RC Time Constant Calculator
Calculate the time constant and charge/discharge timing for resistor-capacitor circuits.
What is an RC time constant?
An RC (resistor-capacitor) circuit's time constant, denoted by the Greek letter tau, equals R multiplied by C (in ohms and farads). It represents the time needed for the capacitor voltage to reach approximately 63.2% of its final value when charging, or to drop to 36.8% when discharging. After five time constants (5*tau), the capacitor is considered fully charged or discharged (over 99%).
RC circuits are fundamental building blocks in electronics. They are used as low-pass filters (smoothing signals), high-pass filters (blocking DC), timing circuits, debounce circuits, coupling/decoupling networks, and many other applications. Understanding the time constant is essential for designing these circuits correctly.
Charging and discharging curves
Charging follows an exponential curve: V(t) = Vmax * (1 - e^(-t/RC)). At 1 tau, voltage reaches 63.2%. At 2 tau: 86.5%. At 3 tau: 95.0%. At 4 tau: 98.2%. At 5 tau: 99.3%. Discharging follows the inverse: V(t) = V0 * e^(-t/RC), dropping to 36.8% at 1 tau, 13.5% at 2 tau, and so on.
How to use this tool
Enter the resistance (ohms, kilohms, or megohms) and capacitance (picofarads, nanofarads, or microfarads). The calculator shows the time constant tau and the voltage at key multiples of tau. It also generates a visual charging/discharging curve so you can see the exponential behavior.
RC as a frequency filter
An RC circuit acts as a low-pass filter with a cutoff frequency of f = 1 / (2 * pi * R * C). Frequencies below this pass through; frequencies above are attenuated. A 10K resistor with a 100nF capacitor gives a cutoff frequency of about 159 Hz โ useful for filtering out high-frequency noise from audio signals.
Worked example
Pair a 10 kฮฉ resistor with a 100 ยตF capacitor. The time constant is ฯ = R ร C = 10,000 ร 0.0001 = 1 second. After one ฯ the capacitor charges to 63% of the supply voltage, after 3ฯ (3 s) to about 95%, and after 5ฯ (5 s) to over 99%, which is usually treated as fully charged.
Common mistakes
A frequent mistake is mixing units โ capacitance must be in farads, not microfarads, before multiplying by ohms, so 100 ยตF is 0.0001 F. Another is assuming the capacitor charges linearly; charging follows an exponential curve, fast at first and slowing as it nears the supply voltage. Forgetting that discharge uses the same ฯ but decays instead of rises is also common.
Frequently asked questions
Why 63.2% and not some round number?
The 63.2% comes from the mathematical constant e (Euler's number, approximately 2.718). After one time constant, the charged fraction is (1 - 1/e) = 0.6321... or 63.21%. This is not an arbitrary choice โ it naturally falls out of the exponential differential equation that governs RC circuit behavior.
Does the time constant depend on the supply voltage?
No. The time constant tau = R * C depends only on the component values. The voltage curve scales with the supply voltage, but the percentage of charge at any given time remains the same. A 5V circuit and a 12V circuit with the same R and C values reach the same percentage of their respective final voltages at the same time.
How many time constants until a capacitor is fully charged?
Mathematically a capacitor never reaches 100%, but after five time constants it is charged to about 99.3%, close enough to be treated as full in practice. Engineers commonly use 5ฯ as the settling time for RC circuits, whether charging or discharging.