Series Impedance Per Unit Length Calculator

Find resistance, reactance, and impedance per unit length. Compare conductor data with simple inputs. Download CSV and PDF reports from one clean calculator now.

Calculator

Hz
°C
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For direct mode, enter inductance from a data table. For geometry mode, the calculator estimates inductance and still uses resistance, frequency, temperature, and path settings.

Formula Used

The main formula is Z′ = R′ + jX′. Inductive reactance is X′ = 2πfL′. Total impedance is Z = Z′ × length. Temperature correction uses R′T = R′ref × [1 + α(T - Tref)] × Kac.

For a transposed three-phase geometry estimate, L′ = μ0μr / 2π × ln(Deq / GMR), where Deq = (Dab × Dbc × Dca)^(1/3). For a two-wire loop, the calculator uses L′ = μ0μr / π × ln(D / GMR).

How to Use This Calculator

  1. Select direct input or geometry estimate.
  2. Enter resistance per unit length and choose its unit.
  3. Enter inductance, or provide spacing and GMR values.
  4. Add frequency, route length, temperatures, and AC factor.
  5. Choose the output unit and press Calculate.
  6. Use CSV or PDF to save the current result.

Example Data Table

Case R L Frequency Length Approximate Z′
Distribution cable 0.164 Ω/km 0.9 mH/km 50 Hz 10 km 0.164 + j0.282743 Ω/km
Overhead feeder 0.08 Ω/km 1.2 mH/km 60 Hz 25 km 0.08 + j0.452389 Ω/km
Control pair 0.05 Ω/m 0.7 µH/m 1000 Hz 100 m 0.05 + j0.004398 Ω/m

Series Impedance Guide

Series impedance per unit length describes the opposition in a line section. It combines resistance and inductive reactance. Engineers use it for cables, feeders, bus runs, and overhead conductors. The value is normally written as R plus jX. R shows real loss. X shows magnetic energy storage. Together they affect voltage drop, short circuit current, and power flow.

Why This Value Matters

A long conductor does not behave like a small jumper. Every meter adds resistance. Every meter also adds inductance. At higher frequency, inductive reactance grows. This calculator helps compare materials, routes, and operating conditions before a layout is finalized. It can also estimate total impedance for a selected length. That is useful for quick studies and report checks.

Main Input Ideas

Enter resistance per length when it is available from a datasheet. Enter inductance per length when your design guide provides it. You may also use the geometry option. It estimates inductance from conductor spacing and GMR. Temperature correction adjusts resistance from a reference value. A skin or proximity factor can be added when alternating current raises effective resistance.

How To Read Results

The calculator returns R, X, magnitude, angle, and total impedance. R is the loss part. X is the reactive part. Magnitude shows the combined size. Angle shows how inductive the line is. Positive angle means the impedance is inductive. Total values are found by multiplying the per length value by the entered route length.

Practical Notes

Use consistent units. Check whether a cable table lists ohms per kilometer, mile, meter, or foot. For three phase transposed lines, use equivalent spacing. For bundled or parallel conductors, use a suitable equivalent value from design standards. The geometry estimate is a practical approximation. Final engineering work should use manufacturer data and accepted design rules.

Common Use Cases

Power studies often need quick line models. A designer may compare copper and aluminum. A technician may check a replacement cable. A student may test frequency effects. The same method supports low voltage feeders, medium voltage cables, and simple transmission examples. Results can be exported, so another person can review the assumptions. Keep notes with every value, especially when data comes from mixed sources. This improves checking and future reuse later.

FAQs

What is series impedance per unit length?

It is the resistance and reactance of a conductor for one chosen length unit. It is written as R′ + jX′ and is often shown in ohms per kilometer, meter, mile, or foot.

How is inductive reactance calculated?

Inductive reactance is calculated with X′ = 2πfL′. Frequency is in hertz. Inductance must be converted to henries per the same length basis before the final value is shown.

Why does temperature change resistance?

Metal resistance changes with conductor temperature. The calculator uses a linear coefficient, alpha. Copper often uses about 0.00393 per °C, but you should enter the value that matches your material.

Can I estimate inductance from spacing?

Yes. Choose geometry mode. Enter conductor spacing, GMR, relative permeability, and the model type. The result is an approximation and should be checked against cable or line data when available.

What does the impedance angle mean?

The angle shows the balance between resistance and reactance. A larger positive angle means the impedance is more inductive. A smaller angle means resistance is a larger share.

How do parallel paths affect the result?

The calculator divides the identical path impedance by the number of paths. This is a practical simplification. Real installations may need mutual coupling and layout checks.

Can I use this for DC circuits?

Yes. Set frequency to zero. The reactance becomes zero, so the impedance mainly follows corrected resistance per unit length and total conductor length.

Is this enough for final engineering design?

No. Use it for estimates, checks, and reports. Final design should use verified manufacturer data, accepted standards, protection studies, and professional review where required.

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