Type a line (24 V DC 10 A 25 m 4 mm2, 400 V 3ph 32 A 50 m 10 mm2 cos 0.85, 24 V DC 20 A 30 m max 3 %) or fill in the fields: the line and the fields stay in step.
Pick the system — DC, single-phase or three-phase AC — and enter the voltage, the current in A or the power in kW with cos phi, the length of the run in m or ft and the cross-section in mm2 or AWG, copper or aluminium. The calculator gives the loop resistance (on three-phase, the resistance of one conductor), the drop in V and per cent, the voltage at the load and the power lost in the cable. Enter a drop limit in per cent instead of a cross-section and it finds the smallest IEC 60228 size that keeps the drop within that limit. The working is shown with your numbers, and the result is a line you can copy.
Only the resistance of the conductor is taken into account, not its reactance; the temperature correction is for copper only. The permissible drop and the current rating of a cable are set by the design of the installation and the rules of the class society or IEC 60092: no limits, current ratings or cable selection advice are given here.
R = rho x L / S. For copper at 20 °C, rho = 1/58 = 0.017241 ohm mm2/m; for aluminium, 0.028264 ohm mm2/m. A copper conductor of 4 mm2 and 25 m: 0.017241 x 25 / 4 = 0.1078 ohm. At another conductor temperature, the resistivity of copper is multiplied by 1 + 0.00393 x (t - 20).
On DC and single-phase the current runs round a loop of two conductors: dU = 2 x I x R, and on AC times cos phi. On three-phase, dU = 1.732 x I x R x cos phi, with the per cent taken of the voltage between phases. 24 V, 10 A, 25 m, 4 mm2: 2 x 10 x 0.1078 = 2.16 V, 8.98 %.
The drop is inversely proportional to the cross-section, so for a limit in per cent S = k x I x rho x L x cos phi / (U x limit / 100), and the next larger IEC 60228 size is taken. 24 V, 20 A, 30 m, 3 %: 28.74 mm2, so 35 mm2 with a drop of 2.46 %.
| Size, mm2 | Copper, ohm/km | Aluminium, ohm/km | Copper, 2 conductors, 10 m, 10 A: drop, V |
|---|---|---|---|
| 0.50 | 34.48 | — | 6.90 |
| 0.75 | 22.99 | — | 4.60 |
| 1 | 17.24 | — | 3.45 |
| 1.5 | 11.49 | — | 2.30 |
| 2.5 | 6.897 | — | 1.38 |
| 4 | 4.310 | — | 0.862 |
| 6 | 2.874 | — | 0.575 |
| 10 | 1.724 | 2.826 | 0.345 |
| 16 | 1.078 | 1.766 | 0.216 |
| 25 | 0.6897 | 1.131 | 0.138 |
| 35 | 0.4926 | 0.8075 | 0.099 |
| 50 | 0.3448 | 0.5653 | 0.069 |
| 70 | 0.2463 | 0.4038 | 0.049 |
| 95 | 0.1815 | 0.2975 | 0.036 |
| 120 | 0.1437 | 0.2355 | 0.029 |
| 150 | 0.1149 | 0.1884 | 0.023 |
| 185 | 0.0932 | 0.1528 | 0.019 |
| 240 | 0.0718 | 0.1178 | 0.014 |
| 300 | 0.0575 | 0.0942 | 0.011 |
The resistance is worked out as rho x L / S, not taken from the IEC 60228 table of maximum resistances: for the stranded and tinned conductors of a real cable it may be a little higher. Aluminium is listed from 10 mm2. For another length or current the drop changes in proportion. 1 ft = 0.3048 m exactly.
Resistivity of annealed copper, 1/58 ohm mm2/m at 20 °C: the international standard of resistance for copper (IEC 60028, 100 % IACS); of aluminium, 0.028264 ohm mm2/m: 61 % IACS, as in the standards for aluminium conductors; the temperature coefficient of copper, 0.00393 per kelvin at 20 °C. Each value is checked against two independent references. The size series is IEC 60228; the AWG sizes follow the ASTM B258 formula. The drop formula is the approximate formula of IEC 60364-5-52 with the reactance term left out.
About 2.16 V, or 8.98 % of 24 V, which leaves 21.84 V at the load. One conductor has R = 0.017241 x 25 / 4 = 0.1078 ohm, the loop twice that, 0.2155 ohm, and the drop is 2 x 10 A x 0.1078 ohm = 2.16 V. The cable turns 21.6 W into heat.
dU = 1.732 x I x R x cos phi, with R the resistance of one phase conductor, and the per cent of the voltage between phases. For 400 V, 32 A, 50 m of 10 mm2 copper at cos phi 0.85: R = 0.017241 x 50 / 10 = 0.0862 ohm, dU = 1.732 x 32 x 0.0862 x 0.85 = 4.06 V, or 1.02 %.
The drop is inversely proportional to the cross-section, so the size needed is S = k x I x rho x L x cos phi / (U x limit / 100), with k = 2 for a two-wire circuit and 1.732 for three-phase. For 24 V DC, 20 A, 30 m and a limit of 3 %: 2 x 20 x 0.017241 x 30 / 0.72 = 28.74 mm2, so the next IEC 60228 size, 35 mm2, which gives 0.59 V, or 2.46 %.
Because the reactance depends on how the cable is built and laid: the insulation, the way the cores lie, an armour. No figures for it are given here. Without it the drop on AC comes out lower than the real one, the more so the larger the cross-section and the lower the cos phi; on DC the reactance has no part, and at cos phi 1 it drops out of the approximate formula used here. The figures are the resistive drop, and the page says so.
The resistance of copper rises by 0.393 % per kelvin above 20 °C: at 70 °C the resistivity is 0.017241 x (1 + 0.00393 x 50) = 0.020629 ohm mm2/m, about 19.7 % more, and the drop rises by as much. The page corrects copper only; the sources for aluminium give different coefficients, so aluminium is worked at 20 °C.
The permissible drop and the current rating of the cable are set by the design of the installation and the rules of the class society or IEC 60092. This page gives no limits and no current ratings; it works out the drop for the figures you enter.
The calculator works out the voltage drop from the figures you enter. When a cable, lugs, glands or a breaker are needed, attach a photograph of the marking or the diagram, and Vessel Core checks the details before an offer goes back.
