Calculators
RC time constant calculator
By Bulan Sarkar
The time constant of a resistor and capacitor is τ = R × C. With R in ohms and C in farads, τ comes out in seconds. After one τ a charging capacitor sits at 63.2 % of the supply voltage, and a discharging one has fallen to 36.8 % of where it started. After 5τ it is at 99.3 %, which most designs treat as fully charged.
Put in R, C and the supply to get τ, the voltage at any moment and the time to reach a target voltage. Or give the delay you want and get the nearest standard resistor. The result shows the spread from capacitor tolerance and warns when leakage could stall a slow timer.
4k7, 4.7k and 4700 all work.
Read as 100 µF. Type 100u for 100 µF, 100n for 0.1 µF.
Blank means 0 V. Use it for a part-charged capacitor.
Type a time to see the voltage then.
Blank uses ±20 % for this type.
Printed on the sleeve. Turns on the leakage check.
- Time constant, τ = RC
- 1 s
- 800 ms to 1.2 s at ±20 %
- Time to reach 9 V
- 1.39 s
- 1.11 s to 1.66 s with tolerance
- Cutoff frequency, 1/(2πRC)
- 0.1592 Hz
- the same pair as a low-pass filter
| After | Time | Voltage | Of the way there |
|---|---|---|---|
| 1τ | 1 s | 7.59 V | 63.2 % |
| 2τ | 2 s | 10.4 V | 86.5 % |
| 3τ | 3 s | 11.4 V | 95 % |
| 4τ | 4 s | 11.8 V | 98.2 % |
| 5τ | 5 s | 11.9 V | 99.3 % |
Equations from OpenStax University Physics Vol. 2, §10.5; cutoff frequency from TI SLOA049D, p. 11; tolerance and leakage limits from Nichicon's UVR catalogue. Checked 8 October 2026.
How a capacitor charges through a resistor
When a capacitor charges through a resistor, the current is largest at the start and drops off as the capacitor voltage rises toward the supply. The voltage follows V(t) = Vs × (1 − e^(−t/RC)). That curve never quite reaches Vs, so engineers count in time constants. Discharge runs the same curve in reverse: V(t) = V₀ × e^(−t/RC).
| Time | Charging (% of supply) | Discharging (% of start) |
|---|---|---|
| 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 % |
Time to reach a voltage
The usual question is how long the capacitor takes to reach a given voltage. A 555 timer trips at two thirds of its supply, and a microcontroller input switches at some fraction of VDD. Rearranging the charging equation gives:
t = R × C × ln(Vs / (Vs − Vtarget))
For discharge from V₀ down to a target, t = R × C × ln(V₀ / Vtarget). The calculator solves either way and also takes a starting voltage other than zero, for a capacitor that is already part charged.
Where the 555's 1.1 comes from
In monostable mode a 555 charges its timing capacitor through R from 0 V until it hits two thirds of VCC (TI SLFS022K, pp. 11–12). Put that into the formula above and t = RC × ln(1 / (1 − 2/3)) = RC × ln 3 = 1.0986 RC. TI rounds that to 1.1 × R × C. The supply cancels out, which is why a 555's timing doesn't move when the supply does.
Why your timing doesn't match the maths
The formulas are exact, but the parts on your bench are not, and three things pull a real circuit away from the numbers.
Capacitor tolerance comes first. Nichicon's standard UVR electrolytics are rated ±20 %, so a “1 second” RC built with one can land anywhere from 800 ms to 1.2 s. For tighter timing, use a film capacitor or trim the resistor.
Then there is leakage. An electrolytic passes a small DC current, and Nichicon allows up to 0.01CV µA after two minutes at rated voltage. That current also flows through your timing resistor, and with a large resistor it can eat a real share of the supply (see example 5).
Last, whatever reads the capacitor voltage (a comparator, an ADC pin, a meter) draws some current. It acts like an extra resistor across C, which both lowers the final voltage and shortens the time constant.
Cutoff frequency of the same RC pair
The same R and C used as a simple low-pass filter roll off at fc = 1 / (2πRC). TI gives this as the formula for a first-order stage in its low-pass filter application note (SLOA049D, p. 11). The calculator shows it next to τ, since both come from the same two parts: fc = 1 / (2π × τ).
Worked examples
1. 10 kΩ and 100 µF
τ = 10,000 × 0.0001 = 1 s. On a 12 V supply the capacitor reaches 7.59 V (63.2 %) at 1 s, 11.4 V (95.0 %) at 3 s and 11.9 V (99.3 %) at 5 s. With a ±20 % electrolytic, τ is really 800 ms to 1.2 s.
2. Time to reach 9 V on a 12 V supply, 47 kΩ and 22 µF
τ = 47,000 × 22 µF = 1.034 s. t = 1.034 × ln(12 / 3) = 1.034 × 1.386 = 1.433 s.
