Calculating A Cable Size
Choosing the right sized cable is not always as easy as it looks.
- Protection against electric shock
- Protection against thermal effects
- Overcurrent protection
- Voltage drop
- Limiting temperatures for terminals of equipment to which the conductors are connected
How to size a cable
Differences between fault current protection and overload current protection
All circuits are designed to protect the cables against fault current (e.g. a short circuit from line to earth of line to neutral). However full overload current protection is not always required (or possible) on some circuits.
Overload protection is required when a cable may conceivably be required to carry a circuit current in excess of its design current for a period of time, either brought about by the circuits user, or by a predictable failure mode of equipment supplied by the circuit. e.g. a user connecting too many high power appliances to a socket circuit.
Overload current protection is not required when we know the fixed current of the appliance, and we install a dedicated cable that is capable of carrying this current. A good example of this would be an electric shower or an immersion heater supply cable where there is no end user action, or typical equipment failure mode that could result in an overload. We will show in the worked examples later on, that it is even possible in some circumstances to safely install an MCB that has a higher rating than the cable's maximum current rating.
Section 433.3.1 of BS7671 also describes other circumstances where overload current protection can be omitted. Note also there are also some classes of equipment where overload current protection may be omitted on safety grounds (typically fire detection and extinguisher systems, life support equipment, some rotating or lifting equipment etc. See section 433.3.3 of BS7671 for full details).
Overload current protection is required for any circuit where a user could potentially raise the current demand from the circuit to above that anticipated in its design. This would be the case with the vast majority of general purpose socket circuits for example.
Sizing conductors for your circuit
How to calculate Iz
Iz and some other terms we will require shortly are defined as:
- Iz - The rated current carrying capacity of the chosen cable, for continuous service, under the particular installation conditions.
- It - The nominal current carrying capacity of the cable. For T&E cable It is taken from this table.
- Ib - The design current of the circuit. This is the starting point for all the calculations. If available, then Ib should be taken from the rated full load current of the appliance. If this is not given, then Ib may be calculated by dividing the VA rating of the appliance by 230 (the nominal voltage). For cases where the VA rating is not provided, then use the quoted power in Watts divided by 230. Note that diversity can be applied to reduce the full load current where permitted (e.g. with a cooker circuit in a domestic environment)
- In - The rated current of the protective device.
- I2 - For completeness we will include I2 - the actual operating current of the protective device. However for domestic work there are only two classes of protective device of interest: Cartridge Fuses, MCBs, and RCBOs where I2 is 1.45 x In, and rewireable fuses where I2 is 2.0 x In, so we can simplify things a little summaries of the requirements given in case 1 and case 2 below:
Having calculated the easy bits: the design current (Ib) and then protective device rating (In) we now need to calculate Iz.
Iz may be found either by reference to the tables in BS7671 (the wiring regs) or the IEE On Site Guide (a subset of which are reproduced here for common domestic cables sizes), or, by calculation based on the various factors that affect the installation.
Case 1: overload protection required
When overload protection is required, we must ensure that:
- In >= Ib (Overload Protective Device rating is equal to or bigger than load)
and also, for cartridge fuse, MCB or RCBO protective devices that:
- Iz >= In (cable rating (as-installed) is equal to bigger than the Overload Protective Device rating)
or for rewireable fuse then:
- Iz >= In / 0.725 (cable must be up-rated to allow for coarser protection from this type of fuse);
Case 2: overload protection not required, due to characteristics of load
Where overload protection is not required then Iz should ideally be greater than or equal to the MCBs nominal rating, (i.e. Iz >= In). However if this can't easily be achieved, then it is also acceptable to opt for Iz > Ib even if Iz is actually less than the nominal rating of the MCB (i.e. Ib <= Iz <= In). Warning: If the latter design option is used, then it should be remembered that the cable size will have been verified as adequate only for the selected appliance, and it may not be adequate for a more powerful appliance even if the MCB could in theory support it.
In summary: when overload protection is not required, then we must ensure that:
- In >= Ib (as for case 1)
- Iz >= Ib (cable rating (as-installed) equal to bigger than load)
but if Iz < In an adiabatic calculation must be performed to verify fault (i.e. short circuit) protection of the cable is still provided (see section below).
