The RC time constant tells you how fast a capacitor charges or discharges through a resistor. This free calculator gives the time constant from your R and C values, draws the charge or discharge curve, and shows the time needed to reach any voltage.
Enter the resistance, the capacitance and the supply voltage, then press Run to watch the capacitor fill. Use the Full screen button at the top right for a larger view.
How to use the RC time constant calculator
- Choose Charge or Discharge.
- Enter the resistance, the capacitance and the supply voltage. You can type values the engineering way, such as 4k7, 100n or 4u7.
- Read the time constant and the other results on the right.
- Press Run to play the curve, or drag the slider to any moment. The boxes under the chart show the voltage and current at that time.
- Use “Time to reach” to get the time for a percentage or a voltage of your choice.
- Open the “Find R or C” tab when you know the time you want and need the part values.
What is the RC time constant?
The RC time constant is the time a capacitor needs to charge to 63.2 % of the supply voltage through a resistor. It is written with the Greek letter tau (τ).
A capacitor does not charge at a steady speed. It charges fast at the start and then slower and slower, because the current falls as the capacitor voltage rises. The time constant describes this curve with one number.
RC time constant formula
The formula is τ = R × C, with R in ohms and C in farads. The result is in seconds.
Example: a 10 kΩ resistor and a 100 µF capacitor give τ = 10 000 Ω × 0.0001 F = 1 second.
The supply voltage is not in the formula. A higher voltage makes the capacitor reach a higher final voltage, but it takes the same time to get there.
Capacitor charging equation
While charging from 0 V, the capacitor voltage is $$V_C(t) = V_S \left(1 – e^{-\frac{t}{\tau}}\right)$$ Vs is the supply voltage and t is the time since charging started.
Capacitor discharging equation
While discharging through the resistor, the capacitor voltage is $$V_C(t) = V_S e^{-\frac{t}{\tau}}$$ After one time constant, the voltage has fallen to 36.8% of its starting value. The current follows the same exponential decay curve: $$i(t) = -\frac{V_S}{R} e^{-\frac{t}{\tau}}$$ Its magnitude is highest at the first moment, with a peak value of $$I_{\text{peak}} = \frac{V_S}{R}$$ and then gradually decreases towards zero.
How long does a capacitor take to charge?
In theory a capacitor never reaches 100 %. In practice, engineers treat it as fully charged after 5 time constants, when it has reached 99.3 %.
For any other level, use:
$$t = -\tau \times \ln\left(1 – \frac{V}{V_S}\right)$$
Two values worth remembering:
- 50 % takes 0.69τ.
- 90 % takes 2.3τ.
With the example above 1τ, the capacitor reaches 90 % after 2.3 seconds and is fully charged after 5 seconds.
RC time constant and cutoff frequency
The same resistor and capacitor also form a low-pass filter. Its cutoff frequency is:
$$f = \frac{1}{2\pi \times R \times C}$$
which is the same as:
$$f = \frac{1}{2\pi \times \tau}$$
The rise time from 10 % to 90 % is about $$2.2\tau$$A slow RC circuit (large τ) has a low cutoff frequency, and a fast one has a high cutoff frequency. The calculator shows both values.
Where RC circuits are used
- Switch debouncing: a small RC filter removes the bouncing of a push button before a microcontroller reads it.
- Reset and power-on delay: the capacitor holds a reset pin low for a short time after power is applied.
- Filtering: RC low-pass filters smooth a PWM signal or remove noise from a sensor signal.
- Timing: simple timers and oscillators use the charge time of a capacitor.
How to choose R and C
Many pairs give the same time constant, so a few practical rules help:
- Resistor: values between 1 kΩ and 1 MΩ work well in most low-voltage circuits. A very small resistor draws a high peak current, and a very large one makes the circuit sensitive to leakage and noise.
- Capacitor: choose a common value first, then calculate the resistor. Resistors come in many more values than capacitors.
- Tolerance: many capacitors have a tolerance of 10 or 20 %, so the real time can differ from the calculated one by the same amount.
The “Find R or C” tab does this work for you. It gives the missing part for the time you want, with the nearest standard value.
Limits of this calculator
The calculator uses an ideal RC circuit. It does not include the resistance of the source, the leakage and series resistance of the capacitor, or temperature effects. For most timing and filter circuits the result is close to a real measurement, within the tolerance of the parts.
Frequently asked questions
What is the time constant of a 10 kΩ resistor and a 100 µF capacitor?
One second. The RC time constant is R × C = 10 000 Ω × 0.0001 F = 1 s.
Why is a capacitor fully charged after 5 time constants?
After 5 time constants the capacitor has reached 99.3 % of the supply voltage. The remaining 0.7 % is too small to matter in most circuits, so 5 τ is used as the practical charge time.
Does the supply voltage change the RC time constant?
No. The time constant depends only on R and C. The voltage changes the final value and the current, but not the time.