Watt hours (Wh) and milliamp hours (mAh) are two common units used to measure electric power and battery capacity respectively. Understanding how to convert between them can be very useful when comparing batteries or calculating power consumption.
Wh measures the total energy used by an electrical device over the period of one hour. For example, a 100 watt light bulb running for 1 hour would consume 100 watt hours of energy. The watt hour is a unit of energy, equal to the power used multiplied by the time period.
Meanwhile, mAh measures the charge capacity of a battery. It refers to how much electric charge a battery can deliver (in milliamps) for one hour until it is fully discharged. A higher mAh rating indicates a battery with greater capacity and longer runtime. For a 10,000 mAh battery, it could theoretically supply 10,000 milliamps (or 10 amps) over 1 hour.
Being able to convert between these units allows us to better understand batteries and their compatibility with devices that have certain power requirements. The conversion also helps compare battery capacities. Understanding the relationship between watt hours and milliamp hours is key.
Why Convert Between Wh and mAh?
Being able to convert between watt hours (Wh) and milliamp hours (mAh) is very useful when comparing batteries and ensuring compatibility between devices and batteries.
Wh measures the total energy capacity of a battery or device over the course of 1 hour. It tells you how much total power it can deliver in an hour. mAh measures the charge capacity of a battery – how much charge it can hold and deliver over its lifespan.
While Wh tells you about total energy, mAh tells you about available charge. Converting between the two units allows you to compare batteries of different voltages to see which has more capacity and better compatibility with your device’s power needs.
For example, you may have a 12V battery with a capacity of 500Wh and want to know if it has more capacity than a 24V battery with 1300mAh. By converting mAh to Wh, you can determine that the 24V battery has higher capacity in Wh and would be the better choice. Without converting, it’s difficult to directly compare mAh and Wh.
Converting also ensures compatibility – if your device needs a minimum of 300Wh, being able to convert mAh to Wh helps you select a battery that meets or exceeds that requirement. The ability to convert between these units provides valuable insight when battery shopping and making sure your batteries match your usage needs.
The Conversion Formula
The key to converting between watt hours (Wh) and milliamp hours (mAh) is a simple formula:
mAh = Wh x V x 1000
Where V is the voltage of the battery in volts (V).
To break this down:
- mAh is the battery capacity in milliamp hours
- Wh is the energy in watt hours
- V is the battery voltage
- 1000 is needed to convert the units correctly
By plugging in the Wh and V values, you can calculate the equivalent mAh battery capacity.
For example, if a device uses 5 Wh of energy, and has a 3.7V battery, the formula would be:
mAh = 5 Wh x 3.7V x 1000
mAh = 18,500 mAh
So a 5Wh usage translates to an 18,500 mAh battery capacity for a 3.7V battery. This formula allows you to convert in both directions between Wh and mAh.
Common Conversions
Wh and mAh are related through a simple formula, but it can be useful to have some common conversions handy. Here are tables showing typical conversions between Wh and mAh for common battery voltages:
AAA and AA Batteries (1.5V)
| Wh | mAh |
|---|---|
| 2 | 1,333 |
| 4 | 2,667 |
| 8 | 5,333 |
| 10 | 6,667 |
9V Batteries
| Wh | mAh |
|---|---|
| 5 | 555 |
| 10 | 1,111 |
| 15 | 1,667 |
| 20 | 2,222 |
12V Lead-Acid Batteries
| Wh | mAh |
|---|---|
| 35 | 2,917 |
| 50 | 4,167 |
| 100 | 8,333 |
| 200 | 16,667 |
Having a reference for these common battery voltages can make quick work of many real-world Wh to mAh conversions.
Converting kWh to mAh
You can also convert between larger kilowatt hour (kWh) units and milliamp hours (mAh). The formula is similar:
mAh = kWh x 1,000 x V
Where kWh is the energy usage in kilowatt hours and V is the voltage of the battery in volts.
For example, if a device uses 5 kWh of energy and has a 12V battery, the mAh capacity needed would be:
mAh = 5 kWh x 1,000 x 12V
mAh = 60,000 mAh
So the device would need a 60,000 mAh 12V battery to operate for 5 kWh. This shows how the conversion formula scales up for larger units.