Method 2 - calculation Iz is calculated by using the formula Iz = It x Ca x Cg x Ci x Cc Where It is column C of the table. Ca is a correction factor due to the ambient temperature (values from table 4B1) Cg is a correction value for cables grouped with other circuits (values from table 4C1) Ci is a correction value for cables in insulation (Table 52.2) Cc is a correction factor of 0.725 for BS3036 fuses and 0.9 for cables "in a duct in the ground" or "buried direct". If a buried cable is protected by a BS 3036 fuse then Cc = 0.725 x 0.9 = 0.653
Worked Example Say we have a radial circuit feeding a pair of 3kW immersion heaters. The cable will be grouped with two other circuits and will pass through an aperture in a fully insulated stud wall, containing 100mm of slab insulation. The ambient temperature of the insulated wall is 40°C. The circuit protection will be a B32 MCB, and the cable is initially specced as 4.0mm² T&E. So we know that Ib = 2 x 3000 / 230 = 26A Initial inspection of column C of the table shows a rating for 4.0mm² cable at 37A. However from the tables below we can see that the ambient temperature of 40°C yields a derating of 0.87 and our total of three circuits grouped together gives a factor of 0.7. Finally the 100mm of insulation introduces a further factor of 0.78. Since the protective device is a MCB there is no factor to apply due to the use of a BS 3036 re-wireable fuse. Iz = 37 x 0.87 x 0.7 x 0.78 x 1 = 17.57A Since overload protection is not required for this circuit, we need to achieve only Iz > Ib as a minimum requirement, however in this case it is clear that we have not achieved this. Even drilling extra access holes for the cable to remove the grouping related factor, will still not meet the target. Hence we will have to increase the cable size to 6.0mm² and drill some extra holes: Reworking with the new It of 47A, and removing the grouping factor we get: Iz = 47 x 0.87 x 1 x 0.78 x 1 = 31.89A This does meet the minimum requirement of Iz > Ib and hence is acceptable. It is however very slightly outside the ideal of Ib <= In <= Iz. (a more practical solution may actually be to wire each heater using its own 2.5mm² T&E cable. Since the reduced load on each of 3kW (13A), will come in with a Iz of just over 18A if one also removes the grouping factor). One could even go further by joining this pair of radials to make a ring!
|Ambient temperature||Derating factor Ca|
|Length in insulation (mm)||Dereating factor Ci|
|Arrangement (cables touching)||Number of circuits||Applicable reference method|
|Bunched in air, on a surface, embedded or enclosed||1.0||0.80||0.70||0.65||0.60||0.57||0.54||0.52||0.50||0.45||0.41||0.38||A to F|
|Single layer on a wall||1.0||0.85||0.79||0.75||0.73||0.72||0.72||0.71||0.70||0.70||0.70||0.70||C|
- The Cg value applies to the number of circuits not the number of cables
- If a cable is to be expected to carry less than 30% of it's grouped rating it may be ignored for the purpose of obtaining the rating factor for the rest of the group
Checking Voltage Drop
|Conductor CSA (mm²)||PVC (max 70° C)
Voltage drop mV/A/m
Checking the Maximum Earth Loop Impedance
|Type B circuit breakers to BS EN 60898|
Having now chosen a cable that is suitable to carry our design current and meet the required voltage drop requirements we now need to check that the cable will allow the MCB , fuse or RCBO to trip the circuit quickly enough in the event of a fault.
|Wire CSA/CPC (mm²)||L + N
|L + CPC |
|1.0 / 1||43.44||43.44|
|1.5 / 1||29.04||36.24|
|2.5 / 1.5||17.78||23.42|
|4.0 / 1.5||11.06||20.05|
|6.0 / 2.5||7.39||12.59|
|10.0 / 4||4.39||7.73|
|16.0 / 6||2.76||5.08|
If the calculated impedance is less than in table 41.3 then the disconnection times are met.
The wiring regs handle this situation with what is known as the adiabatic equation.
- s = sqrt( I² x t ) / k
Where I is the prospective fault current, and t is the time to open the circuit breaker (typically 0.1 secs) k is a constant that takes into account the characteristics of the materials it is made from as well as highest possible short term rise in conductor temperature that it will tolerate without damage. See table below for a list of common values (or see BS7671 table 43.1 for other cables not covered here):
k values for copper conductor cables of CSA < 300mm²
|Copper conductors with
|70°C Thermoplastic (general purpose PVC)||70||160||115|
|90°C Thermoplastic (PVC)||90||160||100|
|60°C Thermosetting (eg Rubber)||60||200||141|
|90°C Thermosetting (eg XLPE)||90||250||143|