# Ampacity Calculation Formula

## Why Calculate the full load Ampacity?

Methods for Ampacity Calculations of Conductors Rated 0–2000 Volts. As per 310.15(A)(1), The allowable Ampacities for conductors rated 0-2000 Volts shall be permitted to be determined by two methods:. Tables as provided in 310.15(B) or. Under engineering supervision, as provided in 310.15(C). Today, I will explain the second method: Under engineering supervision, as provided in 310.15(C). Second Method: Under engineering supervision, as provided in 310.15(C) . In the first method, we select the ampacity from different tables provided in 310.15(B), while in the second method: Under engineering supervision, we will calculate the ampacity, so the second method will be more complex and time consuming and requires engineering supervision. It can, however, result in lower installation costs in some cases, and if calculated properly, it provides a mathematically exact ampacity.

The tables provided in the first method under NEC Article 310.15(B) don't address every type of installation and If there is an installation case not covered by these tables, how can you get the correct minimum ampacity?

- The answer is using the second method: Under engineering supervision, as provided in 310.15(C), The NEC helps clarify what that entails in Annex B through many tables and figures.
- Rule#1: Equation for Conductor Ampacities Calculation Under engineering supervision, as provided in 310.15(C).
- Under engineering supervision, conductor ampacities shall be permitted to be calculated by means of the following general equation:.
- Tc = conductor temperature in degrees Celsius (°C).
- Rdc = dc resistance of conductor at temperature Tc.
- Yc = component ac resistance resulting from skin effect and proximity effect.
- Rca = effective thermal resistance between conductor and surrounding ambient.
- The above equation was developed by J. McGrath and it is called The Neher–McGrath formula.

## Conclusion

Note #1 : Using The Neher–McGrath formula in selection of conductor size at the terminations. Although conductor ampacities calculated using The Neher–McGrath formula may exceed those found in a table of allowable ampacities, such as Table 310.15(B)(16), the limitations for connecting to equipment terminals specified in 110.14(C) have to be followed. For equipment 600 volts and under, the conductor size at the termination must be based on ampacities from Table 310.15(B)(16) because the selection of conductors based on a tables other than Table 310.15(B)(16), can result in overheated terminations at the equipment.

Note #2 : Common Uses of The Neher–McGrath formula . The most common use of the Neher–McGrath formula is for calculation of conductor ampacity in underground electrical ducts (raceways), although the formula is applicable to all conductor installations.

The conductor’s ampacity is based on the rate of heat dissipation through the thermal resistances from all heat sources surrounding the conductor. For conductors in underground electrical ducts, there are several heat sources, as follows, (and as illustrated in Fig.1):. 1- Conductor losses due to the load current I 2R. These losses vary with the load current, conductor material, and conductor cross-sectional area (conductor size).

2- Skin-effect heating if the current is alternating current. The heat developed by the skin effect is due to the shape of the conductor and is based on the configuration of the conductors (i.e., solid, stranded, or compact).

- 3- Hysteresis losses if the duct is steel or other magnetic material. These losses are dependent on the magnetic properties of the electrical duct and the shape of the duct. 4- Heating from other conductors in the duct. This heating is based on the number, location, and proximity of other conductors as well as the losses in the other conductors. The more conductors in the raceway, the greater the heating effect from these conductors is likely to be.
- This factor replaces the adjustment factors in 310.15(B) (3)(a) to the ampacity tables. 5- Mutual heating from other ducts, cables, and so forth, in the vicinity. The closer the other heat sources and the more they surround the duct for which calculations are being made, the greater the heating effect. For example, in the case of a symmetrical nine-duct bank, three ducts high and three ducts wide, the center duct will receive the most heat as a result of mutual heating.
- Heat generated by the following various types of losses is conducted through the different thermal barriers or resistances, as illustrated in above image. Note #4 : Thermal Barriers Or Resistances Surrounding The Conductor. Heat generated by the above heat sources in note#3 are conducted/dissipated through the different thermal barriers or resistances, (as illustrated in Fig.1) there are many thermal barriers as follows:.
- 1- Conductor Insulation. It presents a thermal resistance to heat generated by the conductor due to the I 2R losses, including any dielectric losses. This thermal resistance value depends on the thickness of the insulation and the type of insulating material used. The airspace between the conductor insulation and the surrounding wall or raceway. The thermal resistance of this airspace is based on the number of conductors in the duct, the assumed mean value of the temperature of the air in the duct, and the constants provided in the Neher–McGrath paper, which were determined from experimental data.