Answer first
What this calculator tells you
Calculate the time constant, cutoff frequency and settling time of a resistor-capacitor circuit. Choose a resistor and a capacitor to set a delay or a filter's cutoff. Formula: Time constant τ = R × C; cutoff frequency = 1 ÷ (2π × R × C); time to reach 99 percent = 4.6 × τ. At the worked-example inputs, the time constant (s) is 1. Holding every other input steady, moving resistance (ohms) from 8,000 to 12,000 moves the result from 0.8 to 1.2.
Transparent method
The formula
Choose a resistor and a capacitor to set a delay or a filter's cutoff.
Worked example
Example inputs
How to interpret the result
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.
At the worked-example inputs the time constant (s) is 1. It rises with resistance (ohms) and capacitance (µf).
These are exact physics and chemistry formulas. Real-world results add tolerances from component quality, temperature and measurement error that this calculator does not model.
Before you rely on it
What to check
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.
The common error
Where people go wrong with RC time constant calculator
Expecting the circuit to finish in one time constant. It gets only about 63 percent of the way there, and full settling takes several.
Sensitivity evidence
How resistance (ohms) changes the time constant (s)
Holding every other input at the worked-example value, moving resistance (ohms) from 8,000 to 12,000 moves the time constant (s) from 0.8 to 1.2: a spread of 0.4, or 40% of the worked-example result.
| 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 |
| 10,000worked example | 1 | 0.1592 | 4.6 |
| 11,000 | 1.1 | 0.1447 | 5.1 |
| 12,000 | 1.2 | 0.1326 | 5.5 |
Every input, tested
Which input moves the time constant (s) most
Of the 2 inputs, resistance (ohms) moves the time constant (s) most (0.2 across the range tested) and capacitance (µf) moves it least (0.2).
| Input | Tested from | To | Time constant (s) at each end | Swing |
|---|---|---|---|---|
| Resistance (ohms) | 9,000 | 11,000 | 0.9 to 1.1 | 0.2 (20%) |
| Capacitance (µF) | 90 | 110 | 0.9 to 1.1 | 0.2 (20%) |
Two variables at once
Time constant (s) by resistance (ohms) and capacitance (µf)
Across the grid the time constant (s) runs from 0.64 to 1.4. Moving resistance (ohms) from 8,000 to 12,000 shifts it by 0.4 at the middle column, and moving capacitance (µf) from 80 to 120 shifts it by 0.4 at the middle row, so neither is the bigger lever here.
| 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 |
The highlighted cell is the worked example: 1.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Resistance (ohms) | 10,000 | Enter the resistance (ohms) used in this calculation. |
| Capacitance (µF) | 100 | Enter the capacitance (µf) used in this calculation. |
| Time constant (s) | 1 | |
| Cutoff frequency (Hz) | 0.1592 | |
| Time to 99 percent (s) | 4.6 | |
Inputs, definitions and assumptions
Resistance (ohms)
Enter the resistance (ohms) used in this calculation. The prefilled worked-example value is 10,000.
Capacitance (µF)
Enter the capacitance (µf) used in this calculation. The prefilled worked-example value is 100.
How to use this calculator
- 1Verify the inputs. Gather resistance (ohms) and capacitance (µf) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the time constant (s) at 1. Store your own version of it as Scenario A.
- 3Test one change. Start with resistance (ohms), the input with the biggest effect here: moving resistance (ohms) from 9,000 to 11,000 takes the time constant (s) from 0.9 to 1.1, a swing of 20% of the worked-example figure.
- 4Check the extremes. At half the example resistance (ohms) (5,000) the time constant (s) is 0.5; at double (20,000) it is 2.
People also ask
Frequently asked questions
How do you calculate RC time constant?
Time constant τ = R × C; cutoff frequency = 1 ÷ (2π × R × C); time to reach 99 percent = 4.6 × τ. At the worked-example inputs the time constant (s) is 1.
What does the RC time constant result mean?
Choose a resistor and a capacitor to set a delay or a filter's cutoff. At the worked-example inputs the time constant (s) is 1. It rises with resistance (ohms) and capacitance (µf).
How much does resistance (ohms) change the time constant (s)?
Holding every other input at the worked-example value, moving resistance (ohms) from 8,000 to 12,000 moves the time constant (s) from 0.8 to 1.2, a spread of 0.4.
What are the limits of this RC time constant calculator?
These are exact physics and chemistry formulas. Real-world results add tolerances from component quality, temperature and measurement error that this calculator does not model. The tables on this page test resistance (ohms) only from 8,000 to 12,000; a value outside that range is not tabulated here.
Which input moves the time constant (s) most in the RC time constant calculator?
Ranked by how far each moves the time constant (s) across the range tested: resistance (ohms) (0.2, 20%) and capacitance (µf) (0.2, 20%).
If I double resistance (ohms) in the RC time constant calculator, does the time constant (s) double?
Doubling it from 10,000 to 20,000 takes the time constant (s) from 1 to 2, which is 2.00 times the worked-example figure. So the result scales almost exactly in proportion. Halving it to 5,000 gives 0.5.
How much does capacitance (µf) matter in the RC time constant calculator?
The worked example uses 100. Holding every other input at its worked-example value, moving capacitance (µf) from 90 to 110 takes the time constant (s) from 0.9 to 1.1, a swing of 20% of the worked-example figure.
Which inputs change the cutoff frequency (hz) in the RC time constant calculator?
At the worked-example inputs it is 0.1592. Resistance (ohms) takes it from 0.1768 to 0.1447 and capacitance (µf) takes it from 0.1768 to 0.1447.
Which inputs change the time to 99 percent (s) in the RC time constant calculator?
At the worked-example inputs it is 4.6. Resistance (ohms) takes it from 4.1 to 5.1 and capacitance (µf) takes it from 4.1 to 5.1.
Why do motors draw more current than their wattage suggests?
A motor's power factor is below 100 percent, so it draws extra current that does no useful work. Starting a motor can also draw several times the running current for a moment.
Does the combined gas law work if gas escapes?
No. It assumes a fixed amount of gas. If gas is added or lost, the ideal gas law with the amount of gas as a variable is the right tool.
Sources and evidence
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