Watt Density Calculator
Watt density is the power an element carries divided by the surface it carries it on, in watts per square centimetre. It is the number that decides how long a heating element lasts, and the one most often missing from an order. This page works it out and checks it against your medium.
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Check the Watt Density
Watt density is the power divided by the heated surface of the sheath. Total power decides how fast the job heats; watt density decides how long the element lasts.
The part with resistance wire inside it. The cold ends at each end carry no heat and do not count.
Watt density
Fill in every box and the figure appears here.
— W/cm²
Per element
Safe range in this medium: — W/cm²
Within the safe range for this medium.
Above the safe range. Do not drop the power — the job would never reach temperature. Make the heated length longer, or split the same power across more elements.
Heated length that would bring it into range: — mm
The safe ranges are the same figures the solution pages publish. They assume the element is fully in the medium and that the medium is moving where it is meant to.
The Detail
The formula
Watt density (W/cm²) = power (W) ÷ (π × sheath diameter × heated length)
Put the diameter and the heated length in centimetres, not millimetres. The bracket is the outside surface area of the heated part of the tube — the area the heat actually has to leave through.
For several elements sharing a load, divide the total power by the number of elements first. Each element only carries its own share.
A worked example
A 2000 W cartridge heater, 16 mm across, with 200 mm of heated length:
- Diameter: 1.6 cm, heated length: 20 cm
- Area: π × 1.6 × 20 = 100.5 cm²
- Watt density: 2000 ÷ 100.5 = 19.9 W/cm²
That is fine inside a steel mould, which takes 8 to 20. Put the same element in oil and it will char the oil onto itself within days.
Why the medium sets the limit
The heat has to get from the sheath into whatever surrounds it, and different things accept it at very different rates. Circulating water will take 8 to 12 W/cm² all day. Still water takes less, because there is no flow bringing cold liquid back to the surface. Heavy oil takes 1 to 2, because oil that sits against a hot sheath breaks down and leaves carbon behind. Moving air takes 3 to 5 — and finned elements exist precisely because plain tubes cannot shed enough heat into air.
Metal is the generous case. A cartridge in a well-machined bore is in contact with a solid that conducts heat away quickly, which is why cartridge heaters run at figures that would destroy an immersion element.
Cold ends are not heated length
Every tubular and cartridge element has a section at each end with no resistance wire inside it. Those cold ends exist so the terminals stay cool and the seal survives, and they produce no heat at all. Measuring from end to end inflates the area, which makes the watt density look lower than it is — the mistake always errs in the dangerous direction.
What the calculator cannot see
It assumes the whole heated length is properly in the medium and that the medium is moving where it is meant to. An element half out of the liquid, a cartridge in an oversized bore, or a band heater that is not tight against the barrel is all working at a far higher effective figure than the arithmetic says. Scale and carbon do the same thing over time. Where any of that is likely, design with room to spare rather than sizing to the top of the range.
Common Questions
What is a safe watt density?
It depends entirely on the medium. Circulating water takes 8 to 12 W/cm² and still water 6 to 8. Light oil and diesel take 2 to 3, heavy oil and mazut 1 to 2. Moving air takes 3 to 5. A cartridge in a steel bore takes 8 to 20, because metal carries heat away far better than any fluid.
What happens when the watt density is too high?
The sheath runs hotter than the medium can cool it. In water, a film of steam forms against the sheath and insulates it. In oil, the oil chars onto it and the carbon does the same. In air, nothing carries the heat away at all. In every case the element cooks itself from the inside.
How do I bring a high figure down?
Three ways, and none of them is "use less power". Make the heated length longer. Use a larger sheath diameter. Or split the same power across two or three elements. All three add surface, which is the only thing that lowers watt density.
Is heated length the same as the total length?
No, and using the total length is the commonest mistake on this page. Each end of a tubular or cartridge element has a cold section with no resistance wire in it, so it produces no heat. Only the heated part counts.
Does the figure change once the element is installed?
The figure does not, but what the medium can take does. Limescale, carbon or sludge on the sheath acts as insulation, so an element that was inside the safe range when new can be outside it a year later without anything about the element changing.
My element keeps burning out. Is this why?
It is the first thing to check. If the replacement element is the same power and the same size as the one that failed, and it fails the same way, the design is wrong rather than the part. Work the figure out before ordering another one.
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Call us or send a WhatsApp message for a price, full specifications, or a custom build.
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