Voltage drop, end to end: a worked feeder in calculator #001

Voltage drop is the calculation everyone does and almost nobody documents. This guide walks the whole thing end to end in calculator #001: what each input actually changes, how the number is produced, and how to read the result against the limit you picked. The worked example is a real run — every figure below was taken from the calculator, not typed in by hand.

What the tool is for

A feeder is rarely one cable. It is a run from a board to a starter, then a tail to a local panel, sometimes a change of cross-section along the way, sometimes two cables in parallel. Calculator #001 models that as a chain of segments inside a feeder, and a project holds as many feeders as you need:

• each segment carries its own length, cross-section, cable series, power factor and design current;
• each feeder sums its segments and compares the total against your limit;
• the project keeps the shared context — nominal voltage, system type, ambient and conductor operating temperature.

That structure matters because the drop in a chain is additive, but the percentage is not a single division at the end — each segment is a percentage of its own voltage. The calculator sums them the way the chain actually behaves.

How the number is produced

For every segment the tool computes the loaded impedance and applies the standard voltage-drop expression:

ΔU = b · I · (R·cos φ + X·sin φ)

b = √3   three-phase, line-to-line
b = 2    single-phase and DC (out-and-return)

Three things happen before that formula runs, and they are where most hand calculations go wrong:

1. The resistance is corrected to the operating temperature. The cable library stores R at the series' reference temperature (90 °C for XLPE, 70 °C for PVC). If you set a different conductor temperature, R is scaled by the copper/aluminium temperature coefficient before it is used. Run the same cable at 90 °C instead of 20 °C and the resistance is about 28 % higher — that is the difference between a feeder that passes and one that does not.

2. Reactance is not dropped. X comes from the same library row. On large cross-sections X stops being negligible: at 240 mm² the reactance term is comparable to the resistance term, and ignoring it understates the drop.

3. Parallel conductors divide the impedance. Set n and both R and X are divided by n for that segment — the current is still the full design current.

The calculator ships with a cable library compiled from BS 5467 / BS 7889 / BS 6004 and manufacturer LV tables — R at the declared operating temperature, X, and informative ampacity per size. You can override R and X per segment when you have manufacturer data for the specific drum.

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Worked example: pump feeder P-01

A 55 kW pump fed from a 400 V MCC. Design current 95 A. The run is 70 m of 4-core 35 mm² Cu XLPE/SWA to the starter, then a 25 m tail in 16 mm² to the local control panel, where 32 A of control and auxiliary load sits. Ambient 40 °C, conductors assumed at their 90 °C rating. Limit for the check: 5 %.

Step 1 — project settings

These apply to every feeder in the project, so set them once.

The limit list follows the values engineers actually cite — 3 % for lighting, 5 % for other uses, 8 % where the installation is fed from its own HV supply. Choose the one your specification names; the calculator does not assume it for you.

Step 2 — the two segments

Each card ends with a result strip, so you can see the intermediate values without leaving the input:

Note the ampacity column: 95 A against 151 A and 32 A against 94 A. The cable is not thermally limited here — the question is purely the drop.

Step 3 — the result

Voltage at the control panel: 398.12 V.

Checking it by hand

Segment 1, so you can see there is nothing hidden in the tool:

R = 0.668 Ω/km × 70 m           = 46.76 mΩ
X = 0.072 Ω/km × 70 m           =  5.04 mΩ
sin φ = √(1 − 0.86²)            =  0.5103

ΔU = √3 × 95 × (46.76 × 0.86 + 5.04 × 0.5103)
   = 1.732 × 95 × (40.21 + 2.57) mV
   = 7 040 mV = 7.04 V  →  7.04 / 400 = 1.76 %

The calculator reports 7.040 V and 1.760 %.

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Hand check: the same feeder, on paper

Voltage drop is short enough to verify completely by hand, so there is no excuse for taking a tool's word for it. Here is the same feeder P-01, worked with a pencil against the standard, then compared with the calculator.

Step 1 — check the cable data against IEC 60228

The formula is only as good as R. The library stores resistance at the cable's rated operating temperature (90 °C for XLPE), so back it out to 20 °C and compare with the maximum values IEC 60228:2004, Table 2 publishes for class 2 stranded plain copper:

R20 = R90 / [1 + a20 (90 - 20)] = R90 / (1 + 0,00393 x 70) = R90 / 1,2751

35 mm2:  0,668 / 1,2751 = 0,5239 ohm/km   vs IEC 60228: 0,524 ohm/km   (0,0 %)
16 mm2:  1,470 / 1,2751 = 1,1529 ohm/km   vs IEC 60228: 1,150 ohm/km   (+0,2 %)

Both land on the published maxima. That is the first thing to check in any voltage-drop tool: if the resistance table does not reduce to IEC 60228, nothing downstream can be right.

