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Busbar Ampacity and Temperature Rise Calculator

trafolo.eu / calculators / Busbar ampacity

Busbar rating is usually done by rule of thumb - so many amps per square millimetre. This solves the actual problem instead: loss depends on temperature through resistivity, and the heat removed depends on temperature through both the convection coefficient and radiation. The three are iterated to convergence. Solve for current to find the rating at a temperature limit.

Busbar losing its own I squared R loss to air bar on edgeIconvectionconvectionradiation, epstwI^2 R(T) = h As dT + rad
Loss depends on temperature through resistivity, and the heat removed depends on it through both h and radiation - so the three have to be solved together, not assumed.

On edge convects better, which is why switchboard bars are usually mounted that way.

Inputs — enter your values

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Solve for this against a temperature limit to get the rating.

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Results — computed for you

Common limits are 90 degC for a bare bar and 105 degC for plated joints.

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On a bright bar radiation is negligible; on an oxidised or painted one it can be a third.

Computed from the converged rise, not assumed.

Choosing something to solve for makes Conductor temperature an editable target and computes the chosen input from it.

Formula

Solve for dT such that: I^2 R(T) = h(dT) As dT + eps sigma As (T^4 - Ta^4) R(T) from resistivity at temperature and the AC resistance ratio. h(dT) from the natural convection correlations for the bar face.
dT temperature rise above ambient (K)
As wetted surface area, perimeter times length (m^2)
h natural convection coefficient, itself a function of dT
eps surface emissivity
sigma Stefan-Boltzmann constant

What this model assumes, and where it stops

Assumptions

  • A single isolated bar in unbounded still air.
  • Isothermal bar - no axial gradient along the run.
  • The whole perimeter is available for cooling.
  • Radiation exchange with surroundings at ambient temperature.
  • Steady state, and natural convection correlations for an isolated plate.

Limitations

  • Enclosures change everything. A bar inside a switchboard sees recirculating hot air, not unbounded ambient, and the real rise can be double what an open-air calculation gives.
  • Adjacent phases both block airflow and radiate at each other, so a three-phase set runs hotter than three times this single-bar answer suggests.
  • The perimeter is assumed fully wetted. Mounting insulators and supports block part of it.
  • No proximity effect, so the loss term is optimistic for a real three-phase arrangement.
  • Joints are local hot spots and are not modelled here - a poor joint often sets the rating rather than the bar.
  • Standards ratings include margins and test conditions this first-principles calculation does not reproduce; do not use this to claim compliance.

When you need a 3D field solution instead

Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:

  • Any enclosed busbar system, where the internal air temperature is the answer you actually need.
  • Three-phase arrangements, where phases shade each other from convection and radiate mutually.
  • Bolted joints and terminations, which are usually the hottest point in the system.
  • Bars near steel structure, where induced currents add loss the electrical model does not see.
  • Forced-ventilated switchgear, where the airflow distribution decides the rating.
  • Short-circuit and overload transients, where thermal mass rather than steady state sets the limit.
Try Trafolo 3D FEM Talk to us about your design

Common questions

How much current can a 50 x 6 mm copper busbar carry?

In free air at 30 degC with an emissivity of 0.4, carrying 600 A heats a vertical 50 x 6 mm bar about 23 K, to roughly 53 degC. That is comfortably inside the usual 65 K rise limits, which is why published tables rate this section around 700 to 850 A depending on finish and orientation. Inside an enclosure the local ambient is far higher than the room, so rate against the internal air temperature, not the room.

Does painting a busbar really increase its rating?

Yes, and by more than most people expect. Going from aged bare copper (emissivity about 0.4) to a painted or heavily oxidised surface (about 0.9) drops the same bar’s temperature rise from 23 K to 17 K at 600 A, because radiation share rises to about half of the total heat removal. The paint colour is nearly irrelevant - thermal radiation at these temperatures is far into the infrared.

Why is my busbar hotter than this calculator predicts?

Usually because it is not in free air. This model assumes still room air on all faces; inside a switchboard the air is pre-heated by everything below, neighbouring phases radiate at each other instead of at cold surroundings, and ventilation openings choke the buoyant flow. IEC 61439 handles this with verified temperature-rise tests rather than a formula, which tells you how far a free-air calculation can be pushed.

References

  • Copper Development Association - Publication 22, Copper for Busbars, section on temperature rise
  • IEC 61439-1 - Low-voltage switchgear assemblies, temperature rise limits

Related calculators

  • Busbar AC resistance - DC and AC resistance of a rectangular busbar including skin effect, with the exact strip solution and the perimeter-shell approximation side by side.
  • Natural convection - Convection coefficient for a plate in still air from Rayleigh and Nusselt, for vertical and horizontal surfaces, instead of guessing a value.
  • Joint contact resistance - Constriction resistance of a bolted busbar or terminal joint from Holm theory, with the surface film term that usually decides whether a joint ages well.
  • Voltage drop - Voltage drop along a cable or busbar run for DC, single-phase and three-phase supplies, separating the resistive and reactive contributions.