Wh = mAh x V / 1000 is the formula to convert amp hours (or milliamp hours) to watt hours for battery sizing.
In this formula, Wh is watt hours (the energy delivered), mAh is milliamp hours (the battery’s charge capacity), V is the nominal voltage of the battery, and 1000 converts milliamp hours to amp hours. For amp hours (Ah), use Wh = Ah x V.
What do the variables in the amp hours to watt hours formula mean?
Watt hours (Wh) measure the total energy a battery can deliver. Milliamp hours (mAh) or amp hours (Ah) measure charge capacity. Voltage (V) is the battery’s nominal operating voltage, which must match the specification. Dividing by 1000 converts mAh to Ah.
| Capacity (mAh) | Voltage (V) | Capacity (Ah) | Energy (Wh) |
|---|---|---|---|
| 1000 | 3.2 | 1.0 | 3.2 |
| 2000 | 3.7 | 2.0 | 7.4 |
| 5000 | 3.7 | 5.0 | 18.5 |
| 10000 | 12.8 | 10.0 | 128 |
| 20000 | 12.8 | 20.0 | 256 |
| 50000 | 25.6 | 50.0 | 1280 |
| 100000 | 51.2 | 100.0 | 5120 |
| 200000 | 51.2 | 200.0 | 10240 |
How do you convert amp hours to watt hours with real battery examples?
Example 1: A 12V 100Ah battery. Wh = 100 x 12 = 1,200 Wh.
Example 2: A 51.2V 200Ah battery. Wh = 200 x 51.2 = 10,240 Wh.
Example 3: A 10,000mAh (10Ah) 3.7V cell. Wh = 10 x 3.7 = 37 Wh.
What is the most common mistake in amp hour to watt hour conversion?
The most common mistake is using the wrong voltage or confusing mAh with Ah. For example, using 3.7V instead of 12.8V for a LiFePO4 pack can understate energy by over 60%. Using mAh instead of Ah without dividing by 1,000 can inflate the result by 1,000 times, leading to severe over- or under-sizing. Always check the battery’s nominal voltage and units before calculating.
Why does amp hours to watt hours conversion matter in procurement?
Accurate conversion from amp hours to watt hours determines if a battery meets your application’s energy needs. Overestimating watt hours can result in undersized systems, risking downtime or warranty claims. Underestimating can lead to overpaying for excess capacity. Procurement teams should request both Ah and Wh figures, specify the voltage, and confirm whether energy is stated as nominal or usable after depth-of-discharge limits.
What should you do next?
Check your battery’s datasheet for nominal voltage and capacity, then use the formula to verify the watt hour rating before finalizing your specification.
Frequently asked questions
Can I use the maximum or charging voltage for amp hour to watt hour conversion?
No, always use the nominal voltage specified by the manufacturer. Using maximum or charging voltage will overstate the watt hour value and risk system mismatch.
What is the difference between mAh and Ah in battery sizing?
1 Ah equals 1,000 mAh. Confusing the two leads to a 1,000-fold error in energy calculation, which can result in severe under- or over-sizing.
Does depth of discharge (DoD) affect amp hour to watt hour conversion?
Depth of discharge does not affect the mathematical conversion, but only a portion of the rated Wh is usable if DoD is limited. Always confirm if Wh is nominal or usable.
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