RC Time Constant & Filter Cutoff Calculator

Calculates the RC time constant, the charging time to a target voltage and the cutoff frequency of a low-pass or high-pass RC filter. It also finds reactance and the LC resonant frequency.

How to use

1. On "Time constant", enter "Resistance (R)" and "Capacitance (C)" to see τ and the charging curve; add voltages to get the time to a target.
2. On "Filter cutoff", choose the "Filter type" and enter two of R, C and fc; the third and a Bode plot appear.
3. Type a value in "Check a frequency" to see the gain in dB and the phase at that frequency.
4. On "Reactance and resonance", calculate Xc, XL or the LC resonant frequency in the same way.

How it works

• Units are chosen next to each box, or typed as prefixes such as 4k7, 100n or 2.2u.
• τ = R × C, fc = 1 ÷ (2π × R × C), Xc = 1 ÷ (2π × f × C) and XL = 2π × f × L. A first-order RC filter falls by 20 dB per decade beyond the cutoff.
• Ideal parts are assumed, with no source resistance and no load. A load on the output changes the cutoff.

Questions and answers

How do I calculate the RC time constant?

τ = R × C. With 10 kΩ and 100 µF it is 1 second. After 1τ the capacitor is 63.2% charged, and after 5τ more than 99%.

What is the formula for the cutoff frequency of an RC filter?

fc = 1 ÷ (2π × R × C). With 1 kΩ and 100 nF it is about 1.59 kHz, where the output is −3.01 dB and the phase is ∓45°.

How long does a capacitor take to charge to a given voltage?

t = τ × ln((source − start) ÷ (source − target)). With τ = 1 second and a 5 V source, charging from 0 V to 3.3 V takes about 1.08 seconds.

How do I find the LC resonant frequency?

f0 = 1 ÷ (2π × √(L × C)). With 10 mH and 100 nF it is about 5.03 kHz, where XL equals Xc.