NEC calculations cheat sheet for the Michigan electrician exam

These are the calculations that show up most often on electrician exams, with the 2023 NEC sections to know. It’s a study aid, written in our own words. Your exam is answered from the code book itself, so practice finding each table.

Ohm’s law and power

• E = I × R, I = E ÷ R, R = E ÷ I
• Single-phase power: P = E × I (× power factor for AC loads). Three-phase: P = E × I × 1.732 × PF.
• Current from power: I = P ÷ E (single-phase), I = P ÷ (E × 1.732) (three-phase). Example: a 45 kVA, 208 V three-phase load draws 45,000 ÷ (208 × 1.732) ≈ 125 A.
• Series resistance adds (R = R1 + R2 …). For two parallel resistors, R = (R1 × R2) ÷ (R1 + R2).

Voltage drop

• Single-phase: VD = (2 × K × I × L) ÷ CM. Three-phase: VD = (1.732 × K × I × L) ÷ CM.
• K ≈ 12.9 for copper, 21.2 for aluminum. L is the one-way length in feet; CM is the circular-mil area from Chapter 9, Table 8.
• The NEC’s informational notes suggest about 3% on a branch circuit or feeder and 5% total. That’s a recommendation, not a requirement.

Continuous loads

A continuous load runs for 3 hours or more. Size the overcurrent device and conductors at no less than 125% of the continuous load plus 100% of the noncontinuous load (210.20 for branch circuits and 215.3 for feeders), unless the equipment is listed for 100% operation.

Conductor ampacity

• Start with Table 310.16, using the column for the lowest temperature rating of the terminations (often 60 °C for 100 A and under, 75 °C above that, per 110.14(C)).
• More than three current-carrying conductors in a raceway or cable: 4–6 conductors use 80%, 7–9 use 70%, and 10–20 use 50% (Table 310.15(C)(1)).
• Ambient temperature above 30 °C: multiply by the correction factor in the 310.15(B) tables.
• Small conductor rule (240.4(D)): copper 14 AWG at 15 A, 12 AWG at 20 A, 10 AWG at 30 A maximum overcurrent protection.

Box fill (314.16)

• Volume per conductor (Table 314.16(B)): 18 AWG 1.50, 16 AWG 1.75, 14 AWG 2.00, 12 AWG 2.25, 10 AWG 2.50, 8 AWG 3.00, 6 AWG 5.00 cubic inches.
• Each conductor that enters the box counts as one. A conductor that passes through without a splice also counts as one, and a pigtail that never leaves the box counts as zero.
• Each device yoke (switch or receptacle) counts as two, based on the largest conductor connected to it.
• All equipment grounding conductors together count as one (plus a quarter for each one beyond four), based on the largest.
• Internal cable clamps count as one total. Each fixture stud or hickey counts as one.

Example: a box with four 12 AWG cables (8 insulated conductors, 4 grounds), one receptacle, and internal clamps: 8 + 1 (grounds) + 2 (device) + 1 (clamps) = 12 × 2.25 = 27 cubic inches.

Raceway fill (Chapter 9)

• Table 1 limits: one conductor 53%, two conductors 31%, more than two 40%. A nipple 24 inches or shorter may be filled to 60%.
• Find each conductor’s area in Table 5 (insulated) or Table 8 (bare), total them, and compare with the allowable area for the raceway type and size in Table 4. Annex C gives ready-made counts for same-size conductors.

Motors (Article 430)

• Use the full-load current tables, not the nameplate, for conductors and short-circuit and ground-fault protection: Table 430.248 (single-phase) and Table 430.250 (three-phase).
• Branch-circuit conductors: at least 125% of the table full-load current (430.22).
• Overload protection (430.32): 125% of nameplate current for motors with a service factor of 1.15 or more or a temperature rise of 40 °C or less; 115% for all others.
• Short-circuit and ground-fault protection (Table 430.52): typical maximums are 250% for an inverse-time breaker, 175% for a dual-element time-delay fuse, 300% for a non-time-delay fuse, and 800% for an instantaneous-trip breaker.
• Feeder conductors for several motors: 125% of the largest motor’s full-load current plus the sum of the others (430.24).

Dwelling load (standard method, Article 220)

1. General lighting: 3 VA per square foot of living area.
2. Add two 20 A small-appliance circuits at 1,500 VA each and one laundry circuit at 1,500 VA.
3. Apply the lighting demand factors: first 3,000 VA at 100%, 3,001–120,000 VA at 35%, the rest at 25%.
4. Add fixed appliances (75% demand for four or more, not counting ranges, dryers, space heating, or A/C), the dryer (5,000 VA or the nameplate, whichever is larger), cooking equipment from Table 220.55 (8 kW for one range of 12 kW or less), and the larger of heating or cooling.
5. Divide by 240 V for the service current.

Grounding and bonding sizes

• Grounding electrode conductor (Table 250.66), copper, based on the largest service conductor: 2 AWG or smaller → 8 AWG; 1 or 1/0 → 6 AWG; 2/0 or 3/0 → 4 AWG; over 3/0 through 350 kcmil → 2 AWG.
• A GEC that runs only to rod, pipe, or plate electrodes doesn’t have to be larger than 6 AWG copper; to a concrete-encased electrode, no larger than 4 AWG copper.
• Equipment grounding conductor (Table 250.122), copper, based on the overcurrent device: 15 A → 14 AWG, 20 A → 12, 60 A → 10, 100 A → 8, 200 A → 6, 300 A → 4, 400 A → 3.
• A single rod needs a supplemental electrode unless it measures 25 ohms or less. Rods must be at least 6 feet apart.

Transformers

• Single-phase current: I = (kVA × 1,000) ÷ E. Three-phase current: I = (kVA × 1,000) ÷ (E × 1.732).
• Overcurrent protection for transformers is in 450.3, by voltage and impedance.

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Section numbers refer to the 2023 NEC as adopted in Michigan by the Part 8 Michigan Electrical Code Rules. Always confirm values in your own code book. Exam facts: PSI candidate bulletin.

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