To convert amp hour to watt hour, multiply the amp-hour (Ah) capacity by the nominal system voltage (V). For the most common DIY solar benchmark—a 100Ah battery at 12V—the converted answer is exactly 1,200 watt hours (Wh). The core formula is Wh = Ah × V. If you are sizing that same 100Ah battery for a 24V inverter system, the answer shifts to 2,400Wh. This conversion strictly requires a known, fixed voltage; without it, calculating total energy capacity is physically impossible.
The Core Formula and Common Battery Conversions
Amp-hours measure electrical charge (how many electrons flow over time), while watt-hours measure actual energy (the work those electrons can do). The bridge between them is voltage. Let us substitute the standard values into the formula:
100 Ah × 12 V = 1,200 Wh
Below is a data-dense reference chart for the most common off-grid and DIY solar battery bank sizes. This includes standard sealed lead-acid sizes and raw LiFePO4 prismatics (like the popular Eve LF280K 280Ah cells) configured in series for higher voltage banks.
| Battery Capacity (Ah) | 12V Nominal (Wh) | 24V Nominal (Wh) | 48V Nominal (Wh) |
|---|---|---|---|
| 50 Ah | 600 Wh | 1,200 Wh | 2,400 Wh |
| 100 Ah | 1,200 Wh | 2,400 Wh | 4,800 Wh |
| 200 Ah | 2,400 Wh | 4,800 Wh | 9,600 Wh |
| 280 Ah (Eve LF280K) | 3,360 Wh | 6,720 Wh | 13,440 Wh |
| 300 Ah | 3,600 Wh | 7,200 Wh | 14,400 Wh |
If you are fine-tuning a specific 12V build and need to see how capacity scales around the standard 100Ah mark, here is a quick lookup for neighboring values within a ±20% range:
| Capacity (Ah) | Energy at 12V (Wh) |
|---|---|
| 80 Ah | 960 Wh |
| 90 Ah | 1,080 Wh |
| 100 Ah | 1,200 Wh |
| 110 Ah | 1,320 Wh |
| 120 Ah | 1,440 Wh |
How Voltage, Phase, and Power Factor Shift the Answer
What assumption fixes the answer? In DC circuits, nominal voltage is the sole fixing assumption. But when you move to AC circuits—like sizing a backup generator or analyzing an industrial motor load—the math fractures.
The 120V vs 230V Shift
Amps only measure electron flow; voltage dictates the actual work pushed through the circuit. If an AC load draws 10Ah at 120V (North American standard), that is 1,200Wh. If that exact same 10Ah load is applied to a 230V European mains circuit, it yields 2,300Wh. Never assume a universal Wh value for an AC amp-hour rating without pinning down the regional voltage first.
The 3-Phase Multiplier
For 3-phase AC power (common in heavy workshop machinery and large commercial solar inverters), the single-phase formula breaks down. You must account for the square root of 3 (approx. 1.732) and the system's Power Factor (PF). The formula shifts to: Wh = Ah × V × √3 × PF.
When the Conversion is Meaningless
When is converting Ah to Wh completely meaningless? When you are dealing with AC reactive loads where the Power Factor (PF) is unknown. A compressor motor with a 0.70 PF will do 30% less real work than a resistive space heater (PF 1.0) drawing the exact same amps. If you convert AC amp-hours to watt-hours without knowing the PF, you are actually calculating Volt-Amps (VA), or apparent power, not real watt-hours. As noted in standard AC theory guides on Electronics Tutorials, ignoring PF in inductive loads leads to drastically undersized backup power systems.
Usable Capacity: Why Nameplate Wh Lies
On the workbench, nameplate Wh and usable Wh are two entirely different numbers. The Wh = Ah × V formula only gives you the theoretical maximum energy stored in the cells. To find what you can actually use to run your inverter, you must apply the Depth of Discharge (DoD) limit and account for voltage sag.
- 100Ah AGM Lead-Acid (1,200Wh Nameplate): You must limit discharge to 50% to avoid destroying the battery plates. Usable capacity is only 600Wh. Furthermore, Peukert's Law dictates that if you pull that 600Wh quickly (e.g., running a microwave), the effective capacity drops even further due to internal resistance.
- 100Ah LiFePO4 (1,200Wh Nameplate): Lithium iron phosphate batteries can safely discharge to 80%–90% DoD without degradation. Usable capacity is ~1,020Wh. The Battery Management System (BMS) will cleanly cut off at the low-voltage threshold, meaning you get nearly double the real-world runtime of the AGM for the same nameplate Ah.
Frequently Asked Conversion Questions
Is Wh the same as mAh?
No. Milliamp-hours (mAh) are just Ah divided by 1,000. To convert mAh to Wh, divide the mAh by 1,000, then multiply by voltage. For example, a 5,000mAh power bank at 3.7V is (5000 / 1000) × 3.7 = 18.5Wh.
How do I convert Wh back to Ah?
Divide the watt-hours by the voltage. If you have a 2,400Wh battery bank and want to know the Ah at 24V, the math is 2400 / 24 = 100Ah.
Why do airlines use Wh instead of Ah for lithium batteries?
Because Ah is useless for safety regulations without knowing the voltage. A 10Ah battery at 3.7V (a large phone battery) holds 37Wh. A 10Ah battery at 12V (a small UPS battery) holds 120Wh. The FAA and international aviation authorities limit carry-on lithium batteries based on actual chemical energy (typically a 100Wh limit per battery) to manage thermal runaway risks, making Wh the only standardized metric that matters for flight safety, as outlined by the Department of Energy's aviation battery guidelines.
