Electrical · Free Calculator
RC Time Constant Calculator
Calculate the time constant of a resistor capacitor circuit and the capacitor voltage at any moment during charging or discharging.
τ = R × CChargingDischargingFilters and delays
V
s
Time constant τ1 s
Capacitor voltage at t15.17 V
Percent of final63.2 %
Time to 99 %4.605 s
How this result was calculated
- τ = R × C = 10,000 Ω × 1.000 × 10^−4 F = 1 s
- Vc = V × (1 − e−t/τ) = 15.17 V
Voltage after multiples of τ
| Time | Charging | Discharging |
|---|---|---|
| 1 τ (1 s) | 63.2 % | 36.8 % |
| 2 τ (2 s) | 86.5 % | 13.5 % |
| 3 τ (3 s) | 95.0 % | 5.0 % |
| 4 τ (4 s) | 98.2 % | 1.8 % |
| 5 τ (5 s) | 99.3 % | 0.7 % |
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RC Circuit Equations
τ = R × C
Charging: VC = V × (1 − e−t/τ)
Discharging: VC = V0 × e−t/τ
Charging: VC = V × (1 − e−t/τ)
Discharging: VC = V0 × e−t/τ
Worked example
10 kΩ and 100 µF give τ = 1 s. After 1 s of charging from 24 V the capacitor reaches 63.2 % = 15.2 V.
Key insight: a capacitor is considered fully charged or discharged after 5 τ (99.3 %). Use this to estimate how long a DC bus or filter capacitor holds a dangerous voltage.
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Frequently Asked Questions
What is the RC time constant?
The time for a capacitor to charge to 63.2 % of the supply voltage, or discharge to 36.8 %, through a resistor. τ = R × C.
How long does a capacitor take to fully charge?
About 5 time constants, when it reaches 99.3 % of the final voltage.
What is the cutoff frequency of an RC filter?
fc = 1 ÷ (2π × R × C). For 10 kΩ and 100 nF it is 159 Hz.
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