To convert 15 amps and 120 volts to watts, the direct answer is exactly 1,800 watts. The foundational formula is Watts = Amps × Volts (15A × 120V = 1,800W). However, this exact 1,800W figure assumes a purely resistive DC load or an AC load with a Power Factor (PF) of 1.0. If you are sizing a branch circuit for a continuous load (running for 3 hours or more), NEC Article 210.20 requires an 80% derating, meaning a 15-amp breaker at 120V should only carry 1,440 watts continuously to prevent thermal tripping.
| Breaker Size (Amps) | Nominal Voltage | Max Theoretical Watts | NEC Continuous Limit (80%) | Typical Appliance Application |
|---|---|---|---|---|
| 15A | 120V | 1,800W | 1,440W | General lighting, standard receptacles |
| 20A | 120V | 2,400W | 1,920W | Kitchen small appliance circuits, microwaves |
| 30A | 240V | 7,200W | 5,760W | Standard electric dryers, water heaters |
| 50A | 240V | 12,000W | 9,600W | Electric ranges, large HVAC compressors |
The Core Formulas and the Assumptions That Fix the Answer
The assumption that fixes your wattage answer is the Power Factor (PF) and the phase configuration. In a direct current (DC) circuit, or an alternating current (AC) circuit powering a purely resistive load (like incandescent heaters or toasters), voltage and current are perfectly in phase. The formula is simple:
DC / Resistive AC: Watts = Amps × Volts
However, when you introduce inductive or capacitive loads—such as AC motors, transformers, or fluorescent lighting ballasts—the current waveform lags or leads the voltage waveform. This creates a phase angle difference. To find the true power (Watts) doing actual work, you must multiply by the Power Factor, which ranges from 0 to 1.0:
Single-Phase AC: Watts = Amps × Volts × PF
Three-Phase AC (Line-to-Line): Watts = √3 × Amps × Volts × PF
When is the conversion meaningless? If you are measuring an inductive load with a basic multimeter and you do not know the Power Factor, calculating watts from amps and volts is mathematically meaningless. You are merely calculating Volt-Amps (VA), also known as apparent power. Apparent power dictates the physical size of the wires and breakers you need, but true power (Watts) dictates the actual energy consumed and the mechanical work output. For a deep dive into the physics of phase angles, refer to the Georgia State University HyperPhysics power factor reference.
Neighboring Values and Power Factor Shifts
To understand how minor fluctuations in current or a drop in Power Factor affect your final wattage, here is a localized reference table showing a ±20% range around our baseline 15A / 120V query.
| Amps | Volts | Power Factor | True Power (Watts) | Apparent Power (VA) |
|---|---|---|---|---|
| 12A (-20%) | 120V | 1.0 (Resistive) | 1,440W | 1,440 VA |
| 15A (Baseline) | 120V | 1.0 (Resistive) | 1,800W | 1,800 VA |
| 15A (Baseline) | 120V | 0.8 (Inductive Motor) | 1,440W | 1,800 VA |
| 18A (+20%) | 120V | 1.0 (Resistive) | 2,160W | 2,160 VA |
Notice the third row: a 15A motor with a 0.8 PF draws the exact same true power (1,440W) as a 12A resistive heater, but it demands 1,800 VA of apparent power from your panel. This is why motor circuits require thicker wire and larger breakers than their nameplate wattage might initially suggest—the wiring must handle the apparent current, not just the true power.
How the Answer Shifts: 120V vs 230V vs 3-Phase
Voltage standards and phase configurations drastically alter the wattage output for the exact same amperage. A 15-amp draw yields vastly different thermal and mechanical results depending on the grid architecture. The All About Circuits three-phase power guide details how the √3 (1.732) multiplier bridges line-to-line and line-to-neutral voltages in polyphase systems.
| System Type | Nominal Voltage | Current | Formula Used | Resulting Watts |
|---|---|---|---|---|
| US Single-Phase | 120V | 15A | 15 × 120 | 1,800W |
| EU/UK Single-Phase | 230V | 15A | 15 × 230 | 3,450W |
| US 3-Phase (Line-Line) | 208V | 15A | 1.732 × 15 × 208 | 5,403W |
| US 3-Phase (Line-Line) | 480V | 15A | 1.732 × 15 × 480 | 12,470W |
When designing solar arrays or battery banks, remember that DC systems operate at much lower nominal voltages. If you are pulling 15A from a 12V LiFePO4 battery bank, your wattage is only 180W. To achieve 1,800W at 12V DC, you would need to pull a massive 150 amps, requiring 1/0 AWG or 2/0 AWG battery cables to prevent voltage drop and insulation melting.
Frequently Asked Questions
Why does my 15A breaker trip when I run a 1,800W space heater?
A 1,800W space heater on a 120V circuit draws exactly 15 amps. While a breaker is theoretically rated to hold 15A indefinitely, breakers are thermal-magnetic devices. Running at 100% capacity for more than a few minutes causes the bimetallic thermal strip inside the breaker to heat up and eventually trip. Always size continuous loads to 80% of the breaker rating (1,440W max on a 15A circuit).
Can I use the basic DC formula for my solar panels?
Yes, but you must use the correct voltage and current metrics. Do not use Open Circuit Voltage (Voc) or Short Circuit Current (Isc). To find the actual maximum wattage a panel produces, multiply the Maximum Power Voltage (Vmp) by the Maximum Power Current (Imp). For a typical 400W panel, this looks like 41.5V (Vmp) × 9.64A (Imp) = 400.06W.
Does voltage drop change my wattage calculation?
Yes. If you run 100 feet of 14 AWG NM-B cable on a 15A circuit, you might experience a 3% to 5% voltage drop under full load. Instead of 120V reaching the appliance, it might only see 114V. For a resistive load, the wattage will drop proportionally (114V × 15A = 1,710W). For a constant-power inductive load like a compressor, the appliance will actually draw more amps to compensate for the lower voltage, increasing heat and tripping risk.
