Calculators
RC Time Constant Calculator
Calculate RC time constant, settling time, cutoff frequency, and charge/discharge progress.
Find the RC time constant, approximate 5τ settling time, first-order cutoff frequency, and ideal capacitor charge or discharge percentage at a chosen time.
Time constant (τ)
1000 ms
5τ settling estimate5 s
RC cutoff frequency0.15915494 Hz
Ideal charge at elapsed time63.212056%
Ideal remaining charge when discharging36.787944%
The exponential percentages assume an ideal first-order resistor-capacitor circuit driven by a step. Real source/load resistance, capacitor tolerance, leakage, ESR, and parasitic effects can change measured behavior.
About This Tool
An RC circuit combines resistance and capacitance to create a predictable exponential response. Its time constant, written τ (tau), tells you the characteristic timescale of that response. This calculator converts common resistor and capacitor units, finds τ = R × C, estimates the commonly used 5τ settling time, calculates the corresponding first-order RC cutoff frequency, and shows ideal charging and discharging progress at any elapsed time. It is useful for checking timing networks, debounce circuits, simple filters, sensor conditioning, and electronics exercises without sending entered values anywhere.
How To Use It
- Enter the resistance and choose Ω, kΩ, or MΩ.
- Enter the capacitance and choose a matching unit from farads through picofarads.
- Optionally enter an elapsed time to see the ideal charging percentage and remaining discharge percentage at that instant.
- Use the calculated τ and 5τ values as ideal circuit references, then account for real component tolerances, source/load resistance, leakage, ESR, and parasitic effects in physical designs.
Examples
10 kΩ and 100 µF
R = 10,000 Ω and C = 0.0001 F gives τ = 1 second. At t = 1 second, an ideal capacitor charging from zero has reached about 63.2% of its final step voltage, while a discharging capacitor has about 36.8% remaining.
1 kΩ and 1 µF
The product is 0.001 second, so τ = 1 ms. Five time constants is 5 ms and the corresponding first-order RC cutoff frequency is about 159.15 Hz.
Choosing a debounce timescale
A 10 kΩ resistor with 100 nF gives τ = 1 ms. The ideal exponential is more than 99% through its step response after about 5 ms, although real digital input thresholds and switch behavior must also be considered.
Useful Notes
Time constant formula
For a simple first-order RC network, τ = R × C. When resistance is in ohms and capacitance is in farads, τ is in seconds. Increasing either R or C increases the response time proportionally.
Charging and discharging
For an ideal capacitor charging from zero toward a step voltage, the fraction charged after time t is 1 − e^(−t/τ). For ideal discharge from an initial voltage toward zero, the fraction remaining is e^(−t/τ). At one τ these are approximately 63.2% charged and 36.8% remaining.
What 5τ means
After five time constants, an ideal first-order charging response has completed about 99.3% of its change and a discharge has about 0.67% remaining. Engineers often use 5τ as a practical settling reference, not as a claim that the capacitor becomes mathematically 100% charged.
Relation to cutoff frequency
For a basic first-order RC low-pass or high-pass network, the corner frequency is fc = 1 / (2πRC), which is also 1 / (2πτ). Circuit topology determines whether frequencies above or below that corner are attenuated.
Real-component limitations
Actual circuits depart from the ideal equations because resistor and capacitor tolerances, capacitor leakage and ESR, source resistance, load impedance, temperature, wiring, and parasitic capacitance or inductance alter the effective network. These effects matter especially for very long, very short, or precision timing.
RC timing versus dedicated timers
The basic τ = RC value is not automatically the pulse width of every timer circuit. Devices such as 555 timers and logic inputs switch at specific voltage thresholds, so their timing equations include those thresholds. Use the formula appropriate to the complete circuit rather than treating 5τ as a universal timer equation.
FAQ
Why is one time constant 63.2% when charging?
At t = τ, the charging fraction is 1 − e⁻¹, which is approximately 0.6321 or 63.21%. The complementary exponential e⁻¹ is about 36.79%, the fraction remaining during ideal discharge.
Does supply voltage change the RC time constant?
In the ideal linear RC model, τ depends on resistance and capacitance, not the size of the voltage step. Real components or nonlinear circuit elements can introduce voltage-dependent behavior.
Is 5τ fully charged?
Not exactly. An ideal exponential approaches its final value asymptotically. At 5τ it has reached about 99.3% of the final change, which is often close enough to call practically settled for rough estimates.
Can this calculate an RC filter cutoff?
Yes. It reports fc = 1/(2πRC), the corner frequency for a basic first-order RC filter. The actual transfer behavior depends on whether the circuit is configured as low-pass or high-pass and on source and load impedances.
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