RC Time Constant Calculator
Charge time and cutoff frequency.
Reviewed by the Calculation Machine team · Updated 24 October 2026 · How we check our maths
Your values
ⓘ Live results
- Time constant
- 1 s
- Time to 99% charge
- 5 s
- Voltage after 1τ
- 7.58 V
- Cutoff frequency
- 0.16 Hz
Quick answer
The RC time constant is τ = R × C (ohms × farads = seconds). After one time constant a charging capacitor reaches 63.2% of the supply voltage, and after 5τ it is above 99% and treated as fully charged. A 10 kΩ resistor with a 100 µF capacitor gives τ = 1 s, so it charges to 7.58 V of a 12 V supply in 1 second and is essentially full after 5 seconds.
What the RC Time Constant calculator does
This calculator gives the time constant of a resistor-capacitor circuit, the time to reach full charge (5τ), the capacitor voltage after one time constant, and the −3 dB cutoff frequency when the same R and C form a low-pass or high-pass filter.
It is used for power-on delays and reset circuits, switch debouncing, 555 timer and LED-fade timing, and simple audio or sensor filters. Enter resistance in kilohms and capacitance in microfarads; the result is in seconds.
The model assumes an ideal capacitor charged from a constant DC voltage through a fixed resistor. Real electrolytic capacitors often have a tolerance of ±20% and some leakage, so treat the timing as approximate unless you use film or C0G parts. If your resistance comes from several parts, combine them first with the series/parallel resistor calculator.
The formula
τ = R × C Vc(t) = V × (1 − e^(−t/τ)) fc = 1 ÷ (2π × R × C)
| Symbol | Meaning | Unit |
|---|---|---|
| τ | Time constant | s |
| R | Resistance in series with the capacitor (enter in kΩ) | Ω |
| C | Capacitance (enter in µF) | F |
| V | Supply voltage the capacitor charges toward | V |
| Vc(t) | Capacitor voltage at time t after charging starts | V |
| fc | Cutoff (−3 dB) frequency of an RC filter | Hz |
These are the standard first-order RC equations found in any circuit-analysis textbook. Discharge follows the mirror image, Vc(t) = V × e^(−t/τ). To find the time to reach a particular voltage, rearrange: t = −τ × ln(1 − Vc ÷ V). This page also covers stored charge and energy (Q = C × V and E = ½ × C × V²), which the former capacitor charge calculator handled.
Worked examples
One-second power-on delay
A 10 kΩ resistor and 100 µF electrolytic capacitor on a 12 V supply delay a relay driver after power-up.
Inputs
- Resistance10 kΩ
- Capacitance100 µF
- Supply voltage12 V
Result
- Time constant1 s
- Time to 99% charge5 s
- Voltage after 1τ7.58 V
- Cutoff frequency0.16 Hz
τ is 1 s and the capacitor passes 7.58 V after one second. If the driver switches at about 6 V (half supply), it triggers at 0.69τ, roughly 0.7 s, with ±20% spread from the capacitor tolerance.
Switch debounce filter
A push button on a 5 V logic input is filtered with 1 kΩ and 0.1 µF.
Inputs
- Resistance1 kΩ
- Capacitance0.1 µF
- Supply voltage5 V
Result
- Time constant0.0001 s
- Time to 99% charge0.001 s
- Voltage after 1τ3.16 V
- Cutoff frequency1591.55 Hz
τ is 0.1 ms and the cutoff is about 1.6 kHz, so the filter settles within 0.5 ms. Mechanical contact bounce often lasts a few milliseconds, so a 10× larger resistor or capacitor may be needed.
Low-pass filter for a 3.3 V sensor
A 10 kΩ resistor and 1 µF capacitor smooth an analog sensor reading before a 3.3 V ADC.
Inputs
- Resistance10 kΩ
- Capacitance1 µF
- Supply voltage3.3 V
Result
- Time constant0.01 s
- Time to 99% charge0.05 s
- Voltage after 1τ2.09 V
- Cutoff frequency15.92 Hz
The cutoff is about 15.9 Hz, removing mains hum and fast noise while following slow changes. The output takes about 50 ms (5τ) to settle after a step.
Charge and discharge at each time constant
These percentages hold for any RC circuit, so you can read timings straight off once you know τ.
| Time | Charging (% of V) | Discharging (% of V left) |
|---|---|---|
| 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% |
Stored charge and energy in the capacitor
Once charged, a capacitor holds a charge of Q = C × V and energy of E = ½ × C × V². A 100 µF capacitor at 12 V holds 1.2 millicoulombs and 7.2 millijoules. Energy rises with the square of voltage, so doubling the voltage stores four times the energy — the reason large high-voltage capacitors in power supplies and camera flashes can deliver a dangerous shock long after power is removed.
The charging current starts at V ÷ R (1.2 mA in the 1-second delay example) and decays with the same time constant. Use the Ohm's law calculator to check the initial current against what your supply or GPIO pin can deliver.
Getting real circuits to match the math
- Capacitor tolerance: electrolytics are commonly ±20%; film and C0G ceramics are ±5% or better and drift less with temperature.
- Leakage: with very large resistors (several megohms), leakage current can stop an electrolytic from reaching full voltage.
- Source and load resistance: whatever drives the circuit and whatever reads it add to or shunt R. Include a driver's output resistance in R.
- Reading resistor values: confirm the part with the resistor color code calculator — a 10 kΩ mistaken for 1 kΩ changes the timing tenfold.
How to use the RC Time Constant Calculator
- 1Enter the series resistance in kilohms (4.7 kΩ = 4.7; 470 Ω = 0.47).
- 2Enter the capacitance in microfarads (100 nF = 0.1; 1,000 pF = 0.001).
- 3Enter the supply voltage the capacitor charges toward.
- 4Read τ, the 5τ full-charge time, the voltage after 1τ and the filter cutoff frequency.
Frequently asked questions
How long does it take a capacitor to fully charge?
About five time constants (5 × R × C). At that point it is at 99.3% of the supply voltage, which is treated as fully charged in practice.
Why is one time constant 63%?
Charging follows 1 − e^(−t/RC). At t = RC this equals 1 − 1/e, which is 0.632.
What is the time constant of a 1 kΩ resistor and 1 µF capacitor?
1,000 Ω × 0.000001 F = 0.001 s, or 1 millisecond. The cutoff frequency of that pair is about 159 Hz.
Does discharge take the same time as charging?
Yes, if it discharges through the same resistance. The voltage falls to 36.8% after one time constant and below 1% after five.
How do I calculate the time to reach a specific voltage?
Use t = −RC × ln(1 − Vc ÷ V). Reaching half the supply takes 0.69 × RC, which is why 555 timer formulas contain 0.693.
References
- Fundamentals of Electric Circuits, Alexander and Sadiku — McGraw-Hill
- The Art of Electronics (3rd edition), Horowitz and Hill — Cambridge University Press
About this calculator
- Built and reviewed by the Calculation Machine team · How we build and test calculators
- Last reviewed: October 24, 2026
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