Ib ≤ In ≤ Iz, and everything else is detail

One inequality carries the whole method. The design current must not exceed the device rating, and the device rating must not exceed what the cable can actually carry where it is installed.

Ib  ≤  In  ≤  Iz

Ib is the load. In is the protective device, chosen at or above Ib from the standard ratings. Iz is the cable's tabulated capacity after the correction factors — and that last word is where designs go wrong.

BS 7671 works the inequality backwards. Rather than derating a cable and checking it, you divide the device rating up by the factors to get the tabulated capacity you need, then look for a cable that has it:

It  ≥  In / (Ca × Cg × Ci × Cf)

This is the opposite arithmetic to the NEC method, which multiplies an ampacity down. The two reach similar places, and mixing them produces answers that are wrong in ways nobody notices.

Reference method comes first

Before any factor is applied, the standard asks how the cable is installed — and the answer moves the capacity more than anything else on the page. A 2.5 mm² twin-and-earth is 18.5 A in conduit in an insulated wall and 27 A clipped direct. Same cable, same standard, forty per cent apart.

A — in conduit in an insulated wall. The harshest common method; the heat has nowhere to go.
B — in conduit or trunking on a wall. The usual commercial case.
C — clipped direct. Open to air on one side.
E — free air, multicore. Tray or ladder, spaced off the wall.
F — free air, single-core touching.

If a cable can be clipped instead of buried in a wall, that choice is usually worth a size. It is the cheapest derating you will ever recover.

The four factors

They multiply together, and the combined figure is often harsher than people expect — three of them at 0.8 is already 0.51.

Ca — ambient. Tables assume 30 °C. A 40 °C plant room costs 13 %, a 50 °C one costs 29 %.
Cg — grouping. Two circuits bunched take 0.8, six take 0.57. Count what actually shares the enclosure over its length, not what is in the drawing.
Ci — thermal insulation. Regulation 523.9, and the one that catches domestic work. A cable through 100 mm of loft insulation keeps 81 % of its capacity; totally surrounded, half. A 30 A circuit that needs 4 mm² clipped needs 16 mm² buried in insulation — try it in the calculator.
Cf — BS 3036 rewireable fuse. An extra 0.725, because those fuses run hot and blow imprecisely. Rare in new work, common in anything not rewired since the eighties, and easy to forget when you meet one.

Volt drop

Regulation 525.202: 3 % for lighting, 5 % for everything else, of the nominal voltage. Lighting gets the tighter figure because of what happens either side of the limit — a lamp visibly dims where a motor merely runs a little warmer.

ΔU = mV/A/m × Ib × L / 1000

On long runs it is usually volt drop, not capacity, that sets the size. The calculator says which of the two governed, and gives the longest run the chosen cable supports at your design current — often more useful than the drop figure itself, because it tells you how much slack you have.

Capacities by reference method

70 °C thermoplastic insulated, copper. Blank cells are combinations the standard does not tabulate.

mm²	A	B	C	E	F	mV/A/m 1φ	3φ
1	11	13	15	17	—	44	38
1.5	14	16.5	19.5	22	—	29	25
2.5	18.5	23	27	30	—	18	15
4	25	30	36	40	—	11	9.5
6	32	38	46	51	—	7.3	6.4
10	43	52	63	70	—	4.4	3.8
16	57	69	85	94	—	2.8	2.4
25	75	90	112	119	131	1.75	1.5
35	92	111	138	148	162	1.25	1.1
50	110	133	168	180	196	0.93	0.8
70	139	168	213	232	251	0.63	0.55
95	167	201	258	282	304	0.47	0.41
120	192	232	299	328	352	0.38	0.33
150	219	258	344	379	406	0.3	0.26
185	248	294	392	434	463	0.25	0.21
240	291	344	461	514	546	0.19	0.165
300	334	394	530	593	629	0.155	0.136
400	—	—	634	715	754	0.125	0.11

What this does not do

Earth fault loop impedance. Zs must be low enough for the device to disconnect in time — Regulation 411.4. A cable that passes capacity and volt drop can still fail this, and it is a separate calculation.
The adiabatic check on the CPC. Covered by the earth conductor calculator.
Ring final circuits. A ring is not two radials and is not sized this way.
Diversity. Ib is what you supply, not the connected load.

Which calculator to use

This one for the UK, Ireland and jurisdictions that adopt BS 7671. The NEC calculator for the United States and Canada, where the arithmetic runs the other way and the terminal temperature limit governs. The IS 732 calculator for India, which follows the same IEC parent as BS 7671 but with its own tables and 415 V defaults.

Project		Circuit ref
Prepared by		Date
Checked by		Date

BS 7671 Cable Sizing Calculator — 18th Edition

The circuit

How and where it is installed