Hong Life CalculatorsUnderstanding the reactance and impedance calculator — concept and principle
This calculator works out the inductive and capacitive reactance at a given frequency and combines them with a resistance into the impedance of a series RLC circuit, together with the phase angle and power factor. Use it to predict AC current or check whether a load is inductive or capacitive.
How it is calculated
- Inductive reactance: X_L = 2πfL, with L in henries (mH ÷ 1000).
- Capacitive reactance: X_C = 1/(2πfC), with C in farads (µF × 10⁻⁶). Entering C = 0 means no capacitor, so X_C = 0.
- Net reactance: X = X_L − X_C.
- Impedance magnitude: |Z| = √(R² + X²), from Z = R + jX.
- Phase angle: φ = atan2(X, R) in degrees. Positive means the current lags (inductive); negative means it leads (capacitive).
- Power factor: PF = R / |Z| = cos φ.
The principle
In AC circuits, inductors and capacitors oppose current without dissipating energy. An inductor's opposition grows with frequency because a faster-changing current induces a larger back-voltage. A capacitor's opposition shrinks with frequency because it is charged and discharged more often, passing more current. Their voltages are 90° out of phase with the current in opposite directions, so the two reactances subtract. The resistor's voltage is in phase with the current, at right angles to the reactive part, which is why R and X combine like the sides of a right triangle rather than adding directly.
Worked example
- Inputs: f = 60 Hz, R = 10 Ω, L = 50 mH, C = 100 µF.
- X_L = 2π × 60 × 0.05 = 18.8496 Ω.
- X_C = 1 ÷ (2π × 60 × 100 × 10⁻⁶) = 26.5258 Ω.
- X = 18.8496 − 26.5258 = −7.6763 Ω (net capacitive).
- |Z| = √(10² + 7.6763²) = √158.93 = 12.6065 Ω.
- φ = atan2(−7.6763, 10) = −37.51°; PF = 10 ÷ 12.6065 = 0.7932 (leading).
| Frequency (Hz) | |Z| (Ω) |
|---|---|
| 15 | 101.8828538 |
| 30 | 44.7582815 |
| 45 | 23.46781412 |
| 60 | 12.60654946 |
| 75 | 10.27042449 |
| 90 | 14.56563281 |
| 120 | 26.4031791 |
How to read the result
|Z| tells you the current for a given voltage: I = V/|Z|, so 120 V across this circuit drives about 9.5 A. A phase angle near 0° and PF near 1 means the circuit is almost resistive; near ±90° it is mostly reactive. If X_L and X_C are equal, the circuit is at resonance and |Z| falls to R.
Common mistakes
- Adding R and X arithmetically instead of with the square root of the sum of squares.
- Forgetting the sign: a negative angle means capacitive, a positive angle inductive.
- Using these series formulas for a parallel circuit, where admittances must be combined instead.
Frequently asked questions
Why does a capacitor block DC but pass AC?
At f = 0, X_C = 1/(2πfC) becomes infinite, so no steady current flows; as frequency rises, X_C falls and more current passes.
What does "leading" power factor mean?
The current reaches its peak before the voltage, which happens in capacitive circuits. Inductive loads such as motors give a lagging power factor.
Is impedance measured in ohms?
Yes. Resistance, reactance and impedance all share the unit ohm because each is a ratio of voltage to current.
Sources: C. K. Alexander and M. N. O. Sadiku, Fundamentals of Electric Circuits, McGraw-Hill, chapters on sinusoids and phasors · IEC 60050-131, International Electrotechnical Vocabulary: Circuit theory