OneTaskBy Tim King · Updated
Capacitor and Inductor Calculator
Reactance, RC Time Constant and LC Resonance
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How the Capacitor and Inductor Calculator works
This capacitor and inductor calculator finds capacitive reactance, inductive reactance, RC and RL time constants and the LC resonant frequency. Enter a capacitance, an inductance or both, with a frequency and a resistance, and every result that applies appears with its formula, from filter cut-off frequencies to the Q factor and bandwidth of a tuned circuit.
Capacitors and inductors resist alternating current in opposite ways. A capacitor passes high frequencies and blocks low ones, while an inductor does the reverse. That opposition, called reactance, is measured in ohms like resistance but changes with frequency, which is what makes filters, crossovers, timers, oscillators and radio tuners possible.
How the capacitor and inductor calculator works
The formula for capacitive reactance is Xc = 1 ÷ (2πfC), and inductive reactance is XL = 2πfL. The RC time constant is τ = RC and the RL time constant is τ = L ÷ R; after 5τ a circuit is 99.3% of the way to its final value. The resonant frequency of an LC circuit is f0 = 1 ÷ (2π√(LC)), the point where Xc and XL are equal. With a series resistance, Q = √(L/C) ÷ R and the bandwidth is f0 ÷ Q.
First example. A 100 nF capacitor at 1 kHz has Xc = 1 ÷ (2π × 1,000 × 0.0000001) ≈ 1,592 Ω. With a 10 mH inductor it resonates at 1 ÷ (2π√(0.01 × 0.0000001)) ≈ 5.033 kHz.
Second example. A 100 µF capacitor charging through 10 kΩ has τ = 10,000 × 0.0001 = 1 s, so it is effectively full after 5 s.
How many ohms is a 10 µF capacitor at 50 Hz? Xc = 1 ÷ (2π × 50 × 0.00001) ≈ 318 Ω.
Capacitive reactance of common capacitor values at 50 Hz, 1 kHz, 100 kHz and 10 MHz
| Capacitance | Xc at 50 Hz | Xc at 1 kHz | Xc at 100 kHz | Xc at 10 MHz |
|---|---|---|---|---|
| 10 pF | 318.31 MΩ | 15.915 MΩ | 159.15 kΩ | 1.5915 kΩ |
| 22 pF | 144.69 MΩ | 7.2343 MΩ | 72.343 kΩ | 723.43 Ω |
| 47 pF | 67.726 MΩ | 3.3863 MΩ | 33.863 kΩ | 338.63 Ω |
| 100 pF | 31.831 MΩ | 1.5915 MΩ | 15.915 kΩ | 159.15 Ω |
| 220 pF | 14.469 MΩ | 723.43 kΩ | 7.2343 kΩ | 72.343 Ω |
| 470 pF | 6.7726 MΩ | 338.63 kΩ | 3.3863 kΩ | 33.863 Ω |
| 1 nF | 3.1831 MΩ | 159.15 kΩ | 1.5915 kΩ | 15.915 Ω |
| 2.2 nF | 1.4469 MΩ | 72.343 kΩ | 723.43 Ω | 7.2343 Ω |
| 4.7 nF | 677.26 kΩ | 33.863 kΩ | 338.63 Ω | 3.3863 Ω |
| 10 nF | 318.31 kΩ | 15.915 kΩ | 159.15 Ω | 1.5915 Ω |
| 22 nF | 144.69 kΩ | 7.2343 kΩ | 72.343 Ω | 723.43 mΩ |
| 47 nF | 67.726 kΩ | 3.3863 kΩ | 33.863 Ω | 338.63 mΩ |
| 100 nF | 31.831 kΩ | 1.5915 kΩ | 15.915 Ω | 159.15 mΩ |
| 220 nF | 14.469 kΩ | 723.43 Ω | 7.2343 Ω | 72.343 mΩ |
| 470 nF | 6.7726 kΩ | 338.63 Ω | 3.3863 Ω | 33.863 mΩ |
| 1 µF | 3.1831 kΩ | 159.15 Ω | 1.5915 Ω | 15.915 mΩ |
| 2.2 µF | 1.4469 kΩ | 72.343 Ω | 723.43 mΩ | 7.2343 mΩ |
| 4.7 µF | 677.26 Ω | 33.863 Ω | 338.63 mΩ | 3.3863 mΩ |
| 10 µF | 318.31 Ω | 15.915 Ω | 159.15 mΩ | 1.5915 mΩ |
| 22 µF | 144.69 Ω | 7.2343 Ω | 72.343 mΩ | 723.43 µΩ |
| 47 µF | 67.726 Ω | 3.3863 Ω | 33.863 mΩ | 338.63 µΩ |
| 100 µF | 31.831 Ω | 1.5915 Ω | 15.915 mΩ | 159.15 µΩ |
| 470 µF | 6.7726 Ω | 338.63 mΩ | 3.3863 mΩ | 33.863 µΩ |
| 1 mF | 3.1831 Ω | 159.15 mΩ | 1.5915 mΩ | 15.915 µΩ |
Tips and pitfalls
- Watch the prefixes. Mixing up nF and µF puts the answer out by a factor of 1,000.
- One τ is only 63.2%. Use 5τ for a fully charged or discharged capacitor.
- Parts have tolerances. Ceramic capacitors are often ±10% or worse, so the real resonance will drift.
- Inductors have resistance too. The coil's own wire resistance lowers Q, so include it in R.
FAQ
How do you calculate capacitive reactance?
Use Xc = 1 ÷ (2πfC), with f in hertz and C in farads. A 1 µF capacitor at 1 kHz gives 1 ÷ (2π × 1,000 × 0.000001) ≈ 159 Ω. Reactance falls as frequency rises, so the same capacitor is only about 1.6 Ω at 100 kHz.
What is the RC time constant?
It is the resistance in ohms times the capacitance in farads, giving a time in seconds. After one time constant a charging capacitor reaches 63.2% of the supply voltage, and after five it reaches 99.3%. A 1 MΩ resistor with a 1 µF capacitor gives τ = 1 s, a common timing pair.
How do you calculate the resonant frequency of an LC circuit?
Use f0 = 1 ÷ (2π√(LC)), with L in henries and C in farads. A 1 mH inductor with a 1 µF capacitor resonates at about 5.03 kHz. At that frequency the two reactances cancel, which is how radio tuners select one station and reject the rest.
What is the cut-off frequency of an RC filter?
It is fc = 1 ÷ (2πRC), the frequency where the output has dropped by 3 dB, to about 70.7% of the input voltage. A 1 kΩ resistor and 100 nF capacitor give about 1.59 kHz. Below that a low-pass filter passes signals almost unchanged, and above it they fall away steadily.
What is the difference between capacitive and inductive reactance?
Capacitive reactance falls as frequency rises, while inductive reactance rises with frequency. A capacitor lets current lead the voltage by 90° and an inductor makes it lag by 90°. Combining them gives circuits that pick out or reject a narrow band of frequencies.
See also: all Electronics tools, Physics, Chemistry.
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