Confusing kW (real power) with kVA (apparent power). They are only equal at unity power factor (PF = 1.0). For a motor with PF = 0.85: kVA = kW / 0.85 — a 10 kW motor draws 11.76 kVA. Sizing a transformer or conductor using kW instead of kVA undersizes it by 18%. The second most common mistake: confusing HP nameplate rating (shaft output) with electrical input — a 10 HP motor at 88% efficiency draws 8.47 kW electrical, not 7.46 kW. Always clarify whether a power specification is input or output, and whether it's kW or kVA.

Voltage conversion uses transformers. The turn ratio determines the voltage ratio: V_secondary / V_primary = N_secondary / N_primary. Common North American distribution voltages: 4160V → 480/277V (delta-wye), 480V → 208/120V (delta-wye), 240V → 120V (single-phase center-tap). Power is conserved (minus losses): kVA_primary ≈ kVA_secondary. Current scales inversely with voltage: stepping from 480V to 208V increases current by 480/208 = 2.31×. This is why 480V distribution is standard for commercial buildings — lower current means smaller conductors and lower I²R losses.

A circular mil (cmil) is the area of a circle with diameter of 1 mil (0.001 inch). 1 cmil = π/4 × 10⁻⁶ in² = 5.067 × 10⁻⁴ mm². It simplifies area calculations for round conductors: area in cmils = (diameter in mils)² (no π/4 factor needed). 1 kcmil = 1,000 cmils = 0.5067 mm². Examples: 250 kcmil = 250,000 cmils = 126.7 mm², 500 kcmil = 253.4 mm². The cmil system is used exclusively in North American electrical engineering; international practice uses mm² exclusively.

1 BTU = 1,055.06 J = 0.000293 kWh. 1 kWh = 3,412 BTU. For power (rate of energy): 1 BTU/h = 0.293 W, 1 kW = 3,412 BTU/h, 1 ton of refrigeration = 12,000 BTU/h = 3.517 kW. Common confusion: BTU is energy (quantity), BTU/h is power (rate) — but HVAC industry often drops the '/h' and says 'BTU' when they mean BTU/h. A '60,000 BTU' furnace actually means 60,000 BTU/h = 17.6 kW thermal output. Electric equivalent at 100% efficiency: a 17.6 kW electric heater produces identical thermal output.

Decibels (dB) express ratios logarithmically. For power: dB = 10 × log₁₀(P₂/P₁). For voltage/current: dB = 20 × log₁₀(V₂/V₁). Quick references: +3 dB = 2× power (1.41× voltage), +6 dB = 4× power (2× voltage), +10 dB = 10× power (3.16× voltage), +20 dB = 100× power (10× voltage), -3 dB = 0.5× power. dBm references 1 mW: 0 dBm = 1 mW, +30 dBm = 1 W, +60 dBm = 1 kW. Used in telecommunications, signal processing, and power quality (harmonic levels are often expressed in dB relative to fundamental).

The most expensive errors involve confusing milli- (m, 10⁻³) with mega- (M, 10⁶) — a 10⁹ (one billion) factor error. 10 mΩ (milliohms) is a near-short-circuit; 10 MΩ (megaohms) is near-open-circuit. Other common errors: confusing μF (microfarad) with pF (picofarad) — 10⁶ difference that determines whether a capacitor bank corrects a building's power factor or does nothing detectable. In handwriting, 'mA' (milliamps) vs 'MA' can be ambiguous — always use clear notation. Digital systems should always include the full prefix name when abbreviation could be ambiguous.

Resistance (R, ohms) is the DC opposition to current flow — purely resistive, independent of frequency. Impedance (Z, ohms) is the total AC opposition including resistance (R), inductive reactance (XL = 2πfL), and capacitive reactance (XC = 1/(2πfC)). Z = √(R² + (XL - XC)²). At DC (f = 0): Z = R. At 60 Hz AC: impedance includes the effects of inductors and capacitors. For power conductors: resistance dominates for small sizes (<2 AWG), while reactance becomes significant for larger conductors (>500 kcmil). NEC Chapter 9, Table 9 provides both R and X values for conductors.