mAh × V / 1000 =
0.00 Wh
Conversion formula: Wh = mAh × V / 1000
What Is Milliamp-Hours?
Milliamp-hours, short for milliampere-hours and represented with mAh, is a measure of how much electrical energy a battery can discharge at a specific voltage.
Better still, we can say milliamp-hour is the power capacity of a battery – a marker of how much electric charge a battery can discharge over a one-hour period at the battery voltage.
Milliamp-hour (mAh) is generally a unit of electric charge commonly used to represent battery capacity. Of course, it may also be used to represent the capacity of other power sources not conventionally thought of as batteries – e.g., power banks.
Besides mAh, we can also use ampere-hours (Ah) and watt-hours (Wh) as units of battery capacity.
What Is Watt-Hours (Wh)?
Watt-hour is a unit of energy consumption or production. While it may be used as a unit of any energy, it is typically used to represent electrical energy.
Watt-hour measures how much energy electrical devices consume or how much energy electric power sources can give off.
For instance, if a battery can give off 30 W over 3 hours, its energy production would be 90 Wh. Then, if a refrigerator consumes 600 W of electricity over 2 hours, its energy consumption would be 1200 Wh.
Since watt-hour represents how much energy a battery/power source can discharge over a given period, we can also use it as a unit of battery capacity, like milliamp-hour. Still, you are more likely to find battery capacities written in milliamp-hours or amp-hours.
Why Convert Milliamp-Hours to Watt-Hours?
Ordinarily, we can directly compare the capacities of two different batteries with the same voltage. For instance, we can conclude that a 12-volt, 6000 mAh battery will not last as long as a 12-volt, 10,000 mAh battery.
But if one of those batteries was rated 24 volts while the other was 12 volts, we couldn’t compare how long they would last by just their capacities in mAh. If we do, our comparison may be inaccurate. However, if we convert their capacities from mAh to Wh, our conclusion about their run time would most likely be accurate.
So, if we have one battery, 24 volts, 6000 mAh, and another battery, 12 volts, 10,000 mAh, we’ll have to convert their capacities to Wh before we can compare them. The first battery’s watt-hours would be 144 Wh, while the second would be 120 Wh.
Since 144 Wh is greater than 120 Wh, the first battery will last longer than the second battery under the same conditions of use.
If we had compared their capacities in mAh, we would have concluded that the second battery would last longer. But converting to watt-hours helped us avoid that error.
How to Convert Milliamp-Hours to Watt-Hours (mAh to Wh)
mAh to Wh Conversion Formula
Since Wh is the unit of electrical energy, we need the unit of electrical energy to derive the conversion formula of mAh to Wh.
- The formula for electrical energy:
\(\small{Electrical\ energy\ E = power\ (W) * time\ (h)}\ (1)\)
- We can rewrite (1) as:
\(Wh = W * h\ (2)\)
Next, to show the relationship between electrical energy, voltage, and current (electrical charge), we need the formula for power.
- The formula for power:
\(\small{Power\ (W) = voltage\ (V) * current\ (A)}\ (3)\)
- We can rewrite (3) as:
\(W = V * A\ (4)\)
- Next, we’ll substitute W for V x A in (2):
\(Wh = V * A * h\ (5)\)
- We can rewrite (5) as :
\(Wh = V * Ah\ (6)\)
Formula (6) is the formula for converting ampere-hours (Ah) to watt-hours (Wh). But what we want is the formula for mAh to Wh. Thankfully, since there’s a relationship between Ah and mAh, we can substitute for mAh into (6).
- The relationship between Ah and mAh:
\(Ah = \displaystyle{\frac{mAh}{1000}}\ (7)\)
- Now, let’s substitute Ah for mAh/1000 in (6):
\(Wh = \displaystyle{\frac{V * mAh}{1000}}\ (8)\)
We have our mAh to Wh conversion formula in (8).
Going by (8), we can convert mAh to Wh by multiplying milliamp-hours times voltage before dividing by 1000.
If we ever want to convert watt-hours to milliamp-hours, we can do the reverse. We’ll divide the watt-hour by voltage before multiplying by 1000.
Examples of mAh to Wh Conversion
Example 1: How many watt-hours of energy does a 40,000 mAh, 5V battery hold?
The watt-hours of this battery can be calculated in one step – 40,000 milliamp-hours times 5 volts:
\(\displaystyle{\frac{40\, 000 * 5}{1000}} = 80\ Wh\)
Example 2: A solar fountain pump with a 150 mA, 10V battery has a run time of 2 hours. What is the capacity of the radio’s battery in watt-hours?
We can solve this in two ways. In the first method, we’ll calculate the battery capacity in milliamp-hours (mAh). Then we’ll convert milliamp-hours to watt-hours.
\(\small{battery\ capacity\ in\ mAh = 150\ mA * 2\ h = 300\ mAh}\)
\(\small{converting\ mAh\ to\ Wh = 300 * \displaystyle{\frac{10}{1000}} = 3\ Wh}\)
The second method is pretty much the first method, but in a single step:
\(\small{the\ battery\ capacity\ in\ Wh = \displaystyle{\frac{150*10*2}{1000}} = 3\ Wh}\)
Example 3: What is the energy capacity of a power bank rated 20,000 mAh and 5 volts?
This is another single-step example. We can calculate the power bank capacity in Wh by multiplying milliamp-hours times volts and dividing by 1000:
\(\small{the \ power \ bank \ capacity \ in \ Wh = \displaystyle{\frac{20\, 000 * 5}{1000}} = 100\ Wh}\)
How to Convert mAh to Wh Using Our Calculator
To convert mAh to Wh using our calculator, enter voltage and mAh in their respective fields. Then click on the Calculate option of the mAh to Wh calculator & mAh becomes Wh.
Quick Milliamp Hours to Watt-Hours Conversion Chart
The conversions in our milliamp-hours to watt-hours conversion chart can come in handy when converting common mAh values to Wh at common battery voltages.
How to Convert Milliamp-Hours to Kilowatt-Hours (mAh to kWh)
The conversion formula for milliamp-hours (mAh) to kilowatt-hours (kWh) is similar to that of milliamp hours (mAh) to watt-hours (Wh).
However, since kilowatt-hours (kWh) is larger than watt-hours (Wh) by a magnitude of 1000, the divisor of mAh to kWh conversions is one million, not one thousand.
- In other words:
\(kWh = V * \displaystyle{\frac{mAh}{1000000}}\ (9)\)
- Here’s how we derived (9):
\(Wh = kWh * 1000\ (10) \)
- Then, from (8), we know:
\(Wh = V * \displaystyle{\frac{mAh}{1000}}\)
- So, if we substitute Wh for kWh x 1000 in (8):
\(kWh * 1000 = V * \displaystyle{\frac{mAh}{1000}}\)
\(kWh = \displaystyle{\frac{V * mAh}{1000000}}\ (12)\)