Step 2 — the drop, segment by segment

Segment 1 — MCC to starter, 70 m of 35 mm² Cu XLPE/SWA, I_B = 95 A, cos φ = 0,86, conductors at 90 °C:

R = 0,668 ohm/km x 70 m = 46,76 mohm
X = 0,072 ohm/km x 70 m =  5,04 mohm
sin phi = sqrt(1 - 0,86^2) = 0,5103

dU = b I (R cos phi + X sin phi),  b = sqrt(3) for three-phase
   = 1,7321 x 95 x (0,04676 x 0,86 + 0,00504 x 0,5103)
   = 1,7321 x 95 x 0,042797 = 7,040 V
dU% = 100 x 7,040 / 400 = 1,760 %

Segment 2 — starter to control panel, 25 m of 16 mm², I_B = 32 A, cos φ = 0,90:

R = 1,47 x 25/1000 = 36,75 mohm ;  X = 0,082 x 25/1000 = 2,05 mohm ; sin phi = 0,4359
dU = 1,7321 x 32 x (0,03675 x 0,90 + 0,00205 x 0,4359) = 1,883 V  ->  0,471 %
Feeder total: 7,040 + 1,883 = 8,923 V  ->  2,231 %

Step 3 — check the formula itself against IEC 60364-5-52

Annex G of IEC 60364-5-52:2009 writes the same calculation differently, and the difference confuses people:

u = b ( rho1 L / S x cos phi + lambda L x sin phi ) I_B      with b = 1 for three-phase
                                                                  b = 2 for single-phase
du% = 100 u / U0        (U0 = line-to-neutral voltage)

Annex G's b = 1 with the line-to-neutral voltage and the tool's b = √3 with the line-to-line voltage are the same statement, because U_LL = √3·U₀:

sqrt(3) I R / U_LL  ==  I R / U0        (identical, since U_LL = sqrt(3) U0)

Run segment 1 with Annex G's own default constants — ρ₁ = 0,0225 Ω·mm²/m for copper (that is 1,25 × the resistivity at 20 °C) and λ = 0,08 mΩ/m in the absence of better data:

rho1 L / S = 0,0225 x 70 / 35 = 0,045 ohm      (= 0,643 ohm/km)
lambda L   = 0,08 mohm/m x 70 = 5,6 mohm       (= 0,080 ohm/km)
u = 95 x (0,045 x 0,86 + 0,0056 x 0,5103) = 3,948 V per phase
du% = 100 x 3,948 / 230,94 = 1,710 %

against the calculator's 1,760 %. The 3 % difference is entirely in the input data, not the method: Annex G's flat 1,25 factor corresponds to about 84 °C, while the run above puts the conductor at 90 °C (0,643 versus 0,668 Ω/km), and the real cable's reactance is 0,072 Ω/km rather than the generic 0,080. Both are defensible; only one of them describes the cable on the drum.

What this check tells you to watch

• Which temperature is R quoted at? A resistance taken at 20 °C instead of the operating temperature understates the drop by about 22 % for copper at 90 °C. Annex G handles it with a flat 1,25; the calculator corrects explicitly with α₂₀, which is why the operating-temperature field is not decoration.
• b is a system property, not a fudge factor. √3 line-to-line, 2 for single-phase and DC out-and-return. A three-phase circuit with the neutral fully unbalanced is treated as single-phase (Annex G, Note 3) — that is a doubling, and it is easy to miss.
• Percentages add, volts add — but not across different voltages. Each segment's percentage is taken against its own voltage before summing. In a chain that crosses a transformer, summing volts alone gives nonsense.
• The limit is yours to pick. Table G.52.1 gives 3 % lighting / 5 % other uses for installations supplied from a public LV network, and 6 % / 8 % where the installation has its own LV supply — plus 0,005 % per metre beyond 100 m, capped at 0,5 %. The calculator does not guess which line applies to your project.

Reading the result

2.23 % against a 5 % limit — but that is not the whole answer. Two things deserve a second look before signing this off:

• The limit belongs to the whole installation, not to this feeder. If the origin-to-board run already spends 1.5 %, the pump sees 3.7 % and the margin is thinner than it looks. Model the upstream run as another feeder in the same project and read the overview table.
• 90 °C is the pessimistic case, and it is the right one for a design check. At a realistic 60 °C the resistance is about 9 % lower and the total falls to 2.04 % (8.14 V) — a useful number to know, but the check should stay at the rated temperature.

If it does not pass, the tool makes the three levers explicit: increase S on the segment that dominates (here segment 1 contributes 79 % of the total), split the run into parallel conductors and set n, or fix the power factor at the load. The per-segment strip tells you which lever is worth pulling — there is no point uprating a 25 m tail that costs 0.47 %.

Motor starting is a separate check. The 2 % above is steady-state at 95 A. During start the current is several times that, and the momentary drop must not pull the contactor out or stall neighbouring loads. Re-run the same segments with the starting current and the starting power factor to see it.

FREE and PRO: where the line runs

The calculator is split into two tabs, and for #001 the line is drawn in one place only — how many feeders fit into a single project file.

FREE — open access, no account:

• the complete calculation: any number of segments in a feeder, the cable library with R and X at the declared temperature, temperature correction, parallel conductors, per-segment result strip and the running total;
• the verdict against the limit you selected;
• the full .docx report with the per-segment derivation;
• up to 3 feeders in one project.

PRO:

• more than three feeders in a single project file (unlimited_projects).

The calculation itself is never reduced — the free tier computes exactly what the paid one computes. What you buy is project size, and the calculator says so in its own source comment: "the calculation itself is never reduced — only how many of them fit into a single file."

Where this sits next to the other tools

• Thermal sizing is the other half of the same decision — #004 Cable Ampacity computes Iz per IEC 60287 with soil, grouping and ambient derating, which is what the informative ampacity column here is only hinting at.
• The same cable data feeds the fault study — #002 Short-Circuit uses R and X to get I″k at the board, and from there the withstand check on the same cable.
• For a whole distribution board with dozens of feeders, Electrical Networks runs voltage drop, load flow and fault levels over one schematic instead of tab by tab.

Open calculator #001 →