Electrical & Electronics
RC Timing & Filter Calculator
Calculate RC time constants, capacitor charging and discharging, and passive low-pass or high-pass filter response.
Your inputs
Your results
- Time constant · τ
- —
- Cutoff frequency
- —
- Capacitor voltage
- —
- Voltage fraction
- —
- Voltage gain
- —
- Phase shift
- —
| Time to target | — |
|---|---|
| Voltage gain · dB | — |
τ = R × CExplore RC charging, discharging and first-order filters
Use one resistor and capacitor to estimate a time constant, a capacitor's voltage over time or an ideal filter's frequency response. Charging starts from an uncharged capacitor; discharging starts from your entered initial voltage. Filter modes represent an unloaded first-order RC network. The calculation excludes component tolerance, leakage and additional source or load impedance.
Step by step
- Choose charging, discharging, low-pass or high-pass mode. Enter resistance and capacitance, checking the units: the fields default to kΩ and nF.
- For timing, enter supply or initial voltage, elapsed time in ms and a target percentage. For filtering, enter the positive signal frequency in Hz and compare it with the displayed cutoff frequency.
- Read the matching results and response plot. Timing shows capacitor voltage and time to the target; filtering shows voltage gain, decibels and phase. The plot uses normalized axes, so relate its position to the displayed time constant or cutoff.
Settings and limits
- Time constant and cutoff
- The shared time constant is τ = R × C and cutoff is fc = 1 / (2πRC). Increasing either component increases the time constant and lowers the cutoff. These quantities remain available when you switch between timing and filter modes.
- Target percentage
- The target must be strictly between 0% and 100%. In charging mode it is the fraction of final supply voltage; in discharging mode it is the fraction of initial voltage remaining. The ideal exponential approaches its end value without reaching it in a finite time.
- Gain and phase
- Filter gain is an output-to-input voltage ratio, not a power ratio. Low-pass output is taken across the capacitor; high-pass output is taken across the resistor. The phase result describes the sinusoidal output relative to the input in the selected ideal network.
Worked example
Choose charging with R = 10 kΩ, C = 100 nF, a 5 V supply, 1 ms elapsed time and a 90% target. The time constant is 1 ms and cutoff is about 159.155 Hz.
| R | C | τ | fc | Vc (1 ms) | t (90%) |
|---|---|---|---|---|---|
| 10 kΩ | 100 nF | 1 ms | 159.155 Hz | 3.1606 V | 2.30259 ms |
At 1 ms, capacitor voltage is about 3.1606 V, or 63.2121%; reaching 90% takes about 2.30259 ms. Discharging from 5 V gives about 1.8394 V at the same elapsed time. In low-pass mode at the displayed cutoff, gain is about 0.707107 V/V, with −3.0103 dB and −45° phase.
Questions and troubleshooting
Why does the target time change when I switch to discharging?
The target now means voltage remaining, rather than voltage reached while charging. A high target is reached early in discharge and later in charge. Choose the remaining-voltage percentage that corresponds to your intended threshold.
Can I use this as the response of a loaded filter?
The model assumes that the output does not draw current and that the input source adds no resistance. A significant load or source resistance changes the circuit. Include those effects in a suitable circuit model rather than treating this result as the loaded response.
Why are the timing or filter results blank?
Resistance and capacitance must be positive. Timing requires nonnegative voltage and elapsed time, with a target inside its allowed range; filter frequency must be positive. Correct the highlighted input and ensure the entered unit matches the field.