Part of Analogue and filter calculators
RC Time Constant Calculator
Calculate the RC time constant and capacitor voltage at a selected time for charging and discharging circuits.
Inputs
Choose charge or discharge mode, select what to calculate, then enter the other four values.
Engineering notation is supported: 10k, 100n, 1m, 47u.
Results
After one time constant, a charging capacitor reaches about 63.2% of its final voltage; a discharging capacitor falls to about 36.8% of its initial voltage.
Use RC time constants for charge, discharge, delay, and threshold timing checks
An RC network does not jump instantly to its final voltage. Use this calculator to estimate capacitor voltage versus time, solve timing to a threshold, or size resistance and capacitance for a first-pass delay.
Reset and enable delays
Estimate when a capacitor crosses an input threshold after power-up or shutdown.
Discharge paths
Check how long a capacitor stays charged after power is removed or a bleed path is enabled.
First-order intuition
Use τ to reason about settling before moving into filter, ADC, or comparator details.
Equations and model
The calculator uses the first-order RC exponential response. It assumes a single effective resistance and capacitance during the interval being analysed.
Time constant
One time constant is the product of resistance and capacitance.
Charging voltage
Use for a capacitor charging from 0 V toward a final voltage.
Discharging voltage
Use for a capacitor discharging toward 0 V through a resistance.
R - Resistance
Unit: ohms (Ω)
The Thevenin or effective resistance seen by the capacitor during charge or discharge.
C - Capacitance
Unit: farads (F)
The capacitance being charged or discharged.
τ - Time constant
Unit: seconds (s)
The characteristic time scale of the RC response.
Vc(t) - Capacitor voltage
Unit: volts (V)
The capacitor voltage at a specific elapsed time.
Worked example
The example below is checked against the shared RC time constant calculation helper.
Design question: A 10 kΩ resistor charges a 100 nF capacitor toward 5 V. What is the voltage after 1 ms?
Inputs: R = 10 kΩ, C = 100 nF, t = 1 ms, final voltage = 5 V.
Time constant: τ = R × C = 10 kΩ × 100 nF = 1 ms.
Voltage after one τ: Vc = 5 V × (1 - e⁻¹) = 3.16 V.
Practical meaning: the capacitor has reached about 63.2% of the final voltage, not the full 5 V.
What one, three, and five time constants mean
The percentages are useful design intuition, but a real circuit should be checked against the actual threshold it must cross.
1τ
Charging reaches about 63.2% of final voltage. Discharge falls to about 36.8% of initial voltage.
3τ
Charging reaches about 95.0%. Discharge falls to about 5.0% remaining.
5τ
Charging reaches about 99.3%. Discharge falls to about 0.67% remaining.
Assumptions and limitations
Effective resistance matters
Use the resistance seen by the capacitor, not just a visible series resistor. Driver resistance and parallel paths can change τ.
Thresholds are device-specific
Reset, enable, comparator, and logic inputs have real thresholds, hysteresis, leakage, and timing requirements.
Tolerance can dominate
Capacitor tolerance, leakage, dielectric behaviour, and resistor tolerance can move the actual delay significantly.
Related calculators and next checks
Follow the next check based on whether the RC network is acting as a timing element, a filter, or an energy-storage part.
RC low-pass filter calculator
Use when the same RC network is being treated as a frequency-domain low-pass filter.
RC high-pass and AC-coupling calculator
Use when a series capacitor and resistance set a high-pass or coupling corner.
Capacitor energy calculator
Check stored energy and charge when capacitor size or discharge safety matters.
Analogue and filter hub
Follow related RC, filter, and analogue design workflows.
Power and energy hub
Follow capacitor energy and stored-energy workflows.
FAQ
What does one time constant mean?
For charging, one time constant reaches about 63.2% of the final voltage. For discharging, one time constant leaves about 36.8% of the initial voltage.
Is five time constants fully charged?
Five time constants is about 99.3% charged or about 0.67% remaining during discharge. That is effectively complete for many checks, but precision circuits may need stricter limits.
Can this replace a reset timing check?
No. It provides the RC voltage behaviour. Real reset circuits also depend on input thresholds, leakage, tolerance, hysteresis, and the minimum pulse width required by the device.
Engineering reference
Equations, assumptions, and design guidance
Solves the ideal first-order RC charge or discharge equation for resistance, capacitance, time, capacitor voltage, or reference voltage.
Equations and variables
tau = R * CVc(t) = Vfinal * (1 - exp(-t / tau))Vc(t) = Vinitial * exp(-t / tau)- R
- Resistance (ohm)
- C
- Capacitance (F)
- t
- Elapsed time (s)
- Vc
- Capacitor voltage (V)
Assumptions and limitations
Assumptions
- The source and switch are ideal.
- The capacitor is linear over the voltage range.
- Initial and final voltages match the selected charge/discharge model.
Limitations
- ESR, leakage, dielectric absorption, source resistance, and comparator thresholds are not modelled.
Worked example and design use
10 kOhm and 100 nF charge
Inputs: R = 10 kOhm, C = 100 nF, t = 1 ms, Vfinal = 5 V
Outputs: tau = 1 ms, Vc is about 3.16 V after one tau
Design guidance
- Use worst-case R and C tolerances for timing limits.
- Account for input thresholds and leakage in reset and delay circuits.