Amp Hours to Watt Hours Converter (Ah to Wh)

This amp hours to watt hours calculator converts a battery’s Ah rating into watt-hours (Wh), the energy it stores, and converts watt hours back to amp hours. Enter the capacity and the battery’s nominal voltage; the result is the same Wh figure that appears on power stations, e-bike packs and airline battery rules.

How to convert amp hours to watt hours

An amp-hour is a unit of charge: one ampere flowing for one hour, which equals 3,600 coulombs (NIST SP 811). A watt-hour is a unit of energy. Voltage connects them:

• Wh = Ah × V
• Ah = Wh ÷ V
• For several identical batteries: Wh = Ah × V × number of batteries (series or parallel, the total is the same)

Worked example with the default values

1. Capacity 100 Ah, nominal voltage 12 V
2. Energy: 100 × 12 = 1,200 Wh
3. Reverse check: 1,200 ÷ 12 = 100 Ah
4. The same 100 Ah at 12.8 V (a 12 V LiFePO4 battery) is 100 × 12.8 = 1,280 Wh

Ah to Wh conversion table

Capacity	12 V	12.8 V (LiFePO4)	24 V	48 V
7 Ah	84 Wh	89.6 Wh	168 Wh	336 Wh
20 Ah	240 Wh	256 Wh	480 Wh	960 Wh
50 Ah	600 Wh	640 Wh	1,200 Wh	2,400 Wh
100 Ah	1,200 Wh	1,280 Wh	2,400 Wh	4,800 Wh
200 Ah	2,400 Wh	2,560 Wh	4,800 Wh	9,600 Wh
300 Ah	3,600 Wh	3,840 Wh	7,200 Wh	14,400 Wh

How to convert watt hours to amp hours

Divide the watt-hours by the voltage of the system you are comparing against. This helps when a portable power station lists only Wh and you want to compare it with 12 V batteries.

Energy	at 12 V	at 12.8 V	at 24 V	at 48 V
100 Wh	8.3 Ah	7.8 Ah	4.2 Ah	2.1 Ah
500 Wh	41.7 Ah	39.1 Ah	20.8 Ah	10.4 Ah
1,000 Wh	83.3 Ah	78.1 Ah	41.7 Ah	20.8 Ah
2,000 Wh	166.7 Ah	156.3 Ah	83.3 Ah	41.7 Ah
5,000 Wh	416.7 Ah	390.6 Ah	208.3 Ah	104.2 Ah

Amp hours vs watt hours

Amp-hours tell you how much charge a battery can deliver at its own voltage; watt-hours tell you how much work it can do. Two batteries rated 100 Ah can hold very different amounts of energy: 1,200 Wh at 12 V or 4,800 Wh at 48 V. That is why watt-hours are the fair way to compare batteries of different voltages, and why product labels and the FAA’s lithium battery rules (100 Wh for spare batteries in carry-on without approval) use Wh. For larger banks, divide Wh by 1,000 for kilowatt-hours with the Ah to kWh converter, which also shows usable energy by battery chemistry.

Which voltage to use

• Lead-acid and AGM: 12 V per six-cell battery (2 V per cell).
• Lithium iron phosphate (LiFePO4): about 3.2 V per cell, so a “12 V” battery is 12.8 V nominal and a “48 V” bank is 51.2 V (BU-205).
• Phone and power-bank cells (lithium-ion): about 3.6 to 3.7 V nominal (BU-205); convert small mAh ratings with the mAh to kWh converter.
• Always use the nominal voltage, not the higher charging voltage or the lower voltage near empty.

Rated watt hours vs usable watt hours

The Wh figure from Ah × V is the rated energy. You get less in practice: lead-acid batteries last much longer when discharged only about halfway, and heavy loads reduce the delivered capacity (BU-501). To estimate how long a battery will actually run an appliance, including inverter losses, use the battery runtime calculator.

History: why capacity depends on load

In 1897 the German scientist Wilhelm Peukert showed that the usable capacity of lead-acid cells falls as the discharge current rises (Peukert’s law). Since then, lead-acid Ah ratings have been quoted at a stated slow discharge rate, so a Wh figure calculated from them is an upper bound under heavy loads.

References

• Thompson, A. & Taylor, B. N. (2008). Guide for the Use of the International System of Units (SI). NIST Special Publication 811. doi:10.6028/NIST.SP.811e2008
• Battery University. BU-205: Types of Lithium-ion. batteryuniversity.com

Common mistakes

1. Adding Ah across a series string. Two 12 V, 100 Ah batteries in series are 24 V, 100 Ah: 2,400 Wh, not 200 Ah.
2. Comparing Ah between different voltages. Compare Wh instead.
3. Using a power bank’s 5 V USB output voltage. The mAh rating refers to the internal cell voltage.

Batteries are what let solar and wind supply renewable energy after dark; size a full system with the off-grid solar calculator.