Wh = mAh x V / 1000 is the formula to convert amp hours to watt hours for battery sizing, where Wh is watt hours, mAh is milliamp hours, and V is nominal voltage.
In this formula: Wh (watt hours) is the total energy, mAh (milliamp hours) is the battery capacity, and V (volts) is the nominal voltage of the battery. If your battery is rated in amp hours (Ah), multiply Ah by 1,000 to get mAh before using the formula, or use Wh = Ah x V directly.
| Capacity (Ah) | Voltage (V) | Capacity (mAh) | Energy (Wh) |
|---|---|---|---|
| 1 | 3.2 | 1,000 | 3.2 |
| 2.5 | 3.7 | 2,500 | 9.25 |
| 5 | 12.8 | 5,000 | 64 |
| 10 | 12.8 | 10,000 | 128 |
| 50 | 25.6 | 50,000 | 1,280 |
| 100 | 12.8 | 100,000 | 1,280 |
| 200 | 51.2 | 200,000 | 10,240 |
| 280 | 384 | 280,000 | 107,520 |
How do you convert amp hours to watt hours using the formula?
To convert amp hours to watt hours, multiply the amp hour (Ah) rating by the battery’s nominal voltage (V): Wh = Ah x V. For milliamp hours (mAh), use Wh = mAh x V / 1000. Always use the nominal voltage stated on the battery specification.
What are some worked examples of amp hour to watt hour conversion?
Example 1: A 12V 100Ah battery. Wh = 100 x 12 = 1,200Wh.
Example 2: A 3.7V 2,500mAh cell. Wh = 2,500 x 3.7 / 1000 = 9.25Wh.
Example 3: A 51.2V 200Ah battery. Wh = 200 x 51.2 = 10,240Wh.
What is the most common mistake when converting amp hours to watt hours?
The most common mistake is confusing mAh with Ah, or using the wrong voltage. Using charger voltage instead of battery nominal voltage can overstate energy by 10-20%. Another frequent error is assuming the full rated capacity is usable, when depth-of-discharge limits (e.g., 80% DoD) mean only part of the nominal watt hour value is available in practice. This can result in undersized systems or unexpected runtime shortfalls.
Why does amp hour to watt hour conversion matter in procurement?
Procurement decisions based on amp hours alone risk underestimating or overestimating the true energy available for a given application. Suppliers may quote batteries with identical Ah ratings but different voltages, leading to significant differences in actual energy delivered. Always compare batteries on watt hour (Wh) capacity, and factor in usable energy after depth-of-discharge and efficiency losses. This avoids costly oversizing or system failures due to insufficient runtime.
What should you do next?
Check your battery specification for nominal voltage and capacity, then use the formula to verify the watt hour value before finalizing your procurement.
Frequently asked questions
Can I use the charger voltage instead of battery voltage for the conversion?
No, always use the battery's nominal voltage for amp hour to watt hour conversion. Using charger or system voltage can overstate the energy figure and lead to sizing errors.
How does depth-of-discharge affect usable watt hours?
Depth-of-discharge (DoD) limits mean only a portion of the rated Wh is usable. For example, at 80% DoD, only 80% of the nominal Wh should be counted as usable energy in system design.
Is there a difference between Ah to Wh and mAh to Wh conversions?
The formula is the same, but mAh must be divided by 1,000 to convert to Ah. For example, 2,500mAh x 3.7V / 1,000 = 9.25Wh, while 2.5Ah x 3.7V = 9.25Wh.
AJPOWER-Battery