The Three Pillars: Voltage, Current, and Resistance
Every electrical calculation starts with Ohm's Law: V = I x R (Voltage = Current x Resistance). From this single equation, you derive Power (P = V x I), the foundation of all electrical work.
Voltage (V) is electrical pressure. Current (I, measured in Amps) is flow rate. Resistance (R, measured in Ohms) is restriction. These three values are interdependent — knowing any two lets you calculate the other two.
Power (P, measured in Watts) represents energy consumption. A 120V circuit drawing 15A delivers 1,800W. This is why circuit breakers are rated in amps — they limit current to protect wires from overheating.
Use our Electrician Calculator to instantly compute voltage, current, resistance, or power from any two known values.
Wire Sizing: NEC Code Requirements
The National Electrical Code (NEC) Table 310.16 specifies maximum ampacity for copper and aluminum conductors.
Common residential wire sizes: 14 AWG (15A lighting), 12 AWG (20A kitchens/bathrooms), 10 AWG (30A dryers), 8 AWG (40A ranges), 6 AWG (50A EV chargers).
Critical rule: The 80% continuous load rule means a 20A circuit can only carry 16A continuously (for 3+ hours). Never use wire size based on appliance amp draw alone — account for length, temperature, and bundling.
Aluminum wire requires one size larger than copper for the same ampacity. A 30A circuit needs 10 AWG copper but 8 AWG aluminum.
- 14 AWG = 15A, 12 AWG = 20A, 10 AWG = 30A
- 80% continuous load rule is critical
- Aluminum needs one size larger than copper
- Wire length over 50 feet needs voltage drop correction
Voltage Drop: The Silent Efficiency Killer
Voltage drop formula: VD = (2 x K x I x L) / CM, where K = 12.9, I = amps, L = one-way length in feet, CM = circular mil area.
NEC recommends maximum 3% for branch circuits and 5% total. Exceeding these causes dimmed lights, motor overheating, and energy waste.
Example: 120V circuit, 12 AWG wire (3,310 CM), 16A over 150 feet: VD = 18.7V (15.6% drop). You need 8 AWG wire for this distance.
Rule of thumb: 12 AWG for runs under 75 feet, 10 AWG for 75-120 feet, 8 AWG for 120-175 feet at 15A load.
Three-Phase Power Calculations
Three-phase power formula: P = V x I x sqrt(3) x PF (Watts), where PF is power factor (typically 0.8-0.95 for motors).
480V three-phase panel at 100A per phase: P = 480 x 100 x 1.732 x 0.85 = 70.7 kW. This powers commercial HVAC, elevators, and industrial equipment.
Line-to-neutral voltage = Line-to-line / sqrt(3). So 480V three-phase gives 277V line-to-neutral — commonly used for commercial lighting.
Motor FLA differs from circuit ampacity. A 5 HP, 230V single-phase motor draws ~28A FLA, but NEC requires 125% rated circuit = 35A minimum.
Conduit Fill and Installation Rules
NEC Chapter 9 Table 1: Maximum conduit fill is 40% for 3+ conductors, 31% for 2, 53% for 1.
Example: 1/2-inch EMT (0.303 sq in) at 40% fill = 0.121 sq in. 12 AWG THHN (0.0133 sq in) = 9 conductors max.
Conduit types: EMT (thinwall, easiest), PVC Schedule 40 (underground), Rigid Metal (maximum protection).
Temperature derating: If ambient exceeds 86 F or 3+ current-carrying conductors in one conduit, derate per NEC Table 310.15(B)(3)(a).
Case Study: Residential Panel Upgrade
A 1960s home with 60A service needed a 200A upgrade for AC, EV charger, and induction range.
Wire from utility to panel: 4/0 AWG copper (230A ampacity). Cost: ~$2.50/ft x 50 ft = $125 for main conductor pair.
New 200A panel with 40 spaces: $800-1,500 materials. Total project with licensed electrician: $2,500-4,500.
The upgrade enabled: 50A EV charger (6 AWG), 30A dryer (10 AWG), dedicated 20A kitchen circuits (12 AWG), and future expansion.
Frequently Asked Questions
What wire size for 200 amp service?
Use 4/0 AWG copper or 250 kcmil aluminum per NEC Table 310.16.
How do I calculate voltage drop?
VD = (2 x K x I x L) / CM. For 120V circuits, keep under 3.6V (3%). Use our Electrician Calculator for instant results.
Can I use aluminum wire for branch circuits?
NEC allows aluminum (AA-8000 series) for 8 AWG and larger. Requires anti-oxidant compound and torque-checked lugs.
What is the 80% continuous load rule?
NEC 210.20(A): circuit breaker must be 125% of continuous load. A 20A circuit supports only 16A continuously.
How to calculate three-phase motor amps?
I = P / (V x sqrt(3) x PF). A 10 HP motor at 460V: I = 7,460 / (460 x 1.732 x 0.85) = 11.1A.
What conduit fill does NEC allow?
40% for 3+ conductors. A 3/4-inch EMT holds up to 16 THHN 12 AWG conductors at 40% fill.