To convert DC current to AC current, you cannot simply map Amps to Amps; you must convert through Power (Watts). The exact formula is I_AC = (V_DC × I_DC × η) / (V_AC × PF). For a benchmark 10A DC draw on a 12V battery powering a 120V AC load (assuming 90% inverter efficiency and a 0.9 power factor), the converted AC current is exactly 1.0 Amp. If you are running a 24V system at 10A DC under the same conditions, the AC current jumps to 2.0 Amps. Below, we break down the assumptions that lock in these numbers and provide quick-reference tables for your specific battery bank.
The Core Formula and Quick-Reference Tables
Current is not conserved across an inverter; power is. The DC side delivers watts to the inverter, the inverter loses some heat, and the AC side delivers the remaining watts to the load. Here is the formula with the benchmark values substituted:
- I_AC = AC Current (Amps)
- V_DC = DC Source Voltage (e.g., 12V)
- I_DC = DC Current (e.g., 10A)
- η (Eta) = Inverter Efficiency (e.g., 0.90 for 90%)
- V_AC = AC Output Voltage (e.g., 120V)
- PF = Load Power Factor (e.g., 0.90)
Substitution: I_AC = (12 × 10 × 0.90) / (120 × 0.90) = 108W / 108 = 1.0A.
| DC Current (I_DC) | DC Power (12V) | AC Current (I_AC) |
|---|---|---|
| 8A | 96W | 0.80A |
| 9A | 108W | 0.90A |
| 10A (Base) | 120W | 1.00A |
| 11A | 132W | 1.10A |
| 12A | 144W | 1.20A |
Data-Dense Reference: Common DC to AC Conversions
The following table maps real-world DC amp draws to AC amp outputs for a standard 12V DC to 120V AC system, assuming a high-quality pure sine wave inverter (90% efficiency) and a mixed AC load (0.9 PF).
| DC Amps (I_DC) | DC Watts (12V Nominal) | AC Watts (After 10% Loss) | AC Amps @ 120V (PF 0.9) | Recommended DC Wire (AWG) |
|---|---|---|---|---|
| 5A | 60W | 54W | 0.50A | 14 AWG |
| 15A | 180W | 162W | 1.50A | 12 AWG |
| 20A | 240W | 216W | 2.00A | 10 AWG |
| 30A | 360W | 324W | 3.00A | 8 AWG |
| 50A | 600W | 540W | 5.00A | 6 AWG |
| 100A | 1200W | 1080W | 10.00A | 2/0 AWG |
| 200A | 2400W | 2160W | 20.00A | 4/0 AWG |
Note: DC wire sizing assumes copper, 75°C column, and a short run (<5 ft) to minimize voltage drop. Always verify against NEC Article 310 for your specific installation.
What Assumptions Fix Your Answer?
If you change any of the four variables in the formula, your AC current shifts drastically. Here is what locks the math in place:
- Inverter Efficiency (η): Cheap high-frequency modified sine wave inverters often operate at 80-85% efficiency. Premium low-frequency transformer-based units (like those from Victron Energy or OutBack Power) can hit 93-95%. A drop from 90% to 80% efficiency means your DC current must increase by 12.5% to deliver the same AC watts.
- Power Factor (PF): This is the ratio of real power to apparent power. A purely resistive load (like a space heater or incandescent bulb) has a PF of 1.0. Inductive loads (like fridge compressors, well pumps, or AC motors) often have a PF between 0.6 and 0.8. A lower PF forces the inverter to supply more apparent current to achieve the same real work. Read more on how PF impacts sizing in this All About Circuits breakdown.
- DC Source Voltage: A 10A draw on a 12V battery yields 120W. That exact same 10A draw on a 48V server-rack battery yields 480W. The AC current output will be four times higher on the 48V system.
If someone asks, "I have a 50A DC solar charge controller, how many AC amps is that?" the question is physically meaningless without knowing the battery bank voltage and the AC load's power factor. Asking for a direct Amp-to-Amp conversion without voltage context is like asking "how many gallons of water is 50 mph?" You must anchor the calculation to Watts.
How the Answer Shifts: 120V vs 230V vs 3-Phase
The AC voltage and phase architecture completely dictate the final amperage. Higher AC voltages result in lower AC current for the same wattage, which is why 48V DC systems and 230V AC outputs are preferred for high-power off-grid cabins.
| AC System Architecture | Formula Denominator | AC Amps for 2000W Output (PF 0.9) | Typical Use Case |
|---|---|---|---|
| 120V Single-Phase (US) | V × PF | 18.52A | Standard RV / Small Cabin |
| 230V Single-Phase (EU/AU) | V × PF | 9.66A | Euro Off-Grid / Appliances |
| 208V 3-Phase (US Commercial) | √3 × V × PF | 6.17A | Industrial Motors / HVAC |
| 400V 3-Phase (EU Commercial) | √3 × V × PF | 3.21A | Heavy Machinery / Pumps |
Notice the √3 (1.732) multiplier in the 3-phase denominator. Three-phase power delivers the same wattage at significantly lower current per conductor, reducing copper costs and I²R heating losses in long wire runs.
FAQ: Real-World Inverter Sizing and Wire Gauges
Q: Why does my inverter trip when the AC load nameplate says it only draws 5A?
A: Nameplate amps usually reflect running current at a specific PF. However, inductive motors have a Locked Rotor Amperage (LRA) or startup surge that can be 3 to 6 times the running current. A 5A fridge compressor might demand 25A for 500 milliseconds on startup. If your inverter's surge rating (usually double the continuous rating for high-frequency units) is exceeded, it will fault. Always size the inverter for the surge, not just the continuous formula output.
Q: What size wire do I need on the DC side vs the AC side?
A: The DC side always requires massively thicker wire. In our 1200W example above, the AC side only draws 10A at 120V, which safely fits on standard 14 AWG NM-B Romex. However, the DC side is pulling 100A at 12V. Running 100A through 14 AWG wire would cause a meltdown and fire. You must use 2/0 AWG copper on the DC side to handle the current safely and keep voltage drop under 3%.
Q: Does the formula change if I use a 24V or 48V battery bank?
A: The formula remains identical, but V_DC changes. If you upgrade from a 12V bank to a 48V bank, your V_DC increases by a factor of 4. To deliver the same AC watts, your DC current (I_DC) drops by 75%. This is exactly why large solar arrays and whole-home battery backups (like the Tesla Powerwall) operate at 48V or higher—it keeps the DC amperage manageable and allows the use of smaller, cheaper DC cabling and busbars.
