Every electrical cable has an ampacity, disclosed by the manufacturer (or) included in cable selection tables like IEC 60364-5-52, IS 3961 (or) the National Electrical Code.

The tabular value is valid only under certain reference installation conditions: a constant ambient temperature, a single cable laid in free air or isolation, a defined laying depth, and a standard soil thermal resistance for buried cables.

Rarely are cables laid under these reference conditions. 

They may be bundled in trays, buried at different depths, exposed to greater ambient temperatures, or bedded in heat-poor soil. 

To calculate the cables safe current-carrying capability, engineers apply derating factors to the base ampacity to account for these real-world variances. 

Determining cable size without derating factors is a leading cause of cable overheating, insulation degradation & premature electrical installation failure.

This post describes the Cable Derating Factor Calculator governing formulas, runs through the calculation procedure, and provides completely solved numerical examples for both pass and fail conditions.

Formulas

The derated (actual) current-carrying capacity of a cable is obtained by multiplying its base tabulated rating by every applicable correction factor. 

The general formula is:

Combined Derating Factor (K) = Ca x Cg x Cd x Cs

Where

Ca = Ambient Temperature Correction Factor – corrects for ambient or ground temperature different from the standard reference temperature (usually 30°C in air or 20°C in ground).

Cg = Grouping / Bunching Correction Factor – corrects for mutual heating when multiple circuits are installed together in a tray, duct, or conduit.

Cd = Depth of Laying Correction Factor – applicable to directly buried cables installed at a depth other than the standard reference depth.

Cs = Soil Thermal Resistivity Correction Factor – applicable to buried cables in soil whose thermal resistivity differs from the standard reference value.

Once the combined factor K is known, the derated current capacity is calculated as:

Derated Current Capacity, I(derated) = I(base) x K

Where 

I(base) – manufacturers tabulated current rating of the selected cable in amperes (A).

To verify whether a selected cable is adequate for a given design load, the derated capacity is compared with the design load current, I(load):

If I(derated) >= I(load)  ->  Cable size is ADEQUATE (PASS)

If I(derated) < I(load)  ->  Cable size is INADEQUATE (FAIL)

The spare capacity margin, expressed as a percentage, indicates how much headroom exists between the derated capacity and the actual load:

Margin (%) = [(I(derated) – I(load)) / I(load)] x 100

If the calculated derated capacity is insufficient, the calculator also determines the minimum base current rating that would be required for a cable to satisfy the same load under the same site conditions:

Required Base Rating, I(required) = I(load) / K

Step-by-Step Calculation Procedure

The following sequence is used by the calculator, and should be followed manually when cross-checking results:

Step 1: Identify the base tabulated current rating (I-base) of the selected cable from the manufacturer’s data sheet or the relevant cable standard, based on conductor size, insulation type, and installation method.

Step 2: Determine the ambient temperature correction factor (Ca) corresponding to the actual site ambient or ground temperature, using the applicable standard’s correction table.

Step 3: Determine the grouping correction factor (Cg) based on the number of loaded circuits installed together and their arrangement (touching, spaced, single layer, multi-layer, etc.).

Step 4: For buried cables, determine the depth of laying factor (Cd) and the soil thermal resistivity factor (Cs); for cables in air or trays, both may be taken as 1.

Step 5: Multiply all applicable factors together to obtain the combined derating factor, K = Ca x Cg x Cd x Cs.

Step 6: Multiply the base current rating by K to obtain the derated current capacity of the cable.

Step 7: Compare the derated capacity with the actual design load current to confirm whether the cable size is adequate.

Step 8: If inadequate, either select the next larger standard cable size and repeat the calculation, or recompute the minimum required base rating using I(required) = I(load) / K.

Solved Example 

Solved Example 1 – Cable Size is Adequate

A 3-core armoured cable has a base tabulated current rating of 120 A (single cable in free air, 30°C ambient). The cable will be installed in a tray together with two other loaded circuits at a site ambient temperature of 40°C. The cable is not buried, so depth and soil resistivity factors do not apply. The design load current is 75 A.

Given data:

Calculation:

K = Ca x Cg x Cd x Cs = 0.87 x 0.82 x 1.00 x 1.00 = 0.7134

I(derated) = I(base) x K = 120 x 0.7134 = 85.6 A

Margin (%) = [(85.6 – 75) / 75] x 100 = 14.1%

Result: 

Since I(derated) = 85.6 A is greater than I(load) = 75 A, the cable is ADEQUATE for the application, with a comfortable spare capacity margin of 14.1%.

Solved Example 2 – Cable Size is Inadequate

A 4-core XLPE cable directly buried in the ground has a base tabulated current rating of 150 A (standard reference depth of 0.5 m, standard soil thermal resistivity of 1.2 K.m/W). At the actual site, the cable is buried at a depth of 1.0 m in soil with higher-than-standard thermal resistivity, and is grouped with one other circuit. The ground temperature is elevated relative to the reference value. The design load current is 110 A.

Given data:

Calculation:

K = Ca x Cg x Cd x Cs = 0.93 x 0.87 x 0.95 x 0.88 = 0.6773

I(derated) = I(base) x K = 150 x 0.6773 = 101.6 A

Margin (%) = [(101.6 – 110) / 110] x 100 = -7.6%

Since I(derated) = 101.6 A is less than I(load) = 110 A, the cable is INADEQUATE and cannot safely carry the design load under these site conditions. 

The minimum base rating required for this installation is calculated as:

I(required) = I(load) / K = 110 / 0.6773 = 162.4 A

Result: 

A cable with a base tabulated rating of at least 162.4 A must be selected that is typically the next standard size above 150 A and the derating calculation should be repeated to confirm adequacy.

Points to Remember

• Always source correction factors from the specific standard applicable to the project (IEC, IS, NEC, or local regulation) – factors are not universal across standards.
• Grouping factors reduce sharply as more circuits are bunched together; spacing cables apart can significantly improve their effective rating.
• For buried cables, both depth and soil thermal resistivity should be checked, as poor soil conditions can reduce capacity more than temperature alone.
• A derated capacity that only marginally exceeds the load current leaves little room for future load growth; a reasonable design margin is recommended.
• When multiple derating factors apply simultaneously, their combined multiplicative effect can be considerably more severe than any single factor alone.

Summary

Derating factors must be used correctly for safe cable selection. 

Cable base tabulated ratings only reflect capacity according to ideal reference conditions & practical installations almost often depart from these. 

By applying the ambient, grouping, depth, and soil resistivity correction factors given in the formulas and applied examples above, engineers can accurately determine whether a cable size will perform safely under site conditions or if a larger conductor is required. 

This calculation is automated by the Cable Derating Factor Calculator which rapidly returns the combined derating factor, derated current capacity, pass/fail status for the design load and the minimum base rating needed to safely meet the load.