RC time constant formula
The time constant of an ideal resistor-capacitor circuit is the product of resistance and capacitance.
When resistance is entered in ohms and capacitance in farads, the result is in seconds.
For example, 10 kΩ multiplied by 100 µF gives a time constant of 1 second.
Capacitor charging formula
For an ideal capacitor starting at zero volts and charging through a resistor toward a fixed supply voltage:
After one time constant, the capacitor reaches about 63.2% of the supply voltage. After two time constants it reaches about 86.5%, and after five time constants it reaches about 99.3%.
Capacitor discharging formula
For an ideal capacitor discharging through a resistor from an initial voltage:
After one time constant, about 36.8% of the starting voltage remains. After five time constants, only about 0.67% remains.
RC current formula
The current magnitude begins at its maximum value and falls exponentially as the capacitor charges or discharges.
At the instant an ideal charging circuit is connected, the initial current is V / R. The current then decreases as the capacitor voltage changes.
Time to a target voltage
For charging from zero volts, the time required to reach a chosen fraction of the final voltage is:
For discharging, the time to reach a chosen fraction of the starting voltage is:
A charging capacitor takes about 2.303 time constants to reach 90% of its final voltage.
What does 5τ mean?
An ideal exponential curve approaches its final value continuously rather than reaching it at a single exact moment.
Five time constants is commonly used as a practical settling reference because a charging capacitor is about 99.3% of the way to its final value at 5τ.
RC cutoff frequency
The same resistor and capacitor pair can also define the corner frequency of a first-order RC filter.
A 10 kΩ resistor and 100 µF capacitor have a time constant of 1 second and a cutoff frequency of approximately 0.159 Hz.
Capacitor charge and energy
At a particular capacitor voltage, the ideal stored charge is:
The ideal stored electrical energy is:
Resistance and capacitance units
The calculator supports ohms, kilohms and megohms for resistance. Capacitance can be entered in picofarads, nanofarads, microfarads, millifarads or farads.
The selected units are converted internally before the RC equations are evaluated.
Where RC time constants are used
RC timing relationships appear in delay circuits, filters, switch debouncing, signal coupling, power-on timing and many other first-order analog circuits.
The same R and C pair can therefore be considered in both the time domain through τ and the frequency domain through the cutoff-frequency formula.
Real circuit limitations
These equations describe an ideal first-order RC circuit. Real capacitors have tolerance, leakage, ESR and frequency-dependent behavior. Sources and loads can also add resistance that changes the effective time constant.
For timing-critical designs, component tolerance and the resistance of the surrounding circuit should be considered rather than relying only on nominal R and C values.
Related electrical calculations
To combine multiple capacitor values, use the Series & Parallel Capacitor Calculator.
For resistor combinations, use the Series & Parallel Resistor Calculator.
For voltage, current and resistance relationships, use the Ohm's Law Calculator.
This calculator models an ideal first-order RC circuit. It does not model capacitor leakage, ESR, source resistance, load resistance, dielectric absorption, component tolerance or other non-ideal behavior unless those effects are included in the resistance or capacitance values you enter.
Frequently asked questions
What is the RC time constant?
It is resistance multiplied by capacitance: τ = R × C.
How charged is a capacitor after one time constant?
An ideal capacitor charging from zero reaches about 63.2% of its final voltage after 1τ.
How much voltage remains after one time constant while discharging?
About 36.8% of the starting voltage remains after 1τ.
How long does an RC circuit take to fully charge?
The exponential curve does not reach exactly 100%, but 5τ is commonly used as a practical near-full-charge reference at about 99.3%.
Does the RC time constant depend on voltage?
No. In the ideal model, τ depends on resistance and capacitance. Supply voltage changes the voltage and current levels but not RC.
Using this calculator effectively
The RC Time Constant Calculator models an ideal resistor-capacitor circuit during charging or discharging. It calculates the RC time constant, capacitor voltage and current at a chosen time, target time, 5τ settling time, cutoff frequency, charge and stored energy.
Common uses
- Estimating capacitor charging or discharging behavior from resistance and capacitance.
- Finding the time required for a capacitor to reach a chosen percentage of its final or starting voltage.
- Checking the relationship between an RC time constant and the corresponding first-order filter cutoff frequency.
Tips for a better estimate
- Use the total effective resistance seen by the capacitor when the surrounding circuit adds meaningful source or load resistance.
- Check capacitor tolerance and leakage when the timing result is sensitive to component variation.
- Treat the result as a first-order ideal model because ESR, dielectric effects and external loading can change real behavior.
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