Busbar Size and Short-Circuit Formulas

Busbar formulas: the cross-section from the current and a design current density, the number of bars, the short-circuit withstand area and the mass per metre.

The formulas

I is the load current in amperes, J the design current density in A/mm², Isc the fault current in amperes, t its duration in seconds and k a constant for the material and the temperature rise from the standard or the maker. The current density is a rule of thumb: it depends on the temperature rise allowed, the enclosure, the ambient temperature, the paint and the arrangement of the bars, so use the ratings from the maker or the standard for the real busbar. The 1.2 A/mm² here is only an example for copper. Bars in parallel carry less than the sum of their areas because of the skin and proximity effects, and the bar must also be checked for the electromagnetic force of a fault (see the conductor forces article).

Worked example: a 2,000 A bar

Copper at 1.2 A/mm² with 100 × 10 mm bars.

1. A = 2000 / 1.2 = 1,667 mm²
2. Ab = 100 × 10 = 1,000 mm², so n = 1.667 rounded up to 2 bars
3. The actual current density is 2000 / 2,000 = 1 A/mm²

Worked example: the short-circuit area

40 kA for 0.5 s with k = 115 (an example value).

1. A ≥ 40,000 × √0.5 / 115 = 246 mm²

Worked example: mass per metre of a 100 × 10 mm bar

1. Copper: 1000 × 10⁻⁶ × 8960 = 8.96 kg/m
2. Aluminium: 1000 × 10⁻⁶ × 2700 = 2.7 kg/m

Current at 1.2 A/mm² for common bars (example density)

Frequently asked questions

Is 1.2 A/mm² a rule?

No. It is an example. The allowed current density depends on the temperature rise, the enclosure and the cooling, so take the rating from the busbar maker or the standard.

Why is the rating of two bars not twice that of one?

The current crowds to the outside of the bars, and the bars heat each other, so the second bar adds less than its area. Spacing the bars helps.

Does the short-circuit check use the fault duration?

Yes. The heat grows with I² × t, so the area goes with the current times the square root of the time.

Copper or aluminium?

Aluminium needs about 1.64 times the area for the same resistance, but it is lighter, as the mass figures above show.

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