Electrical Conversions + Field Math Reference

Why this matters

Field electricians do quick math constantly - what's the amp draw of this 1500W heater? Will this 20A circuit support 3 motors? What's voltage drop on 100 ft run? The math is simple but the formulas are forgotten without practice. This is the field card every electrical-trade tech should keep handy.

Ohm's Law (the foundation)

E = I × R (Voltage = Current × Resistance). E = volts; I = amps; R = ohms (Ω). Rearrangements: I = E / R; R = E / I. Wheel memory aid: E above, I and R below - cover any one to see the formula.

Watts (Power) Law

P = E × I (Power = Voltage × Current). Rearrangements: I = P / E; E = P / I. Combined with Ohm's: P = I² × R; P = E² / R. Common conversions: 1 kW = 1,000 W; 1 MW = 1,000,000 W; 1 kWh = 1,000 Wh (energy); 1 HP = 746 W. Field tip: 1 HP motor ≈ 1 kW input (efficiency 80 - 85%).

Amp-watt-volt quick lookup (120V)

100W → 0.83A; 200W → 1.67A; 500W → 4.17A; 750W → 6.25A; 1000W → 8.33A; 1200W → 10A; 1500W → 12.5A; 1800W → 15A; 2400W → 20A. 80% rule: continuous load (3+ hrs) limited to 80% capacity - 15A circuit → 12A continuous; 20A circuit → 16A continuous.

Power at 240V

Common 240V circuits: 1500W → 6.25A, 2000W → 8.33A, 3000W → 12.5A, 4000W → 16.67A, 4800W → 20A, 6000W → 25A, 7200W → 30A, 9600W → 40A, 12000W → 50A. Why 240V more efficient: same power, half the current, and because conductor loss goes as I squared times R, a QUARTER of the heat loss in the wire.

Common appliance power draws (120V)

LED bulb 9 - 15W (0.1A); refrigerator 150 - 700W (1 - 6A); toaster 800 - 1500W (7 - 13A); microwave 600 - 1500W (5 - 13A); coffee maker 600 - 1200W (5 - 10A); vacuum 800 - 1400W (7 - 12A); hair dryer 800 - 1800W (7 - 15A); space heater 750 - 1500W (6 - 13A); window AC 5K BTU 450W (4A); window AC 12K BTU 1200W (10A); computer + monitor 200 - 400W (2 - 3A).

240V appliances

Water heater (40-gal) 4500W (19A); electric dryer 5000W (21A); electric range peak 9600W (40A); central AC 3-ton 3500W (15A); heat pump 3-ton 3500W (15A); electric furnace 15 kW 15000W (63A); EV charger Level 2 7200W (30A); tankless water heater 28000W (117A).

Voltage drop calculation

NEC suggests max 3% drop on branch circuits, 5% total feeder + branch. Formula (single phase): VD = 2 × K × I × L / CM (K = 12.9 copper at 75°C, 21.2 aluminum at 75°C). Max ONE-WAY run for 3% drop on 120V, at the stated load, copper: #14 → 15A 35 ft; #12 → 15A 60 ft / 20A 45 ft; #10 → 15A 95 ft / 20A 70 ft / 30A 45 ft; #8 → 15A 150 ft / 20A 115 ft / 30A 75 ft; #6 → 15A 240 ft / 20A 180 ft / 30A 120 ft. On 240V the same conductor and load doubles the distance. Solution: upsize wire for long runs.

Conductor ampacity + service entrance

NEC Table 310.16 (75°C copper): #14 → 20A (limited 15A breaker), #12 → 25A (20A breaker), #10 → 35A (30A breaker), #8 → 50A, #6 → 65A, #4 → 85A, #2 → 115A, #1 → 130A, 1/0 → 150A, 2/0 → 175A, 3/0 → 200A, 4/0 → 230A, 250 kcmil → 255A, 350 kcmil → 310A, 500 kcmil → 380A. Derating for ambient temp + multiple conductors per NEC 310.15.

