Impedance Converter
Free Impedance Converter for tech & electronics units. Enter a value to see equivalent measurements across systems. Enter your values for instant results.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Impedance Converter
Calculator
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Formula: |Z| = sqrt(R^2 + X^2) | Phase = atan(X/R) | Y = 1/Z | Q = |X|/R
Worked example โ Impedance = 10 ohms at 36.87 degrees
Formula
|Z| = sqrt(R^2 + X^2) | Phase = atan(X/R) | Y = 1/Z | Q = |X|/R
Impedance Z is a complex quantity with resistance R as the real part and reactance X as the imaginary part. The magnitude is the Pythagorean combination of R and X. The phase angle indicates whether the circuit is inductive (positive) or capacitive (negative). Admittance Y is the inverse of impedance, and quality factor Q measures energy storage efficiency.
Worked Examples
Example 1: Speaker Impedance Calculation
Problem:A speaker has 8 ohms resistance and 6 ohms inductive reactance at 1 kHz. Find the total impedance.
Solution:|Z| = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10 ohms Phase = atan(6/8) = 36.87 degrees Q = 6/8 = 0.75
Result:Impedance = 10 ohms at 36.87 degrees
Example 2: Filter Circuit Impedance
Problem:A circuit has 220 ohms resistance and 150 ohms capacitive reactance. Calculate impedance and admittance.
Solution:|Z| = sqrt(220^2 + 150^2) = sqrt(48400 + 22500) = sqrt(70900) = 266.27 ohms Phase = atan(150/220) = 34.29 degrees Admittance = 1/266.27 = 3.756 mS
Result:Impedance = 266.27 ohms, Admittance = 3.756 mS
Frequently Asked Questions
What is impedance and how does it differ from resistance?
Impedance is the total opposition to alternating current (AC) flow in a circuit, measured in ohms. Unlike resistance, which only opposes DC or the real part of AC, impedance includes both resistance (real component) and reactance (imaginary component). Reactance arises from capacitors and inductors that store and release energy. Impedance is represented as a complex number Z = R + jX, where R is resistance and X is reactance.
How do you calculate impedance magnitude and phase angle?
Impedance magnitude is calculated using the Pythagorean theorem: |Z| = square root of (R squared plus X squared), where R is resistance and X is reactance. The phase angle theta equals arctan(X / R), which gives the angle between voltage and current waveforms. A positive phase angle indicates inductive behavior (current lags voltage), while a negative phase angle indicates capacitive behavior (current leads voltage).
What is admittance and how does it relate to impedance?
Admittance is the reciprocal of impedance, measured in siemens (S). It represents how easily AC current flows through a circuit. Admittance Y = 1/Z = G + jB, where G is conductance (real part) and B is susceptance (imaginary part). Conductance G = R / (R squared + X squared) and susceptance B = -X / (R squared + X squared). Admittance is useful in parallel circuit analysis where impedances are difficult to combine directly.
What is the quality factor Q in impedance?
The quality factor Q is the ratio of reactance to resistance: Q = |X| / R. It measures how much energy is stored versus dissipated per cycle in a reactive component. A high Q indicates low energy loss and sharp frequency selectivity, important in filters and resonant circuits. For example, a Q of 10 means the component stores 10 times more energy than it dissipates per cycle. Typical Q values for inductors range from 10 to 200.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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