RC Time Constant Calculator (τ = RC)
Calculate the RC time constant τ = RC, the corner frequency of an RC filter, and the time to full charge (5τ). Enter resistance in ohms and capacitance in µF.
How to use this tool
- Enter resistance (r) and capacitance (c) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your time constant τ (s) and the full breakdown beneath it.
The RC time constant τ = R × C (seconds) describes how quickly a capacitor charges or discharges through a resistor. After one τ the capacitor reaches ≈63.2% of full charge; after 5τ it is ≈99.3% charged (considered fully charged). The corner frequency of an RC low-pass filter is f_c = 1/(2πRC).
Formula
Time Constant: τ = R × C
Corner Frequency: fc = 1 / (2πτ)
Full Charge Time: 5τ = 5 × R × C
Where R is in ohms and C is in farads (input in µF is divided by 106).
How it works
The RC time constant τ defines how quickly a capacitor charges or discharges through a resistor: after one time constant, the capacitor voltage reaches approximately 63.2% of its final value. The capacitor is considered fully charged after five time constants (99.3%).
The corner (or cut-off) frequency fc is the −3 dB point of the RC low-pass or high-pass filter formed by the same components. At this frequency, output power is halved. Capacitance is entered in microfarads and converted internally to farads for the calculation.
Worked example
Worked example — 10 kΩ and 10 µF
- Inputs: R = 10,000 Ω, C = 10 µF = 10 × 10−6 F.
- τ = 10,000 × 10 × 10−6 = 0.1 s (100 ms).
- Corner frequency fc = 1 / (2π × 0.1) ≈ 1.59 Hz.
- Full charge time = 5 × 0.1 = 0.5 s.
τ: 0.1 s | τ (ms): 100.0 ms | Corner Frequency: 1.59 Hz | Full-charge time (5τ): 0.5 s
Key terms
- Time Constant (τ)
- The time (in seconds) for a capacitor to charge to 63.2% of its final voltage, or discharge to 36.8% of its initial voltage, through a resistor.
- Corner Frequency (fc)
- The frequency at which the output of an RC filter is attenuated by −3 dB (power halved). Calculated as 1/(2πτ).
- Full Charge Time (5τ)
- After five time constants a capacitor is effectively fully charged (>99%). This is the practical rule-of-thumb used in circuit timing design.
- Low-Pass Filter
- An RC configuration where the output is taken across the capacitor. Frequencies well below fc pass with little attenuation; higher frequencies are attenuated.
- Microfarad (µF)
- A unit of capacitance equal to 10−6 farads, commonly used for electrolytic and ceramic capacitors in timing and filter circuits.
Frequently asked questions
- What is the time constant used for?
- The time constant tells you how fast an RC circuit responds. In filters it sets the -3 dB frequency; in timing circuits it controls pulse width.
- How do I convert nF or pF to µF?
- 1 µF = 1000 nF = 1,000,000 pF. A 100 nF cap = 0.1 µF; a 10 pF cap = 0.00001 µF.