Dwelling service entrance per NEC Table 310.12 (copper / aluminum): 100A → 4 AWG / 2 AWG; 125A → 2 AWG / 1/0; 150A → 1 AWG / 2/0; 175A → 1/0 / 3/0; 200A → 2/0 / 4/0. Non-dwelling services size off Table 310.16 instead.

Motor + 3-phase + transformer + battery

Motor amperage: single-phase A = HP × 7 - 10 at 230/240V (efficiency dependent), roughly double that at 115/120V, which is why the 120V list below runs higher than the rule; three-phase A = (746 × HP) / (1.732 × V × η × PF). FLA (Full Load Amps): nameplate value used for sizing. SF (Service Factor): can run at SF × FLA continuously. LRA (Locked Rotor Amps): startup, 6 - 8 × FLA. Common 120V single-phase: 1/4 HP 5A, 1/2 HP 9A, 3/4 HP 12A, 1 HP 16A, 1.5 HP 20A, 2 HP 24A, 3 HP 34A.

3-phase: P = √3 × V × I × PF = 1.732 × V × I × PF. V_line = 1.732 × V_phase (Y-wired). Common voltages: 120/208V (low-V commercial), 277/480V (commercial), 480V delta (industrial). Advantages: more power per wire, smoother torque, smaller motors.

Transformer: VA = V × A; common sizes 7.5 kVA (small commercial), 25 kVA (utility pole), 50/75/100 kVA (commercial), 200/500+ kVA (industrial).

Battery: capacity = Ah × V = Wh. AA 1.5V × 2,500 mAh = 3.75 Wh. Auto 12V lead-acid 50 Ah = 600 Wh. Lithium 12V 100 Ah = 1,200 Wh. Tesla Powerwall 13.5 kWh. Run time = Wh battery / W load = hours.

Common conversions

1 BTU/hr ≈ 0.293 watts (heating)

1 ton cooling = 12,000 BTU/hr = 3,517 watts

3-ton AC system: 36,000 BTU/hr cooling capacity; uses ~3.5 kW input.

1 horsepower = 745.7 watts (or 2,545 BTU/hr)

Power factor (PF)

PF = real power / apparent power. Resistive (heaters) PF = 1.0; motors PF = 0.7 - 0.95; LED lighting PF = 0.9 - 1.0. Low PF causes industrial utility penalty; capacitor banks correct it.

Field calculation examples

How many 100W LEDs on 15A 120V at 80%? 15 × 120 = 1800W; 80% = 1440W; / 100 = 14 LEDs. Wire size for 50 ft 12A continuous at 120V? 12A continuous = 80% of a 15A circuit, so #14 clears ampacity, but the drop is 2 × 12.9 × 12 × 50 / 4107 = 3.77 V = 3.1%, right at the edge. Pull #12 and it drops to 2.0%. Breaker for 4 kW pool heater 240V? 4000 / 240 = 16.67A; continuous / 0.8 = 20.8A → 25A or 30A breaker. 1500W heater on 1200 Wh battery? 1200 / 1500 = 0.8 hr = 48 minutes.

Shortcuts: Watts = Volts × Amps (most common); 120V × 12A = 1440W (15A at 80%); 240V × 30A = 7200W (EV charger); HP × 746 = Watts; kW × 1.34 = HP; 1 ton AC = 12,000 BTU/hr ≈ 1 kW input.

Common electrical math mistakes

Forgetting 80% rule (continuous loads overload). Ignoring voltage drop (long runs need wire upsize). Confusing single-phase + three-phase formulas. Forgetting motor starting current LRA (breaker trips on startup). Wrong ampacity for cable type (NM derated vs THHN). Skipping derating (too many wires in conduit, ambient temp).

References

• NEC Table 310.16 (ampacity)
• NEC Chapter 9 (formulas, tables)
• Mike Holt + Trade School electrical math curriculum
• Manuall internal: Conductor Ampacity Reference, Service Entrance + Meter Base