RC Time Constant Calculator
Calculate the RC time constant (τ = R × C) and charging/discharging percentages for resistor–capacitor circuits.
What the RC time constant calculator does
The calculator multiplies resistance by capacitance to give the time constant τ (tau) of a resistor-capacitor circuit, then lists how far the capacitor has charged or discharged after 1τ, 2τ, 3τ, 4τ and 5τ. Enter resistance in ohms and capacitance in farads, press Calculate, and the result appears in seconds with automatic scaling to milliseconds or microseconds.
The formula
For a resistor R in series with a capacitor C:
τ = R × C
With R in ohms and C in farads, τ is in seconds. The time constant is the time the capacitor voltage takes to reach 63.2% of its final value while charging, or to fall to 36.8% of its starting value while discharging. The full curves are:
- Charging: V(t) = Vsource × (1 − e−t/τ)
- Discharging: V(t) = Vinitial × e−t/τ
The number 63.2% is simply 1 − 1/e, where e ≈ 2.718. It is not a design choice; it falls out of the exponential solution to the circuit equation.
Charge and discharge table
| Elapsed time | Charged to | Remaining while discharging |
|---|---|---|
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 3τ | 95.0% | 5.0% |
| 4τ | 98.2% | 1.8% |
| 5τ | 99.3% | 0.7% |
Engineers treat 5τ as “fully charged” because the remaining 0.7% is below the tolerance of most components. If you need a precise time for a specific voltage, rearrange the charging equation: t = −τ × ln(1 − V/Vsource).
Worked example
A 1 kΩ resistor feeds a 1 µF capacitor from a 5 V supply. τ = 1000 × 0.000001 = 0.001 s, or 1 ms. After 1 ms the capacitor sits at 3.16 V, after 2 ms at 4.32 V, and after 5 ms at 4.97 V. To reach exactly 4.0 V takes t = −1 ms × ln(1 − 4/5) = 1.61 ms.
Change the resistor to 10 kΩ and τ becomes 10 ms; change the capacitor to 100 nF instead and τ drops to 100 µs. Resistance and capacitance affect the time constant equally, so you can trade one for the other. In practice, very large resistances make the circuit sensitive to leakage and noise, and very large capacitances are physically bulky, so designers usually keep R between about 1 kΩ and 1 MΩ.
Entering capacitance correctly
Capacitors are rarely labelled in farads. Convert before you type:
| Marking | Farads | Scientific |
|---|---|---|
| 100 pF | 0.0000000001 | 1 × 10−10 |
| 10 nF | 0.00000001 | 1 × 10−8 |
| 100 nF (0.1 µF) | 0.0000001 | 1 × 10−7 |
| 1 µF | 0.000001 | 1 × 10−6 |
| 470 µF | 0.00047 | 4.7 × 10−4 |
Ceramic capacitors often carry a three-digit code: 104 means 10 × 104 pF = 100 nF.
Where the time constant matters
Low-pass and high-pass filters
The same RC pair forms a first-order filter with cutoff frequency fc = 1 / (2π × τ). A 1 ms time constant gives a cutoff of 159 Hz. Use the RC low-pass filter calculator or RC high-pass filter calculator when you start from a frequency rather than a time.
Switch debouncing
Mechanical switches bounce for 1 to 10 ms. An RC network with τ of a few milliseconds, followed by a Schmitt trigger input, smooths the bounce into a single clean edge. A 10 kΩ resistor and 100 nF capacitor (τ = 1 ms, 5τ = 5 ms) is a common starting point.
Power-on delays and soft start
Reset circuits and soft-start controls use an RC network to hold a line low until the supply settles. For a delay of 100 ms you might pick 100 kΩ and 1 µF; the exact threshold depends on the logic level of the input that reads the capacitor voltage.
Sample-and-hold and ADC inputs
An ADC’s internal sampling capacitor must charge through the source resistance within the acquisition window. If the source impedance is 10 kΩ and the sampling capacitor is 10 pF, τ is 100 ns; the acquisition time should allow at least 5τ to 10τ for full-resolution accuracy.
Timing with a 555 or comparator
Oscillators and one-shots built around a 555 timer set their periods with RC networks. The chip’s thresholds at 1/3 and 2/3 of the supply correspond to fixed multiples of τ, which is why the datasheet formulas contain constants such as 0.693 and 1.1.
Component choices that change the real τ
- Tolerance. A 20% electrolytic capacitor and a 5% resistor can put the real time constant 25% away from the calculated one. Use 1% resistors and film or C0G/NP0 ceramic capacitors for timing.
- Temperature drift. X7R ceramics can lose 15% of their capacitance across their rated range; Y5V parts can lose far more.
- Leakage. Electrolytic capacitors leak enough current to matter when R is above roughly 100 kΩ, which stretches or caps the charging curve.
- Source and load impedance. The resistance seen by the capacitor includes the output resistance of whatever drives it and any load in parallel, not just the resistor you placed.
Related calculators
The capacitor charge time calculator solves for the time to reach a chosen voltage. The capacitive reactance calculator gives the AC impedance of the capacitor at a given frequency, and the LC resonant frequency calculator covers the inductor-capacitor case.
External references
Frequently asked questions
Why is the time constant in seconds when I multiply ohms by farads?
An ohm is a volt per ampere and a farad is a coulomb per volt. Their product is coulombs per ampere, and an ampere is a coulomb per second, so the result is seconds.
Does the supply voltage change τ?
No. A higher voltage means more charge is stored, but the current is proportionally higher, so the time to reach any given percentage is the same.
What is the time constant for resistors or capacitors in combination?
Combine them first. Series resistors add; parallel capacitors add. Then multiply the equivalent R by the equivalent C.
How long until the capacitor is fully charged?
Mathematically it never quite reaches the supply voltage. In practice 5τ (99.3%) is treated as full, and 7τ (99.9%) for precision work.
Can I use this for an RL circuit?
The form is the same, but the time constant is τ = L / R with L in henries. The percentages in the table apply to current in an inductor exactly as they apply to voltage on a capacitor.