Impedance Calculator
Enter a resistance and a net reactance to get the magnitude of a series RLC impedance in ohms — and see how the two combine like the sides of a right triangle.
Resistance and reactance combined
Enter the resistance and the net reactance and the calculator returns the impedance magnitude |Z| = √(R² + X²) in ohms.
Mind the sign of X
Net reactance is positive when the circuit is inductive and negative when it is capacitive — either way, squaring it makes the impedance the same.
What is impedance?
The opposition to alternating current
This impedance calculator turns two values — the resistance R and the net reactance X, both in ohms — into the magnitude of the impedance of a series RLC circuit. Impedance is the total opposition a circuit presents to an alternating current. It combines the resistance, which does not depend on frequency, with the reactance contributed by inductors and capacitors, which does. Because the resistive and reactive parts act at right angles to each other, they do not simply add: they combine like the two legs of a right triangle, and the impedance is the hypotenuse. The result is the single number that links voltage and current amplitudes in an AC circuit, the figure behind speaker matching, filter design, and antenna tuning.
Enter a resistance and a net reactance in ohms to get the impedance magnitude in ohms instantly.
The impedance magnitude is the square root of the sum of the squares of the resistance and the net reactance, where the net reactance is the inductive reactance minus the capacitive reactance (X = X_L − X_C).
|Z| = √(R² + X²)Suppose a series circuit has a resistance of 3 Ω and a net reactance of 4 Ω. Square each one to get 9 and 16, add them to reach 25, then take the square root to find an impedance of 5 Ω. Because both terms are squared, the sign of the reactance never changes the answer: a 4 Ω inductive reactance and a 4 Ω capacitive reactance (which you would enter as −4) both yield the same 5 Ω.
The formula is exact for a series RLC circuit, but a few practical points are worth keeping in mind.
Magnitude only, and net reactance must be pre-computed
This calculator returns the magnitude of the impedance, not its phase angle, and it expects the net reactance you have already worked out (X = X_L − X_C) at your operating frequency. Reactance changes with frequency, so a value valid at one frequency is wrong at another. Resistance cannot be negative, but the net reactance can: enter a negative value for a capacitive circuit and zero at resonance, where the impedance equals the resistance alone.