3kw cooker - 20amp fuse and 4mm cable?

I have a 3kw dual fuel cooker installation in a couple of weeks and have discovered that I do not have a dedicated circuit in place for this (the existing small oven is plugged in to a standard socket). I realise I need to run a cable from my fuse box, and hence have carried out some research... I came up with the following:
3kw appliance = 13amps, so if I use a 20 amp fuse at the consumer unit, I can then use 4mm cable which seems to take btwn 25 and 30 amps....
I thought I had this all sussed, until I spoke to someone who said.....
3kw appliance needs 30amp fuse and 6mm cable. Is this correct or just erring on the side of caution??
The run is about 19 metres, and will be under floorboards, except for a couple of metres of trunking down the wall.
Any advice greatly appreciated!
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I'm planning to run mine off a socket! OK, the ring main I intend to use is pretty unloaded. However, if you wish to use a separate circuit (i.e. your socket circuit is loaded with high current items such as dishwashers and washing machines) then 4mm and a 20A breaker would be fine.
I'd probably use a 16A breaker myself, but 6mm cable. Cable isn't expensive, it is the redecorating after laying it that is, so you might as well lay it now you've got the chance. The 6mm cable will run a large electric cooker, giving you options in the future. Not that I'd want to recommend getting one.
If future upgradability doesn't worry you and you aren't running the cable in insulation, then 2.5mm cable would be fine for this circuit, assuming voltage drop/earth loop impedence is fine for the length.
Christian.
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Conventional Final Circuits, a radial wired in 4mmsq with a 20A fuse (even the ancient rewireable-with-a-four-inch-nail type) or "normal" TypeB MCB or RCBO is fine for a run of 43m, more or less regardless of how it runs. Indeed, wiring in 2.5mmsq is OK for 27m with a cartridge fuse or a TypeB MCB.
As others have said, if you want to do this for just this specific appliance, a 2.5mmsq run will be OK ass-U-ming you'll use a normal MCB, with the advantage that you'll either have 2.5mmsq already to hand, or will find it sensible to buy a 100m reel at normal cheap-as-chips prices from an electrical counter (it's such a high-volume item that it's sold close to cost, at around 15 quid or so). On the other hand, if you're buying a cut length of thicker cable, I'd future-proof by putting in the 6mmsq stuff so that you or subsequent owners can run a beefier all-electric cooker off the same wiring, with a cooker control unit in place of the 20A dual-pole switch I'm guessing you're planning for this hob.

plug-in appliance - used to be a common rating for kettles, though most are 2.2 or 2.4kW these days; some fan heaters are 3kW. You don't see Monster cables attached to those, do you? In fact without a "step-down" 13A fuse in a fused connection unit or similar, you'd be *less* safe with a 30A fuse as the only overcurrent protection for your hob and 6mmsq cable than the more closely-rated 20A one, even with 2.5mmsq cable!

advice/regs-lookup to be tailored to what you're actually doing, rather than full of "if this... if that..."! (All it needed to be a Perfect enquiry would've been more precision over what you meant by "fuse" - old-style rewireable, rarely-used-but-useful cartridge type, or the near-omnipresent MCB).
Cheers, Stefek
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