RC time constant calculator
Enter R and C, get the time constant and charge.
What is the RC time constant?
τ = R × C, in seconds when R is in ohms and C in farads. It sets how fast a capacitor charges or discharges through a resistor (OpenStax University Physics).
How much does a capacitor charge in one time constant?
To 1 − e⁻¹ = 63.2% of its final voltage. After 2τ it is at 86.5%, after 3τ 95.0%, and after 5τ 99.3% — close enough to full for most purposes.
And when discharging?
The voltage falls to e⁻¹ = 36.8% of its starting value after one time constant, and to 0.7% after five.
Example
A 10 kΩ resistor with a 100 μF capacitor: τ = 10,000 × 0.0001 = 1 second. After 2 seconds the capacitor is 86.5% charged.
What is the charging formula?
V(t) = V₀ (1 − e^(−t/τ)) while charging and V(t) = V₀ e^(−t/τ) while discharging, where V₀ is the supply or starting voltage.
How long does it take to reach a given voltage?
Solve the charging equation for the time: t = −τ ln(1 − V ÷ V₀). The charging voltage reaches 99% of the supply after 4.6 time constants and 99.9% after 6.9. The 10% to 90% rise time, which engineers often quote, is 2.20 time constants. Because the curve only approaches the supply voltage, it never reaches 100% in finite time.
Does the source resistance count?
Yes. τ uses all the resistance in the charging loop. OpenStax's relaxation-oscillator example has a 100 Ω resistor and 1 Ω of internal resistance with a 50 mF capacitor: τ = 101 Ω × 0.05 F = 5.05 s, not 5.00 s.
How the equations work
A capacitor charged through a resistor draws a current that starts at the supply voltage divided by the resistance and then falls exponentially as the capacitor voltage rises and leaves less voltage across the resistor. The same time constant, τ = RC, governs the current, the capacitor voltage and the voltage across the resistor. The equations assume one resistor in series with an ideal capacitor, a constant supply and a capacitor that starts empty when charging. Real parts have tolerances, which add straight into τ, and a leaky capacitor or a load in parallel changes the curve.
Worked example
OpenStax uses an intermittent windshield wiper: a 10.00 mF capacitor charged from 12.00 V, with the wiper triggered when the capacitor reaches 10.00 V, and a delay of 10 seconds wanted. Solving t = −τ ln(1 − 10 ÷ 12) for τ gives 5.58 s, so the resistor is 558.11 Ω, the value OpenStax finds. Checking it the other way, 558.11 Ω with 10.00 mF has τ = 5.58 s, and after 10 s the capacitor is 83.3% charged, or 10.00 V on a 12.00 V supply.
Common mistakes
Unit slips are the biggest source of wrong answers. A 10 kΩ resistor with a 100 µF capacitor gives τ = 1.00 s; typing 100 as farads instead of microfarads gives 1,000,000 s. Leaving out the source resistance is the next. A third is expecting a full charge after one time constant, when the capacitor has only reached 63.2%. The last is mixing up charging and discharging: while discharging the voltage falls from its starting value, to 36.8% after one time constant.
Sources: OpenStax, University Physics Volume 2, section 10.5, “RC Circuits,” including Examples 10.8 and 10.9 (openstax.org, read October 27, 2026). Time to reach a given fraction and the 2.2 τ rise time follow from the charging equation. Related: capacitor calculator, 555 timer calculator, series and parallel calculator, resonant frequency calculator. How we check our calculators.