Electrician Math Formula Sheet

Ohm's Law & Power (Art. 100)

Voltage Drop (NEC Art. 210.19 Note)

Single-phase: VD = (2 × K × I × D) ÷ CM

Three-phase: VD = (1.732 × K × I × D) ÷ CM

NEC recommendation: Max 3% VD branch circuit; max 5% total (feeder + branch)

Find wire size: CM = (2 × K × I × D) ÷ Allowed VD

Common Conductor CM Areas

Load Calculations (NEC Art. 220)

Dwelling general lighting: 3 VA/sq ft (Art. 220.12)

Small appliance circuits: 2 circuits × 1,500 VA = 3,000 VA (Art. 220.52(A))

Laundry circuit: 1,500 VA (Art. 220.52(B))

Demand factors (Table 220.42):

Range demand (Table 220.55): see NEC table for household cooking equipment.

Water heater, dryer, A/C, heat: 100% of nameplate (unless demand factor applies)

Minimum service amperage formula:

Amps = Total VA ÷ (Voltage × 1.732) (3-phase)
Amps = Total VA ÷ Voltage (1-phase)

Motor Circuit Sizing (NEC Art. 430)

FLA = Full Load Amps (from NEC Table 430.248 for 1-phase, 430.250 for 3-phase)

Multiple motors on one branch circuit: Largest motor × 125% + sum of all others (Art. 430.24)

Transformer Calculations (NEC Art. 450)

1-Phase: kVA = (V × I) ÷ 1,000

3-Phase: kVA = (V × I × 1.732) ÷ 1,000

Turns ratio: V₁/V₂ = N₁/N₂ = I₂/I₁

Secondary current: I = kVA × 1,000 ÷ V (1-phase)

Transformer OCPD max (Table 450.3(B) — secondary supervised):

Conduit Fill (NEC Ch. 9, Table 1)

Formula: Fill % = Total conductor area ÷ Conduit inner area × 100

Conductor cross-section areas: NEC Annex C tables. Conduit inner areas: Ch. 9 Table 4.

Box Fill (NEC Art. 314.16)

Volume per conductor (Table 314.16(B)):

Required volume = (Total conductor count) × (In³ per conductor from table above)

Box must provide ≥ required volume.

Exam Tips — Math Problems

1. Write every step. Partial credit does not exist on the real exam — but writing steps helps you catch arithmetic errors before selecting an answer.
2. Identify what you are solving for first. Circle the unknown variable before picking a formula.
3. Check if a demand factor applies. Many load calc questions include a trick: students add 100% of everything and miss the demand table.
4. Round motors UP to next standard ampere for OCPD sizing (Art. 240.6(A)).
5. Voltage drop: remember 2× for single-phase (current travels out AND back). Three-phase uses 1.732 not 2.
6. Box fill: grounds count as ONE total, not one per ground wire. Easy point to miss.
7. Calculator allowed? Most state journeyman/master exams allow a basic calculator. Check before exam day. NEC open-book — bring your codebook and tab it.