RC Time Constant Calculator
Enter resistance and capacitance to find the RC time constant and related values.
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Understanding RC Time Constants
An RC circuit combines a resistor and capacitor. The time constant \u03c4 (tau) equals R \u00d7 C and determines how quickly the capacitor charges or discharges.
In one time constant, a capacitor charges to 63.2% of the applied voltage. It takes approximately 5 time constants to reach 99.3% (considered fully charged for most practical purposes).
RC circuits are used as filters, timing circuits, and smoothing circuits. The cutoff frequency fc = 1/(2\u03c0RC) defines where the filter attenuates the signal by 3dB.
The RC time constant τ (tau) = R × C determines how fast a capacitor charges or discharges through a resistor. After one τ, the capacitor reaches 63.2% of full charge. It reaches 99.3% after 5τ — considered "fully charged" for practical purposes.
Example: a 10kΩ resistor and 100μF capacitor give τ = 10,000 × 0.0001 = 1 second. The capacitor charges to ≈9V in 5 seconds from a 9V source. After removing the source, it discharges to 37% (≈3.3V) in one second.
RC circuits are also used as low-pass filters. The cutoff frequency f_c = 1 / (2π × R × C). Frequencies below f_c pass; above it are attenuated. A 10kΩ + 100μF RC has f_c ≈ 0.16Hz — only DC and very slow signals pass.
Practical RC circuits are used for debouncing switches, smoothing power supply ripple, setting delays in 555 timer circuits, and anti-aliasing filters before ADC inputs. The formula works in any consistent unit system — use Ω and Farads to get seconds.
See also: Ohm's Law Calculator · Voltage Divider Calculator