Amp Hours to Watt Hours (Ah to Wh) Conversion Calculator

What Is Amp-Hours (Ah)?

Amp-hours is a measure of the amount of electrical charge an electric power source will discharge within one hour at a specific voltage.

Amp-hours (Ah) is not the only unit used to represent battery capacity. Other units like milliamp-hours (mAh) and watt-hours (Wh) also represent battery capacity. However, it is more common to find amp-hours (Ah) and milliamp-hours (mAh).

What Is Watt-Hours (Wh)?

Watt-hours is a unit of measure of electrical energy. It represents the amount of energy used up or discharged by an electrical device when the device uses or produces a certain amount of power over one hour.

As mentioned earlier, watt-hour (Wh) may be written on a battery pack to represent the battery’s energy capacity. When used that way, it represents how much energy the battery can discharge over a one-hour period.

How to Calculate Amp Hours to Watt Hours (Ah to Wh)

Conversion Formula

Let’s derive the formula to convert amp-hours to watt-hours.

Watt-hours is a unit of electrical energy, and electrical energy equals power multiplied by time. Going by that, we can say:

electrical energy (Wh) = power (W) x time (h) (1)

Power equals voltage multiplied by current (amperage). So, we can represent it as:

power (W) = voltage (v) x current (A) (2)

Now, we’ll substitute power for voltage x current into (1):

electrical energy (Wh) = voltage (v) x current (A) x time (h)

We can rewrite the above as:

Wh = v x A x h

= v x Ah

Now, we have: Wh = v x Ah

Basically, to calculate watt-hours from amp-hours, multiply amp-hours times battery voltage.

Conversion Examples

If we have a solar power system whose battery’s capacity is 100 Ah with a battery voltage of 20 volts, how many watt-hours is the battery?

The battery’s capacity in watts-hours would be:

100 x 20 = 2000 Wh

How many watt-hours is stored in two lithium batteries, one of which is rated 50 amp-hours 20 volts while the other is 40 amp-hours 24 volts?

The energy capacity of the first battery:

50 x 20 = 1000 Wh

Energy capacity of the second battery :

40 x 24 = 960 Wh

Total capacity of both batteries:

1000 + 960 = 1960 Wh

How many watt-hours is a 200 amp-hours 12 volts solar generator?

200 x 12 = 2400 Wh

The battery is 2400 Wh.

Why Convert Amp Hours to Watt Hours?

We need to convert amp-hour to watt-hour to correctly compare the capacities of batteries with different voltages.

If we were to directly compare the capacities of batteries with different voltages, our comparison would be off. This holds true because the energy stored in a battery depends not only the amount of charge given off over one hour, but also on the battery voltage.

To put things in context, if we have two lead-acid batteries A and B, and A is rated 10 Ah 12 volts while B is rated 10 Ah 20 volts, both of them will give off similar amounts of electrical charge over an hour. However, B will store more energy than battery A.

Battery B would have a capacity of 10 x 20 = 200 Wh, while Battery A would have a capacity of 10 x 12 = 120 Wh. Hence, battery B will store more energy than A.

Amp-Hours to Watt-Hours Conversion Chart

Amp-hours to watt-hours conversion chart for a battery voltage of 12v:

Amp-hours to watt-hours conversion chart for a 20v battery:

Amp-hours to watt-hours quick chart for a 24v battery:

Watt-Hours vs Kilowatt-Hours (Wh vs kWh)

The difference between watt-hours and kilowatt-hours is the magnitude they measure. While kilowatt-hours measures in thousands (kilo), watt-hours measures in units. However, both remain units of electricity.

Units that measure higher magnitudes are useful when we have large quantities. For one, they can make things more concise. For instance, instead of writing 10,000 Wh, we can write its equivalent in kWh (10 kWh). The kWh equivalent is shorter and makes things easier.

How to Convert Amp-Hours to Kilowatt-Hours (Ah to kWh)

The formula for converting amp-hours to kilowatt-hours (Ah to kWh) is similar to that of converting amp-hours to watt-hours (Ah to Wh). The main difference being that the Ah to kWh conversion has a divisor (1000), while the Ah to Wh conversion doesn’t.

KWh = Wh/1000 (1)

Wh = v x Ah (2)

Substituting Wh for v x Ah into (1) for kWh, we’ll get the following formula:

kWh = v x Ah/1000

Here’s an example:

How many kilowatt-hours is a 30 amp-hours 12 volts battery?

kWh = 12 x 30/1000 = 360/1000 = 0.36 kWh

Amp-Hours vs Milliamp-Hours (Ah vs mAh)

Amp-hours and milliamp-hours are both units of battery capacity. However, the magnitudes they measure differ. While amp-hour measures in units, milliamp-hour measures in thousandths.

Units that measure lower magnitudes are useful when we have smaller quantities. The value of some smaller quantities can get lost in calculation if we use regular units for them. But by switching them to units of lower magnitudes, we can avoid this.

Besides, using units of lower magnitudes like mAh for smaller quantities makes for concision. It’s easier to write 0.1 mAh than its equivalent, 0.0001 Ah.

How to Convert Milliamp-Hours to Watt Hours (mAh to Wh)

The formula for converting milliamp-hours to watt-hours (mAh to Wh) is about the same as that for converting amp-hours to watt-hours (Ah to Wh). However, since the magnitudes of measurement of Ah and mAh differ, the mAh to Wh conversion needs a constant to make up for that difference.

Ah = mAh/1000 (1)

Wh = v x Ah (2)

Substituting Ah for mAh/1000 into (1) gives us:

Wh = v x mAh/1000

How to Convert Watt-Hours to Amp-Hours (Wh to Ah)

Converting watt-hours (Wh) to amp-hours (Ah) is about as simple as converting amp-hours to watt-hours. The quantities involved in both conversions are even the same.

Let’s derive the formula:

Wh = v x Ah (1)

Making Ah the subject of (1) by dividing both sides by v:

Ah = Wh/v

So, to convert watt-hours to amp-hours, all we have to do is divide watt-hours by the voltage of the source.

Here’s an example of converting watt-hours to amp-hours:

How many amp-hours is a 20 watt-hours 12 volts battery?

Ah = 20/12 = 1.67 Ah

When Will You Need to Make Watt- and Amp-Hour Calculations?

Watt-hours and amp-hours calculations are primarily for gaining insight into battery capacity. As mentioned earlier, if you are trying to compare two batteries with the same amp-hours but different voltage, you’ll have to convert their capacity to watt-hours. Else, your comparison would be inaccurate.

On another level, amp-hours to watt-hours calculations and watt-hours to amp-hours calculations can help you gain insight into the features to use in an electrical system.

With factors like wire gauge and discharge rate depending on amperage, knowing capacity in amp-hours is crucial. So, if your battery’s rating ever comes in Wh, you may have to convert it to Ah. Knowing how many amp-hours your appliances require is also vital here.

To figure out how many amp-hours your appliances require or use daily, add up their wattages and multiply the total wattage by 24 hours. This will be their total daily consumption in watt-hours.

Next, convert watt-hours to amp-hours by dividing watt-hours by the voltage of the system. Now, the result is your appliances’ daily amp-hours.

The Difference Between Watt and Watt-Hours

While watt is a unit of measure of power, watt-hours is a unit of measure of electricity. This is the primary difference between watt and watt-hours.

Watt is a measure of the time rate of energy consumption in a system. It can be used in all kinds of measurements involving power.

Watt-hours, as we mentioned earlier, is a measure of the amount of energy discharged or consumed by an electrical device when it uses or gives off a certain amount of watts over an hour.

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