Enter a resistor value and a capacitor value to find the time constant. This helps you estimate how fast the capacitor charges or discharges.
How to use the RC Time Constant Calculator
Enter resistance and capacitance
Enter R (resistance) and pick the unit. Enter C (capacitance) and pick the unit. The calculator converts both to base units (ohms and farads) before calculating.
Read the time constant
Click “Calculate” to get the RC time constant (tau). You will also see common reference points at 1x tau, 3x tau, and 5x tau.
Optional: choose charging or discharging
Open “Advanced options” and choose “Charging” for a rising step response, or “Discharging” for a falling response.
Optional: enter a time or a target percent
If you enter a target percent, the calculator solves for the time needed. If you leave target percent blank and enter a time, it shows the capacitor level at that time.
Optional: show voltage instead of percent
Enter start voltage and final voltage to also show capacitor voltage at time t. For charging, a blank start voltage defaults to 0 V. For discharging, a blank final voltage defaults to 0 V.
How this RC Time Constant Calculator works
1) Unit conversion
The calculator converts your inputs into SI base units:
- Resistance: ohm, kOhm, and MOhm are converted to ohms.
- Capacitance: pF, nF, uF, mF, and F are converted to farads.
- Time (if used): ns, us, ms, s, min, and hr are converted to seconds.
2) Time constant (tau)
For a first order RC circuit, the time constant is:
tau = R x C
This is the standard definition used for a series RC step response. See RC time constant (Wikipedia) and RC transient response (Analog Devices).
3) Reference points at 1x, 3x, and 5x tau
The calculator shows common milestones based on the exponential step response:
- At t = 1 x tau: charging reaches about 63.2% of the final value, discharging falls to about 36.8% remaining.
- At t = 3 x tau: charging is about 95.0%, discharging is about 5.0% remaining.
- At t = 5 x tau: charging is about 99.3%, discharging is about 0.7% remaining.
These percentages come directly from the exponential forms (using e^(-t/tau)). See RC time constant (Wikipedia).
4) Level after a specific time
If you enter a time t, the calculator computes a percent level using the standard RC exponent:
- Charging (percent of final value): level = 1 – e^(-t/tau)
- Discharging (percent remaining): level = e^(-t/tau)
This matches the usual capacitor voltage step response forms. See RC time constant (Wikipedia) and RC transient response (Analog Devices).
5) Time needed for a target percent
If you enter a target percent, the calculator solves for t by rearranging the same exponent:
- Charging to fraction f of final value: t = -tau x ln(1 – f)
- Discharging to fraction f remaining: t = -tau x ln(f)
Here, f is your percent divided by 100. These come from rearranging the standard charging and discharging equations. See RC time constant (Wikipedia).
6) Optional voltage at time t
If you provide start and final voltages, the calculator uses the first order solution:
V(t) = Vfinal + (Vstart – Vfinal) x e^(-t/tau)
This is a general step response form for a first order RC. See RC transient response (Analog Devices) and RC time constants (All About Circuits).
Assumptions and limits
- This models an ideal first order RC response (one resistor, one capacitor, step input).
- It does not model capacitor ESR, leakage, or a non-ideal source resistance unless you include those effects in R.
- For extreme inputs, the internal exp() call is capped to avoid numeric overflow.
Sources
- RC time constant (Wikipedia)
- Activity: Transient Response of an RC Circuit (Analog Devices Wiki)
- Voltage and Current Calculations, RC and L/R Time Constants (All About Circuits)