 0.159 Hz.
Does the supply voltage change the time?
No. The percent charged after each tau is the same for any supply voltage, though the actual volts reached scale with it.
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Scope and safety
Low-voltage hobby use only. These results are arithmetic from the formulas shown, not an engineering design or professional advice. Real parts vary with tolerance, temperature and age, so check the datasheet for every part. Never work on mains-powered circuits from a calculator result, and treat lithium and other rechargeable batteries with care.