The following table shows common kWh to mAh conversions:
| Voltage (V) | kWh | mAh |
|---|---|---|
| 12V | 1 kWh | 12,000 mAh |
| 24V | 1 kWh | 24,000 mAh |
| 36V | 1 kWh | 36,000 mAh |
kWh to mAh Table
| kWh | mAh at 3.7V | mAh at 7.2V | mAh at 11.1V |
|---|---|---|---|
| 0.1 | 27,027 | 13,514 | 8,649 |
| 0.5 | 135,135 | 67,568 | 43,244 |
| 1 | 270,270 | 135,135 | 86,489 |
| 2 | 540,540 | 270,270 | 172,978 |
| 5 | 1,351,351 | 675,676 | 432,244 |
| 10 | 2,702,702 | 1,351,351 | 864,889 |
When dealing with large battery capacities, it can be useful to convert kilowatt hours (kWh) to milliamp hours (mAh). This table provides some common kWh to mAh conversions for different battery voltages.
To use the table, first determine the voltage of your battery pack. Then find the kWh value you want to convert in the left column. Look across that row to find the equivalent mAh capacity for the voltage of your pack.
For example, if you have a 10 kWh battery pack at 11.1V, lookup 10 kWh in the left column. Then go across that row to the 11.1V column, which shows a mAh capacity of 864,889 mAh.
Using a table like this makes it easy to quickly convert between kWh and large mAh values when evaluating and comparing battery capacities.
Calculating Wh for Batteries
To help understand how to calculate watt hours (Wh) for different battery capacities, let’s walk through some examples:
For a 10,000 mAh battery:
- Let’s assume it’s a 3.7V battery (typical for many lithium-ion batteries)
- The formula is: Wh = mAh x V
- So for 10,000 mAh at 3.7V:
- Wh = 10,000 x 3.7
- Wh = 37,000
Therefore, a 10,000 mAh 3.7V battery has a capacity of 37 Wh.
For a 5,000 mAh battery:
- Again we’ll assume 3.7V
- Plugging this into the formula:
- Wh = 5,000 x 3.7
- Wh = 18,500
So a 5,000 mAh 3.7V battery stores 18,500 Wh of energy.
This shows how you can calculate the total energy capacity in watt hours for any size battery once you know the mAh rating and voltage. Converting between these units helps compare batteries and make sure you select one with adequate capacity for your needs.
FAQs
What is the formula to convert watt hours to milliamp hours?
The formula to convert watt hours (Wh) to milliamp hours (mAh) is:
mAh = Wh x V x 1000
Where V is the battery voltage.
How do I calculate the watt hours for a 10,000 mAh battery?
To calculate the watt hours for a 10,000 mAh battery, you need to know the battery voltage. For a typical 3.7V lithium-ion battery, the calculation would be:
Wh = (10,000 mAh) / (3.7V x 1000)
= 10,000 / 3,700
= 2.7 Wh
So a 10,000 mAh 3.7V battery would have 2.7 Wh of capacity.
What are the watt hours for a 5,000 mAh battery at 5V?
For a 5,000 mAh battery at 5V, the calculation is:
Wh = (5,000 mAh) / (5V x 1000)
= 5,000 / 5,000
= 1 Wh
So a 5,000 mAh 5V battery would have 1 Wh of capacity.
How do I convert kilowatt hours to milliamp hours?
To convert kilowatt hours (kWh) to milliamp hours (mAh), you use essentially the same formula:
mAh = kWh x 1,000,000 / V
Where V is still the battery voltage. For example, for a 3.7V battery:
1 kWh = 1,000,000 mAh / 3.7V = 270,270 mAh
So 1 kWh equals 270,270 mAh for a 3.7V battery.
Conclusion
Converting between watt hours (Wh) and milliampere hours (mAh) is a very useful skill when dealing with batteries and power consumption. To summarize the key takeaways:
- Wh measures the total energy used by a device over 1 hour. mAh measures the charge capacity of a battery.
- The formula to convert between them is: mAh = Wh x V x 1000, where V is the battery voltage.
- There are standard conversion tables for common battery voltages like 5V, 12V, 24V.
- The same concept applies when converting kWh to mAh, using a similar formula.
- With these conversions, you can calculate the Wh for any mAh battery, or vice versa. This helps compare battery capacities and ensure compatibility between devices.
- When shopping for a battery, you can use these conversions to make sure it will meet your device’s power needs.
- For designers, these conversions assist in properly sizing a battery pack to match expected energy consumption.
In summary, converting between watt hours and milliamp hours bridges the gap between power usage and battery capacity, enabling more informed comparisons and choices when dealing with electrical power and batteries. The simple formulas and conversion tables make these translations easy.