RC Time Constant Calculator
Time constant, five-tau charge time, and cutoff frequency from R and C.
What it does
Resistor-capacitor circuits charge and discharge in a curve that engineers describe with a single number: the time constant, written tau. Multiply the resistance in ohms by the capacitance in farads and you have it. One tau is the time the capacitor takes to reach 63.2 percent of the applied voltage.
The curve never quite arrives. After one tau the gap is 36.8 percent, after two it is 13.5 percent, and after five time constants the capacitor sits above 99 percent charged in any practical sense. That is why datasheets and lab writeups quote five tau as the settling time for an RC pair.
The same two parts form a low-pass filter. Frequencies well below the cutoff pass through, frequencies well above it fall away, and at the cutoff itself the output drops to 70.7 percent of the input, which is the half-power point. The cutoff frequency is 1 / (2 pi R C).
Unit scales do the heavy lifting in real circuits. A 10 kilohm resistor with a 100 microfarad capacitor gives a one second time constant, slow enough to see with a stopwatch. Flip to a 1 kilohm resistor and a 1 microfarad capacitor and the same math lands at one millisecond, fast enough to shape an audio signal.
The calculator accepts three resistance scales and five capacitance scales, converts everything to ohms and farads, and reports time constants in seconds, milliseconds, microseconds, or nanoseconds. The cutoff frequency follows the same pattern through hertz, kilohertz, and megahertz.
How to use
- Enter the resistance and pick its unit.
- Enter the capacitance and pick its unit.
- Read the time constant first.
- Read five time constants as the practical full charge time.
- Read the cutoff frequency for filter work.
- Keep resistor and capacitor tolerances in mind: 5 to 20 percent swings are normal.
Formula
- tau
- Time constant in seconds: resistance in ohms times capacitance in farads.
- R
- Resistance in ohms after the unit conversion.
- C
- Capacitance in farads after the unit conversion.
- cutoff
- Frequency where the filter output falls to 70.7 percent, in hertz.
The charge equation is V(t) = Vs x (1 - e^(-t/tau)), which gives 63.2 percent at one tau and 99.3 percent at five. The cutoff uses the same product: higher R or higher C means a slower circuit and a lower cutoff frequency.
Worked example
Example: 10 kilohms with 100 microfarads
Resistance 10 kilohms, capacitance 100 microfarads.
- Convert the resistance: 10 kilohms = 10,000 ohms.
- Convert the capacitance: 100 microfarads = 0.0001 farads.
- Time constant: 10,000 x 0.0001 = 1 second.
- Five time constants: 5 seconds to pass 99 percent charged.
- Cutoff frequency: 1 / (2 x pi x 1) = 0.159 Hz.
Reference table
| Time | Charge reached |
|---|---|
| 1 tau | 63.2 percent |
| 2 tau | 86.5 percent |
| 3 tau | 95.0 percent |
| 4 tau | 98.2 percent |
| 5 tau | 99.3 percent |
Limits
- Assumes an ideal resistor and capacitor; real parts carry tolerance and leakage.
- Ignores the source impedance and any load attached to the capacitor.
- Applies to first-order RC circuits only, not to RLC or op-amp active filters.
- Large electrolytic capacitors often have wide tolerance, sometimes 20 percent or more.
Common mistakes
- Entering microfarads while the unit selector still reads nanofarads.
- Mixing scales, such as kilohms with millifarads, and reading the result as if it were the expected range.
- Forgetting that five time constants is the practical charge time, not one.
- Using the cutoff frequency as a sharp wall; the roll-off is gentle, about 20 decibels per decade.
- Ignoring capacitor leakage in timing circuits that hold a charge for minutes.
Try it yourself
Quick checks. Answers sit tucked under each question.
1 kilohm with 1 microfarad?
One time constant 1 ms, five time constants 5 ms, cutoff 159.155 Hz.
4.7 kilohms with 10 nanofarads?
One time constant 47 µs, five time constants 235 µs, cutoff 3.386 kHz.
What percentage of the supply does the capacitor hold after one time constant?
63.2 percent. The remaining gap shrinks by 63.2 percent with each further time constant.
Questions
What is an RC time constant?
The product of resistance and capacitance, in seconds. It sets how fast the capacitor charges through the resistor.
Why is 63.2 percent the one-tau figure?
The charging curve is exponential: 1 - e^-1 equals 0.632, so the capacitor reaches 63.2 percent of the supply in one tau.
Why use five time constants?
At five tau the capacitor sits above 99 percent charged, which is close enough to full for timing and settling purposes.
How does this connect to filters?
The same RC pair makes a low-pass filter whose cutoff sits at 1 / (2 pi R C), the frequency where output falls to 70.7 percent.
What units does the calculator want?
Any of the offered scales. It converts ohms, kilohms, and megohms plus farads through picofarads into base units before the math.
Is the time constant the same for discharging?
Yes. The discharge curve falls to 36.8 percent in one tau, mirroring the charge curve, with the same time constant.