Introduction
The amperage formulas look simple — divide watts by volts — but each version exists for a reason, and using the wrong one is the fastest way to get a wrong answer. This guide derives all four formulas the calculator uses, shows where each applies, and works through the arithmetic step by step so you can check any result by hand.
If you just need the answer, the Amperage Calculator runs the right formula for your setup automatically. But knowing why the formulas differ — and what power factor and √3 are actually doing — is what keeps you from feeding the calculator the wrong inputs.
The Foundation: P = V × I
Everything starts from the definition of electrical power: power (watts) equals voltage (volts) times current (amps). Rearranged to solve for current:
I = P ÷ V
This says: the current a device draws is its power consumption divided by the voltage pushing the current through it. Higher voltage means less current for the same power — which is why a 1,500 W heater draws 12.5 A at 120 V but only 6.25 A at 240 V. For the applied, non-derivation reference, see the complete guide.
Formula 1: DC and Resistive AC
For DC circuits and for AC loads that are purely resistive (heaters, incandescent lamps, toasters), the simple form is exact:
I = P ÷ V
Worked example: 1,500 W ÷ 120 V = 12.5 A. Check: 120 × 12.5 = 1,500 ✓.
Why “resistive AC” qualifies: in a purely resistive load, voltage and current rise and fall in perfect sync, so the average power is exactly V × I — no correction needed. This covers most heating and lighting loads.
Formula 2: Single-Phase AC with Power Factor
Motors, compressors, transformers, and many electronics don’t draw current in sync with voltage — some of the current sloshes back and forth without doing useful work. Power factor (PF) measures how much of the supplied power is real work:
I = P ÷ (V × PF)
Worked example: a 1,500 W motor, PF 0.85, on 120 V: 120 × 0.85 = 102; 1,500 ÷ 102 = 14.7 A. Compared with the resistive 12.5 A, the motor draws about 18% more current for the same useful power.
Think of it this way: the supply must deliver 1,500 ÷ 0.85 ≈ 1,765 volt-amps of “apparent power” to get 1,500 watts of real work. Current follows apparent power, not real power — which is why ignoring power factor always underestimates current on inductive loads. Typical planning values: motors 0.7–0.9 (use 0.8 if unknown), welders ~0.7, modern LED drivers 0.9+. The Watts Calculator is useful when you need to convert between real and apparent power.
Formula 3: Three-Phase AC
Three-phase power delivers energy over three conductors, each carrying a sine wave offset by 120°. The total power is:
P = √3 × V × I × PF
Rearranged:
I = P ÷ (√3 × V × PF)
Here V is the line-to-line voltage (between any two phases), and √3 ≈ 1.732 comes from the 120° phase geometry — each phase’s voltage vector adds at 120°, and the line-to-line voltage is √3 times the phase-to-neutral voltage.
Worked example: 10,000 W three-phase, 208 V line-to-line, PF 0.85:
Step 1 — Denominator. 1.732 × 208 = 360.256; 360.256 × 0.85 = 306.22.
Step 2 — Divide. 10,000 ÷ 306.22 ≈ 32.6 A per phase.
Step 3 — Sanity check. If it were single-phase: 10,000 ÷ (208 × 0.85) = 56.6 A. Three-phase spreads the same power over three conductors, so ~32.6 A per conductor is the right order of magnitude — between half and two-thirds of the single-phase figure.
Formula 4: Ohm’s Law
Ohm’s law relates voltage, current, and resistance:
V = I × R → I = V ÷ R → P = I² × R
Worked example: a heating element measures 9.6 Ω. At 120 V: I = 120 ÷ 9.6 = 12.5 A, and P = 120 × 12.5 = 1,500 W — consistent with the watts formula, as it must be, since both describe the same physics.
Ohm’s law is the fallback when you have resistance but no wattage rating — common with heating elements, old equipment, and troubleshooting. Measure resistance with a multimeter (power disconnected), plug in the supply voltage, and you have the current. For combining per-load results into project totals, see the estimating guide.
Choosing the Right Formula
| Situation | Use this | Inputs needed |
|---|---|---|
| Battery, solar, vehicle (DC) | I = P ÷ V | Watts, DC volts |
| Heater, lamp, toaster (resistive AC) | I = P ÷ V | Watts, AC volts |
| Motor, compressor, welder (single-phase) | I = P ÷ (V × PF) | Watts, volts, power factor |
| Three-phase motor or equipment | I = P ÷ (√3 × V × PF) | Watts, line-to-line volts, PF |
| Known resistance, no wattage | I = V ÷ R | Volts, ohms |
The most damaging formula mistake is using single-phase math on a three-phase load: for the 10,000 W example above, single-phase math gives 56.6 A instead of 32.6 A — wire and breakers sized to 56.6 A would be needlessly oversized, and the reverse error (dividing a three-phase load by a phase-to-neutral voltage) undersizes dangerously. When the phase setup is unclear, the common mistakes guide shows how to recognize which system you’re looking at.
Related Guides
- Complete Guide — the full amperage reference these formulas belong to.
- Common Mistakes — formula mix-ups and how to catch them.
- Estimating Guide — applying these formulas across a whole project.
- Amperage FAQ — quick answers on volts, amps, and watts.
- Pro Tips — field-tested workflow advice for using these numbers.
Frequently Asked Questions
Why is there a √3 in the three-phase formula?
Three-phase voltages are 120° apart; the line-to-line voltage equals √3 times the phase-to-neutral voltage. The factor converts the three-phase power equation to use the line-to-line voltage you actually measure.
When can I ignore power factor?
For purely resistive loads (heaters, incandescent lamps) and DC circuits, PF = 1.0 and the simple I = P ÷ V is exact. For motors, compressors, and most electronics, ignoring it underestimates current.
Do I use line-to-line or line-to-neutral voltage in three-phase?
Line-to-line — the voltage between two phases (e.g., 208 V or 480 V). Using the 120 V phase-to-neutral figure is a classic error that nearly doubles the answer.
How do amps, volts, and watts relate?
Watts = volts × amps (DC/resistive AC). For AC with reactive loads, volt-amps (V × I) is the apparent power; multiply by power factor to get real watts.
Get Your Number
Pick the formula that matches your setup — DC, resistive AC, single-phase with power factor, or three-phase — and the arithmetic is one division. The Amperage Calculator runs all four automatically; your job is selecting the right scenario and entering honest inputs. When the hand-check and the calculator agree, you can trust the number.
Disclaimer: planning estimates only — formulas give theoretical current draw; real installations involve inrush current, voltage variation, and derating. Verify with a licensed electrician and your local authority having jurisdiction before sizing, installing, or modifying any circuit.
