Calculate RC circuit time constant, charge time, and cutoff frequency
Electrical Calculator
RC time constant — Quick answer
The RC time constant (τ) is the time for a capacitor charging through a resistor to reach ~63.2% of its final voltage. After 5τ the capacitor is effectively fully charged.
τ = R × C (seconds) VC(t) = Vfinal × (1 − e-t/τ) (charging) VC(t) = V0 × e-t/τ (discharging)
R — resistance (Ω)
C — capacitance (F)
τ — time constant (s)
V0 — initial voltage on capacitor
Worked example: R = 10 kΩ, C = 1 μF. τ = 10,000 × 1×10-6 = 10 ms. At t = 10 ms, voltage = 0.632 × Vsupply. Full charge (~99.3%) at 5τ = 50 ms.
Charging percentage vs time (multiples of τ)
Time (multiples of τ)
Charge %
Discharge %
1τ
63.2 %
36.8 %
2τ
86.5 %
13.5 %
3τ
95.0 %
5.0 %
4τ
98.2 %
1.8 %
5τ
99.3 %
0.7 %
7τ
99.9 %
0.1 %
Standard / source: Classical RC circuit theory; first described in 19th-century telegraph engineering (Lord Kelvin).
Used for: Filter cutoff frequency design (fc = 1/(2πRC)), debounce circuits, timing delays, low-pass / high-pass filters, oscilloscope probe compensation.
⚡ RC Time Constant Calculator
Formula
This calculator uses the standard rc time constant calculator formula:
Time Constant Formula
τ = R × C (seconds)
Frequently Asked Questions
What is the RC time constant?⌄
The RC time constant (τ) is the time it takes for a capacitor to charge to approximately 63.2% of the supply voltage through a resistor. It equals R × C in seconds.
How long does it take an RC circuit to fully charge?⌄
After 5τ (five time constants), the capacitor is considered fully charged to 99.3% of the supply voltage.
What is the formula for RC time constant?⌄
τ = R × C, where R is resistance in ohms and C is capacitance in farads. τ is in seconds.
How do I calculate the cutoff frequency of an RC filter?⌄
fc = 1 / (2π × R × C). This is the −3 dB frequency where the filter attenuates the signal to 70.7% of its input amplitude.
What is a low-pass RC filter?⌄
A low-pass RC filter passes low-frequency signals and attenuates high-frequency signals above the cutoff frequency fc = 1/(2πRC).
How does capacitance affect charge time?⌄
A larger capacitor takes longer to charge. Doubling the capacitance doubles the time constant τ and thus doubles the charge time.
Need Advanced Calculations?
Use the full AI Calculator suite — 350+ precision engineering and science calculators with PDF report export.