Cable Impedance Calculator: Formula and Limits

A cable impedance calculator estimates the electrical opposition a cable presents to alternating current, using its resistance and reactance at a specified frequency. Entering the cable’s resistance, inductive reactance, and capacitive reactance gives the impedance magnitude; the result is a mathematical estimate, not a cable safety or suitability rating.

Formula

For a simple series-equivalent model, impedance is a complex quantity with resistance on the real axis and net reactance on the imaginary axis:

Z = R + j(X_L − X_C)

Its magnitude, which is the first calculator result, is:

|Z| = √[R² + (X_L − X_C)²]

• Z is complex impedance, measured in ohms (Ω).
• |Z| is impedance magnitude, in ohms.
• R is resistance, in ohms.
• X_L is inductive reactance, in ohms.
• X_C is capacitive reactance, in ohms.
• j denotes a 90-degree phase rotation in complex-number notation.

The second result is the phase angle, φ = arctan[(X_L − X_C)/R], in degrees. Positive net reactance gives a positive, inductive angle; negative net reactance gives a negative, capacitive angle. This calculator uses the ordinary arctangent ratio, so the angle is not a substitute for a full quadrant-aware phase calculation in cases where resistance is zero.

Worked Example

Using the exact defaults in the calculator:

• Resistance: R = 10 Ω
• Inductive reactance: X_L = 20 Ω
• Capacitive reactance: X_C = 0 Ω

First find net reactance: X = 20 − 0 = 20 Ω.

Then calculate the impedance magnitude:

|Z| = √(10² + 20²) = √(100 + 400) = √500 = 22.3607… Ω, which rounds to 22.36 Ω.

The phase angle is arctan(20/10) = arctan(2) = 63.4349…°, which rounds to 63.43°. These outputs describe the simplified series model, not a particular cable installation.

What Cable Impedance Means

Resistance is the opposition that dissipates electrical energy as heat. Reactance arises from electric and magnetic fields and changes with signal frequency. Together, resistance and reactance determine impedance, which affects current, voltage drop, phase relationships, and how a cable interacts with its source and load.

A cable is not always adequately described by one lumped resistance and two reactances. At low frequencies and short lengths, a simple equivalent circuit may be useful. At higher frequencies or over longer runs, a cable behaves as a distributed transmission line: voltage and current vary along its length, and its characteristic impedance and propagation delay matter. The calculator’s lumped formula does not calculate characteristic impedance.

For a sinusoidal signal, inductive reactance is X_L = 2πfL, while capacitive reactance is X_C = 1/(2πfC). Here, f is frequency in hertz, L is inductance in henries, and C is capacitance in farads. These equations show why a reactance value must correspond to a stated frequency. This calculator accepts reactances directly; it does not infer them from cable dimensions or material.

When to Use the Calculator

Use it when you already have resistance and reactance values for a cable model at the frequency of interest and want their combined magnitude. For example, a model with 3 Ω resistance, 4 Ω inductive reactance, and 0 Ω capacitive reactance has a magnitude of √(3² + 4²) = 5 Ω. If both inductive and capacitive effects are present, subtract them algebraically before combining with resistance: they oppose one another in this simplified model.

To apply the result to an actual cable, first identify what the given values represent. Resistance may be specified per unit length, per conductor, or for a complete loop. Reactance may be given per unit length and at a stated frequency. Convert all inputs to the same basis before calculation: for example, do not combine ohms per kilometre with total ohms. The arithmetic itself accepts ohms; it does not know the cable length or correct a mismatched unit basis.

For a simple AC circuit, the magnitude can help relate RMS voltage and current through |V| = |I||Z| when the model and circuit conditions justify that relation. It does not by itself give real power: phase and power factor also matter. In an ideal sinusoidal series circuit, the power factor is related to the phase angle by cos φ.

How to Choose Input Values

Get values from a reliable cable specification, measurement, or appropriate circuit model, and check the following before entering them:

• Frequency: Reactance changes with frequency. Values at one frequency should not be reused blindly at another.
• Length and configuration: Confirm whether figures apply per metre, per kilometre, per foot, or to the whole cable, and whether the return conductor is included.
• Conductor temperature: Resistance can change as conductor temperature changes. Use a value appropriate to the conditions being modelled.
• System model: Confirm whether the cable is being treated as a series element, a transmission line, or part of a larger network.
• Units: All three calculator inputs must be in ohms. Convert milliohms to ohms by dividing by 1,000.

Limits and Common Misconceptions

Impedance is not the same as resistance. Resistance is a real-valued component; impedance includes frequency-dependent reactance. Nor does impedance magnitude alone tell you whether a cable is safe, adequately sized, or compatible with equipment. Those judgments can require current, temperature, installation conditions, fault conditions, insulation ratings, applicable standards, and manufacturer data. Do not use this general calculator to choose wire gauge, breakers, or other safety-critical equipment; consult a qualified professional and relevant specifications.

A frequent mistake is adding all three values as ordinary numbers. Reactances have signs: inductive and capacitive reactance oppose each other. Another is assuming that two cables with the same impedance magnitude behave identically. Their phase angles may differ, as may their frequency response and transmission-line characteristics. Finally, the displayed two-decimal rounding is for readability; calculations needing greater precision should retain unrounded values where possible.

Frequently Asked Questions

What is the formula for cable impedance?
For a simple series model, Z = R + j(X_L − X_C), and its magnitude is √[R² + (X_L − X_C)²]. All components must use consistent units and conditions.

Is cable impedance the same as characteristic impedance?
No. This calculator combines lumped resistance and reactances. Characteristic impedance is a transmission-line property determined by distributed cable parameters; it is especially relevant to signal reflections on longer or higher-frequency links.

Does cable impedance depend on frequency?
Yes. Inductive and capacitive reactance depend on frequency, and a cable’s effective resistance can also vary with frequency. State the frequency when using or comparing impedance values.

Can I calculate impedance from cable length alone?
No. Length alone is insufficient. You also need relevant electrical parameters, such as resistance and reactance per unit length, and must know the frequency and whether the values describe one conductor or a complete circuit.

Why can capacitive reactance be subtracted?
In the simple series model, inductive reactance is positive and capacitive reactance is negative in the complex impedance. Their net reactance is therefore X_L − X_C; resistance is then combined with that net value using the magnitude formula.

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in r | Resistance | ohm | 10 | 0
in xl | Inductive reactance | ohm | 20 | 0
in xc | Capacitive reactance | ohm | 0 | 0
out z | Cable impedance magnitude | ohm | sqrt(r^2 + (xl - xc)^2) | 2
out phase | Impedance phase angle | degrees | atand((xl - xc) / r) | 2