Electricity · Industrial electricity

Single-phase / three-phase AC voltage drop

Calculate AC cable voltage drop from the conductor linear resistance and reactance for single-phase or balanced three-phase circuits.

Created Sep 17, 2026v1.0

By Thibaut Grzelak, Mechanical Analysis Engineer

Industrial electricity

Results

Voltage drop ΔU

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Calculated voltage difference along the cable.

Relative voltage drop

—%

Voltage drop relative to nominal voltage U.

Load-end voltage U₂

—

Estimated voltage at the load after the cable voltage drop.

Relation and numerical substitutionΔU = k · L · I · (R cosφ + X sinφ)

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L is the one-way distance from source to load, not the total conductor length. R and X are conductor resistance and reactance per unit length; units are converted consistently with L. Single-phase uses factor 2 for the outgoing and return path; balanced three-phase uses √3. The calculation uses 0 < cos φ ≤ 1 and does not size cable cross-section, ampacity or protection.

01Formulas and symbols

Formulas used

sinφ√(1 − cos²φ)Sine of the phase angle

ΔU₁φ2 · L · I · (R cosφ + X sinφ)Single-phase voltage drop with the outgoing and return path

ΔU₃φ√3 · L · I · (R cosφ + X sinφ)Balanced three-phase voltage drop

ΔU%100 · ΔU / URelative voltage drop

U₂U − ΔUEstimated load-end voltage

02Assumptions and limits

Scope of validity

L is the one-way distance from source to load, not the total conductor length.
R and X are conductor resistance and reactance per unit length; units are converted consistently with L.
Single-phase uses factor 2 for the outgoing and return path; balanced three-phase uses √3.
The calculation uses 0 < cos φ ≤ 1 and does not size cable cross-section, ampacity or protection.

03Validation example

Reference numerical case

Single-phase: U = 230 V, I = 32 A, L = 50 m, R = 0.727 Ω/km, X = 0.08 Ω/km and cos φ = 0.85.
sin φ = √(1 − 0.85²) ≈ 0.5268.
ΔU ≈ 2.112 V, or 0.918% of 230 V.
U₂ ≈ 227.888 V.

04References

Technical references

IEC 60364-5-52 — Low-voltage electrical installations: selection and erection of wiring systems.

FAQ

L ?

L is the one-way distance from source to load, not the total conductor length.

R / X ?

R and X are conductor resistance and reactance per unit length; units are converted consistently with L.

1φ / 3φ ?

Single-phase uses factor 2 for the outgoing and return path; balanced three-phase uses √3.

U / I / cosφ ?

Nominal voltage U · Current I · Power factor cos φ.