How to use the rc filter time constant calculator
- Enter the resistance and pick ohms, kilohms or megohms.
- Enter the capacitance and pick picofarads, nanofarads, microfarads or millifarads.
- Read the time constant, the corner frequency, the time to settle to the share you choose and the 10 to 90 percent rise time.
- In the advanced options, enter a test frequency and a filter type to get the gain, in decibels, and the phase at that frequency.
Formula
time constant tau = R x C
corner frequency fc = 1 / (2 x pi x R x C)
time to reach a share p of the final value: t = -tau x ln(1 - p)
rise time from 10 to 90 percent = tau x ln(9) = 2.197 x tau
low-pass gain = 1 / sqrt(1 + (f / fc)^2), high-pass gain = (f / fc) / sqrt(1 + (f / fc)^2)
R is in ohms and C in farads, so tau is in seconds. At the corner frequency the gain is 0.7071, which is -3.01 dB. After one time constant a charging capacitor reaches 63.2 percent of its final voltage.
10 kilohms and 100 nanofarads
A 10 kilohm resistor with a 100 nanofarad capacitor has a time constant of 10,000 x 100 x 10^-9 = 0.001 s, 1 ms. The corner frequency is 1 / (2 x pi x 0.001) = 159.15 Hz. The voltage reaches 99 percent of its final value after 0.001 x ln(100) = 4.605 ms and the 10 to 90 percent rise takes 2.197 ms.
At a test frequency of 500 Hz the low-pass gain is 1 / sqrt(1 + (500 / 159.15)^2) = 0.3033, or -10.36 dB, with a phase of -72.34 degrees. A 1 kilohm resistor with a 1 microfarad capacitor gives the same 1 ms time constant, and 1 megohm with 10 picofarads gives 10 microseconds.
Charging, discharging and filtering
The same R and C numbers describe three jobs. A capacitor charges through a resistor along a rising curve and discharges along a falling one, and in both cases the time constant sets the speed. A low-pass filter passes slow signals and cuts fast ones, with the corner at the frequency above. A high-pass filter does the reverse, which is useful to block a steady offset.
Limits of the ideal model
Real parts have tolerances that can be ten percent or more for common capacitors, and capacitor values change with voltage and temperature. A load on the output changes the filter, and so does the resistance of the source. For a stable design, buffer the output and choose parts with the tolerance you need. Pair the results with the ADC Resolution Calculator when the filter feeds a converter.
More electronics and audio tools
For related electronics and audio work, try the AWG Wire Gauge Converter, Audio Buffer Latency Calculator and BPM to Delay Time Calculator.
Assumptions and limits
- The resistor and capacitor are ideal, with no stray inductance or leakage.
- The filter output is not loaded, and the source has no resistance of its own.
- The input is a step for the timing results and a steady sine wave for the gain and phase.
- The settle-to share must be above 0 and below 100 percent.
- The resistor, capacitor and test frequency in the form are examples to replace with your own.
Frequently asked questions
Why is 63.2 percent special?
After one time constant, a charging capacitor has covered 1 minus 1 over e of the way to its final value, which is 63.2 percent. After five time constants it is within 1 percent.
How do I pick R and C for a corner frequency?
Choose one and solve for the other with R x C = 1 / (2 x pi x fc). For 159 Hz the product is 1 millisecond, which suits 10 kilohms and 100 nanofarads or 1 kilohm and 1 microfarad.
Is the corner frequency the same as the cutoff?
Yes. It is also called the -3 dB point, where the output power has fallen to half and the voltage to about 70.7 percent. It is not a sharp edge, because a first-order filter rolls off gently.
How fast does a first-order filter roll off?
Above the corner, the gain falls by 6 dB for each doubling of the frequency, or 20 dB per decade. A steeper roll-off needs more stages.