Impedance Z Calculator: Find Magnitude and Phase

An impedance Z calculator finds the complex impedance of a resistor, inductor, and capacitor connected in series at a chosen frequency. Enter resistance, inductance, capacitance, and frequency; the calculator returns impedance magnitude and phase, with the real and imaginary components for context.

Formula

This calculator models a series RLC circuit using complex impedance. Its total impedance is Z = R + j(X_L − X_C), where j is the imaginary unit, defined by j² = −1. The inductive reactance is X_L = 2πfL, and the capacitive reactance is X_C = 1/(2πfC).

• R is resistance in ohms (Ω).
• L is inductance in henries (H).
• C is capacitance in farads (F).
• f is frequency in hertz (Hz), or cycles per second.
• X_L and X_C are reactances in ohms.
• j indicates the imaginary component; it is not an additional physical component.

The real component is R, and the imaginary component is X_L − X_C. The magnitude is |Z| = √(R² + (X_L − X_C)²). The phase angle is θ = arctan((X_L − X_C)/R). A positive angle means the net reactance is inductive; a negative angle means it is capacitive. The calculator’s phase output uses degrees.

Worked Example

Using the defaults—R = 100 Ω, L = 0.01 H, C = 0.0001 F, and f = 1000 Hz—first find each reactance:

• X_L = 2π × 1000 × 0.01 ≈ 62.83 Ω.
• X_C = 1/(2π × 1000 × 0.0001) ≈ 1.59 Ω.
• Net reactance = 62.83 − 1.59 ≈ 61.24 Ω.

Then |Z| = √(100² + 61.24²) ≈ 117.26 Ω. The phase is arctan(61.24/100) ≈ 31.49°. The real part is 100.00 Ω and the imaginary part is 61.24 Ω. These are the results rounded to the calculator’s displayed precision.

What Impedance Z Means

Impedance is the opposition a circuit presents to alternating current (AC). It includes resistance, which dissipates electrical energy, and reactance, which arises from energy storage in inductors and capacitors. Unlike resistance alone, impedance generally depends on signal frequency.

Complex notation keeps both effects in one quantity: Z = R + jX, where X is net reactance. The magnitude tells how large the total opposition is, while the phase describes the timing relationship between voltage and current. For an ideal series circuit, voltage leads current when the net reactance is inductive; current leads voltage when it is capacitive.

How to Use and Interpret the Calculator

Enter component values in SI units and use the frequency of the AC signal being analyzed. The calculator assumes the three components are connected in series and that their values can be treated as ideal and constant at that frequency.

1. Enter resistance in ohms. For example, 2.2 kΩ is 2200 Ω.
2. Convert inductance to henries: 10 mH is 0.01 H, and 100 µH is 0.0001 H.
3. Convert capacitance to farads: 100 µF is 0.0001 F, while 10 nF is 0.00000001 F.
4. Enter frequency in hertz. A frequency of 1 kHz is 1000 Hz.
5. Read magnitude and phase together; use the real and imaginary outputs if a calculation requires the complex form.

Ohms, henries, farads, and hertz are metric/SI units. In US customary settings, electrical quantities are still commonly specified with these same units and prefixes; there is no separate customary unit system needed for this calculation. Prefixes such as kilo (10³), milli (10⁻³), micro (10⁻⁶), and nano (10⁻⁹) must be converted correctly.

Resonance, Comparisons, and Limits

In an ideal series RLC circuit, resonance occurs when X_L = X_C. The resonance frequency is f₀ = 1/(2π√(LC)). At that frequency, the imaginary component cancels, the phase is zero, and the impedance magnitude equals R. Away from resonance, the net reactance changes with frequency, so both magnitude and phase can change.

This is not the same as adding the three component values or treating reactances as ordinary resistances. Reactances have signs in the complex sum: inductive reactance is positive and capacitive reactance is negative. Their magnitudes can cancel each other, while resistance remains in the real component. The magnitude is calculated only after combining those components.

The calculator does not determine impedance for parallel circuits, networks with multiple branches, transformers, or components whose behavior requires a frequency-dependent model. For a parallel network, admittance (the reciprocal of impedance) is often the more convenient quantity to combine. Real components can also have tolerances, parasitic resistance, and other non-ideal effects; measurements or a detailed circuit model may be needed when those factors matter.

Common Input and Interpretation Mistakes

• Mixing prefixes: entering 10 instead of 0.01 for 10 mH changes the inductive reactance by a factor of 1000.
• Using the wrong topology: the equations here are for components in series, not parallel.
• Ignoring phase: impedance magnitude alone does not show whether the circuit is net inductive or capacitive.
• Confusing radians and degrees: the displayed phase is in degrees. Some formulas and software use radians instead.
• Overreading precision: two decimal places are a display choice, not a claim that component values are known that accurately.

At zero frequency, the ideal capacitor’s reactance formula has a division by zero, so the calculator requires a positive frequency. A zero resistance also makes the displayed arctangent expression unsuitable for describing the sign of phase in every limiting case; for ordinary passive RLC calculations, use a positive resistance when you need a conventional phase angle.

Frequently Asked Questions

What does Z stand for in an impedance calculator?
Z is the symbol for complex impedance. It combines resistance and reactance; its magnitude is measured in ohms, and its angle describes phase.

How do I calculate impedance from resistance and reactance?
For a series combination, write Z = R + jX. Its magnitude is √(R² + X²), and its phase is arctan(X/R), with attention to the correct quadrant when using a general complex-number tool.

Is impedance the same as resistance?
No. Resistance is the real component of impedance. Impedance also includes reactance, which depends on frequency for ideal inductors and capacitors.

Why does impedance change with frequency?
Inductive reactance rises with frequency, while capacitive reactance falls as frequency rises. Their balance therefore changes the circuit’s total impedance and phase.

Can I use this calculator for a parallel RLC circuit?
No. This calculator uses the series formula. Parallel branches must be combined using the appropriate impedance or admittance relationships.

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in r | Resistance | ohm | 100 | 0
in l | Inductance | H | 0.01 | 0
in c | Capacitance | F | 0.0001 | 0
in f | Frequency | Hz | 1000 | 0
out z | Impedance magnitude | ohm | sqrt(r^2 + (2*pi*f*l - 1/(2*pi*f*c))^2) | 2
out phase | Impedance phase | degrees | atand((2*pi*f*l - 1/(2*pi*f*c))/r) | 2
out re | Real part | ohm | r | 2
out im | Imaginary part | ohm | 2*pi*f*l - 1/(2*pi*f*c) | 2