How to change from Wh to Ah (and from Ah to Wh) using a formula
The conversion between watt-hours (Wh) and ampere-hours (Ah) depends on the system voltage or voltage. The relationship between these two units is given by the formula:
Ah = Wh /V
Where:
- Ah is the capacity in amp hours.
- Wh is the capacity in watt hours.
- V is the voltage in volts.
To convert from amp hours to watt hours, you can use the following formula:
Wh = Ah × V
If you know the Wh capacity of a battery and the nominal voltage, you can calculate the Ah capacity by dividing the Wh by the voltage. And vice versa, if you know the capacity in Ah and the nominal voltage, you can calculate the Wh by multiplying the capacity in Ah by the voltage.
Note that these unit conversions are only direct if the voltage is constant during the time the power is being used. In systems where the voltage varies, the relationship may not be so simple.
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Practical example to convert Wh to Ah (and Ah to Wh)
Suppose you have a battery with a capacity of 300 watt-hours (Wh) and operates at a voltage of 12 volts (V). To convert from watt-hours (Wh) to ampere-hours (Ah), you can use the formula:
Ah = Wh /V
In this case, the formula would be:
Ah = 300 Wh / 12 V
Performing the division, we obtain:
Ah = 25 Ah
Therefore, the battery capacity is 25 amp-hours.
If instead you know the capacity in amp-hours (Ah) and want to convert it to watt-hours (Wh), you can use the formula:
Wh = Ah × V
For example, if you have a battery with a capacity of 30 amp hours (Ah) and operates at 12 volts (V), the formula would be:
Wh = 30 Ah × 12 V
Performing the multiplication, we obtain:
Wh = 360 Wh
Therefore, the battery capacity is 360 watt hours.
Watt-hour (Wh) ampere-hour (Ah) equivalence tables
Table of examples of Wh-Ah and Ah-Wh conversions (for a voltage of 12V):
Wh | Ah |
|---|---|
5 | 0.42 |
10 | 0.83 |
25 | 2.08 |
50 | 4.17 |
100 | 8.33 |
250 | 20.83 |
500 | 41.67 |
600 | 50 |
700 | 58.33 |
800 | 66.67 |
1000 | 83.33 |
2000 | 166.67 |
3000 | 250 |
4000 | 333.33 |
5000 | 416.67 |
Ah | Wh |
|---|---|
1 | 12 |
5 | 60 |
10 | 120 |
25 | 300 |
30 | 360 |
50 | 600 |
60 | 720 |
70 | 840 |
80 | 960 |
90 | 1080 |
100 | 1200 |
200 | 2400 |
300 | 3600 |
400 | 4800 |
500 | 6000 |
Downloadable quick conversion tables
Download our free quick conversion tables in pdf from amp-hours to watt-hours and from watt-hours to amp-hours, for different voltages.
How watt hours and amp hours are used and related
Watt-hours (Wh) and ampere-hours (Ah) are units of measurement of energy and electrical charge, respectively. While watt-hours measure the total amount of energy consumed or stored during a period of time, amp-hours measure the total amount of electrical charge flowing through a circuit during that same period.
Let’s say you’re using a lithium-ion battery to power a device. Battery capacity is usually specified in ampere-hours (Ah). This indicates how much electrical charge the battery can provide at a certain current rate for one hour before it runs out. For example, if you have a 10Ah battery, it can supply 1 amp of current for 10 hours, or 2 amps of current for 5 hours, and so on.
Now, if we look at the power consumed by a device, we use watt-hours (Wh). Power is calculated by multiplying voltage by current, and if we do this over a period of time, we get the total energy consumed in watt-hours. For example, if you have a light bulb that consumes 10 watts and you turn it on for 3 hours, it will have consumed 30 watt-hours of energy.
So while amp hours give us an idea of how much electrical charge a battery can provide, watt hours tell us how much energy an electrical device consumes or produces during operation. They are two ways of measuring different but related aspects of electricity.