RC Time Constant: formula
Enter resistance in ohms and capacitance in microfarads. A 10-kΩ part must be entered as 10,000 Ω; 100 µF is 0.0001 F in the underlying equation. Use actual component specifications or measured values and identify the ideal first-order circuit boundary.
RC Time Constant: worked example
| Resistance (ohms) | 10,000 |
|---|---|
| Capacitance (µF) | 100 |
| Time constant (s) | 1 |
| Cutoff frequency (Hz) | 0.1592 |
| Time to 99 percent (s) | 4.6 |
A real network can include source resistance, loading, leakage, equivalent series resistance and component tolerances. The first-order step model does not include those effects automatically. Its low-pass cutoff expression applies to the stated topology; another network needs its own transfer function.
RC Time Constant: changing Resistance (ohms)
| Resistance (ohms) | Time constant (s) | Cutoff frequency (Hz) | Time to 99 percent (s) |
|---|---|---|---|
| 8,000 | 0.8 | 0.1989 | 3.7 |
| 9,000 | 0.9 | 0.1768 | 4.1 |
| 10,000 (example) | 1 | 0.1592 | 4.6 |
| 11,000 | 1.1 | 0.1447 | 5.1 |
| 12,000 | 1.2 | 0.1326 | 5.5 |
RC Time Constant: compare input ranges
| Input | Tested from | To | Time constant (s): low input | Time constant (s): high input | Swing |
|---|---|---|---|---|---|
| Resistance (ohms) | 9,000 | 11,000 | 0.9 | 1.1 | 0.2 (20%) |
| Capacitance (µF) | 90 | 110 | 0.9 | 1.1 | 0.2 (20%) |
RC Time Constant: individual input comparisons
| Input | Value | Time constant (s) | Cutoff frequency (Hz) | Time to 99 percent (s) |
|---|---|---|---|---|
| Resistance (ohms) | 8,000 | 0.8 | 0.1989 | 3.7 |
| 9,000 | 0.9 | 0.1768 | 4.1 | |
| 10,000 | 1 | 0.1592 | 4.6 | |
| 11,000 | 1.1 | 0.1447 | 5.1 | |
| 12,000 | 1.2 | 0.1326 | 5.5 | |
| Capacitance (µF) | 80 | 0.8 | 0.1989 | 3.7 |
| 90 | 0.9 | 0.1768 | 4.1 | |
| 100 | 1 | 0.1592 | 4.6 | |
| 110 | 1.1 | 0.1447 | 5.1 | |
| 120 | 1.2 | 0.1326 | 5.5 |
RC Time Constant: combined input changes
| Resistance (ohms) / Capacitance (µF) | 80 | 100 | 120 |
|---|---|---|---|
| 8,000 | 0.64 | 0.8 | 0.96 |
| 9,000 | 0.72 | 0.9 | 1.1 |
| 10,000 | 0.8 | 1 | 1.2 |
| 11,000 | 0.88 | 1.1 | 1.3 |
| 12,000 | 0.96 | 1.2 | 1.4 |
RC Time Constant: which assumptions move the result?
RC Time Constant: values and definitions
| Quantity and definition | Value used |
|---|---|
| Resistance (ohms) | 10,000 |
| Capacitance (µF) | 100 |
| Time constant (s) | 1 |
| Cutoff frequency (Hz) | 0.1592 |
| Time to 99 percent (s) | 4.6 |
RC Time Constant: half and double Resistance (ohms)
| Resistance (ohms) | Time constant (s) |
|---|---|
| 5,000 | 0.5 |
| 10,000 | 1 |
| 20,000 | 2 |
Common error: Expecting the circuit to finish in one time constant. It gets only about 63 percent of the way there, and full settling takes several.
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A resistor and a capacitor together set how quickly a voltage changes. The time constant is the product of the two: 10,000 ohms and 100 microfarads give 1 second. After one time constant a charging capacitor reaches about 63 percent of its final voltage, and after 4.6 constants about 99 percent.
The same product sets a filter's cutoff, here about 0.159 hertz.
Convert capacitance to farads before you multiply, or use the microfarad value the page asks for. The prefix is the easy place to be off by a million.
See resistance combinations on the resistor calculator, voltage on the voltage divider page and power on the Ohm's law calculator. The frequency converter changes units, and the exponential growth and half-life calculators describe the same kind of curve. The LED resistor page covers another basic circuit.
What is the time constant of an RC circuit?
The product of resistance and capacitance. After one time constant a charging capacitor reaches about 63% of its final voltage.
How long does a capacitor take to fully charge?
Roughly five time constants, by which point it is above 99% charged.
What is the cutoff frequency?
The frequency at which a simple RC filter passes about 70% of the signal, equal to one over two pi times the resistance and capacitance.