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

What Is a Watt-Hour?

At its simplest, watt-hours = power over a period of time (one hour). Watt-hours (Wh) is a measure of how much energy an electrical system uses when a given amount of power is consumed over a one-hour period.

Wh typically represents electrical power consumption. However, when used to describe energy sources like a battery pack, it represents how much energy the battery can supply or discharge when a certain amount of power is supplied over one hour. In other words, watt-hours can also represent a battery’s energy capacity.

What Is an Amp-Hour?

Amp-Hours = current supplied over a period of time (one hour). Amp-hours (also ampere-hours) is a measure of how much electrical charge a source of electricity can give off over one hour. Basically, a rating of 1 amp-hour (Ah) means an electrical system can supply 1 ampere of current every one hour.

Amp-hour is typically used to define battery capacity. Alternatives like milliamp-hours and watt-hours may also be used. However, watt-hours is not as commonly used as the other two.

Why Convert Watt Hours to Amp-Hours?

When sizing an electrical system such as a solar system, we have to convert watt-hours to amp-hours. Amp-hours gives us an insight into the most appropriate features to use in the system.

For instance, different wire gauges are only suitable when used within certain amperage capacities. Going beyond such capacities might damage the wires. With battery capacity in watt-hours, we cannot readily tell the amperage capacity of a solar power system. But in ampere-hours, there’s better clarity.

Another instance in which this applies is when choosing the fuse. Fuse ratings typically come in amps. So, to figure out the best fuse to use in your solar energy system, knowing the battery’s capacity in amp-hours is essential.

Ordinarily, we wouldn’t have to do this conversion since batteries are usually rated in amp-hours (Ah) or milliamp-hours (mAh). But in rare cases, batteries come with their capacity written in watt-hour.

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

Conversion Formula

To derive the formula to calculate amp-hours from watt-hours, we need two formulas: the formula for electrical energy and the formula for power.

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

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

Now, we’ll substitute power for voltage (v) x current (A) into (1) to derive an equation that shows the relationship between Wh and Ah:

Electrical energy (Wh) = voltage (v) x current (A) x time (h) (3)

We can rewrite (3) as:

Wh = v x A x h

= v x Ah (4)

Next, we’ll make Ah the subject of (4) by dividing both sides by v:

Ah = Wh/v

What the final equation basically indicates is that to convert watt-hours to amp-hours, divide watt-hours by voltage.

Now that we have our conversion, let’s try out some examples.

Example 1: How many amp-hours is a 12 v battery bank rated 40 Wh?

This is a pretty straightforward example; all we have to do here is divide 40 by 12:

amp-hours rating of the battery = 40/12 = 3.3 Ah

Example 2: If we have two lead-acid batteries, one rated 12v 50Wh, the other rated 20v 65Wh, which of them would have the higher discharge rate over the same period?

Discharge rates of batteries are directly dependent on their capacity in Ah. So, to figure out the discharge rate of the given lead-acid batteries, we must calculate in amp-hours.

For the first battery = 50/12 = 4.17 Ah

For the second battery = 65/20 = 3.25 Ah

Since we are comparing the discharge rates of the batteries over the same period, the first battery would have a higher discharge rate than the second battery.

Example 3: Say we have a solar power system with a battery power rating of 250 W, battery voltage of 20v, and a battery life of 5 hours. What is the capacity rating in ampere-hour?

So, we know how many watts the battery generates and how long it can generate said wattage for. Using those two details, we can calculate the energy stored by the battery (Wh).

The battery’s Wh = 250 x 5 = 1250Wh

Now that we know how much energy the battery stores, we can calculate the amp-hour capacity rating by dividing Wh by voltage.

The battery’s Ah rating = 1250/20 = 62.5 Ah

Watt-Hours to Amp-Hours Conversion Chart

Here’s a quick watt-hours to amp-hours conversion chart for a 12v battery:

Here’s a quick watt-hours to amp-hours chart for a 20v battery:

Here’s a quick watt-hours to amp-hours chart for a 24v battery:

Here’s a quick watt-hours to amp-hours chart for a 48v battery:

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

The conversion from watt-hours (Wh) to milliamp-hours (mAh) is similar to the conversion from watt-hours (Wh) to ampere-hours (Ah). However, because mAh measures in thousandths, we must adjust the conversion by multiplying with 1000.

So, while this is the conversion for Wh to Ah:

Ah = Wh/v

This is the conversion for Wh to mAh:

mAh = Wh x 1000/v

Let’s try the conversion out with two examples.

Example 1: We have a portable power station with a wattage of 50 W, voltage of 12v, and runtime of two hours. What is the capacity of the station in milliamp-hours?

Since we know how much power the station produces and how long it can produce said wattage for, we can calculate its Wh.

capacity in Wh = 50 x 2 = 100Wh

Now that we know the station’s capacity in Wh, we can calculate its capacity in mAh.

capacity in mAh = 100 x 1000/12 = 8,333.3 mAh

Example 2: How many milliamp-hours is a 12 v battery rated 8Wh?

capacity in mAh = 8 x 1000/12 = 666.67 mAh

How Can You Convert Ah to Wh?

We can calculate watt-hours (Wh) from amp-hours (Ah) using the following formula:

Wh = v x Ah

Basically, to convert amp-hours to watt-hours, multiply amp-hours by voltage.

Let’s try the conversion out with some examples.

Example 1: How many watt-hours does a 12v car battery rated 77 Ah store?

Since we know the voltage and amp-hours, the calculation would be straightforward.

The amount of watt-hours the battery stores = 12 x 77 = 924 Wh

Example 2: If we have two lithium batteries with one rated 12v 10Ah and the other rated 24v 8Ah, which of the two batteries stores more energy when fully charged?

When comparing the storage capacity of batteries, using their Wh instead of amp-hours gives us a more accurate comparison. This is especially true when they have different voltages.

So, to know which of our lithium batteries stores more energy, we have to calculate their capacity in Wh.

The watt-hours of the first battery = 12 x 10 = 120 Wh

The watt-hours of the second battery = 24 x 8 = 192 Wh

Going by our calculation, the 24v 8Ah battery will store more energy than the 12v 10Ah battery.