3. Discharging 470 µF from 12 V to 1 V through 1 kΩ
τ = 470 ms. t = 0.47 × ln(12 / 1) = 0.47 × 2.485 = 1.168 s.
4. The 555's 1.1, worked through
For 91 kΩ and 100 µF, the exact time to two thirds of VCC is RC × ln 3 = 9.997 s, and the datasheet's rounded formula gives 10.01 s. Going the other way, the calculator's “find R” mode asks for 91.02 kΩ for exactly 10 s and picks 91 kΩ from E24, -0.026 % off. The 555 timer calculator handles the rest of the chip.
5. When leakage wrecks a slow timer
1 MΩ and a 10 µF, 16 V electrolytic on a 5 V supply, aiming for the two-thirds point at 3.33 V. Ideal time: 11 s. The catalogue limit for this capacitor is 0.01 × 10 × 16 = 1.6 µA. Through 1 MΩ that is a 1.6 V drop, so in the worst case the capacitor levels off near 3.4 V, barely above the threshold, and takes 39.3 s to get there instead of 11 s. A little more leakage and it never trips at all. To avoid it, use a smaller R with a bigger C, or switch to a film capacitor.
Nichicon states the leakage only as a maximum at rated voltage. At 5 V on a 16 V part the real figure is usually much lower, so read this as the worst case.
6. Cutoff frequency, 10 kΩ and 100 nF
fc = 1 / (2π × 10,000 × 100 × 10⁻⁹) = 159.2 Hz. τ for the same pair is 1 ms.
Tips and tricks
- Choose C first, then R. Capacitors come in fewer values and wider tolerances, so fix C and let the “find R” mode pick a standard resistor around it.
- Keep R below about 1 MΩ when an electrolytic sets the time. Above that, leakage and the input current of whatever reads the voltage start to matter more than the maths.
- Use the 3τ point for rough estimates. At three time constants the capacitor is 95 % of the way, which is close enough for most “is it charged yet” questions.
- Discharge the capacitor before each timing test. A part-charged capacitor starts higher up the curve and gives a short first reading; the start-voltage field shows by how much.
- Measure C before trusting a long delay. A meter with a capacitance range settles the ±20 % question in seconds. Read the marking with the capacitor code calculator first.
- A multimeter on the capacitor loads it. A typical 10 MΩ meter across a 1 MΩ timing resistor pulls the final voltage down by about 9 % while you watch.
What we would do
For a power-on delay, a debounce or an LED fade, an electrolytic and a resistor under 100 kΩ are fine; expect the time to land within the capacitor's ±20 %. For a delay longer than about 10 seconds, or one that has to repeat within a few per cent, use a film capacitor of 1 to 10 µF with a larger resistor, or hand the timing to a 555 or a microcontroller and keep the RC for filtering. If the calculator shows a leakage warning, change R or the capacitor before you build.
Questions people ask
What is the RC time constant?
It is R multiplied by C. With R in ohms and C in farads the answer is in seconds. In one time constant a charging capacitor covers 63.2 % of the gap to the supply, and a discharging one loses 63.2 % of its voltage.
How long does a capacitor take to charge fully?
In theory it never quite gets there, because each time constant closes only 63.2 % of the gap that is left. In practice designers call 5 time constants full: the capacitor is then within 0.7 % of the supply.
Why 63.2 %?
After a time equal to RC the charging equation gives 1 − e^(−1), which is 0.632. Nothing in the circuit is special at that point; it is just where t/RC equals 1.
Does the supply voltage change the time constant?
No. τ depends only on R and C. A higher supply charges the capacitor to a higher voltage in the same time, so the time to reach a fixed fraction of the supply stays the same. The time to reach a fixed voltage, say 3 V, does change with the supply.
Is the RC time constant the same as the 555 timer formula?
They are linked. A 555 one-shot charges its capacitor from 0 V to two thirds of the supply, which takes ln 3 × RC, or 1.0986 RC. TI rounds that to 1.1 × R × C in the datasheet.
Related calculators
Time a pulse or an oscillator with the 555 timer calculator, read a capacitor's value off its body with the capacitor code calculator, and read R with the resistor colour code calculator. To set a comparator threshold such as two thirds of the supply, use the voltage divider calculator. For a whole project built on RC timing, follow the 555 LED flasher system.
Sources: OpenStax, University Physics Volume 2, §10.5 “RC Circuits”, eq. 10.8–10.11; Texas Instruments, xx555 Precision Timers datasheet, SLFS022K (revised March 2026), pp. 11–12; Texas Instruments, Active Low-Pass Filter Design, SLOA049D (revised February 2023), p. 11; Nichicon, UVR series catalogue CAT.8100M, p. 1. Checked 8 October 2026.
One email a month from the bench
New circuits, lessons, part guides and calculators, on the first Sunday of each month.