How do you convert amp hours to watt hours?

When expressed in ampere-hours, the voltage of the battery is taken into account. When expressed in watt-hours, the result is obtained by multiplying the ampere-hours with volts. A 100 Ah and 12 V battery therefore stores 1200 Wh. Conversely, if you divide the watt-hours by the voltage, you obtain the ampere-hours.

How long does a battery last?

You divide the available energy by the power consumption of the device. You multiply the capacity in ampere hours with the voltage to get watt hours, and then again with the actual usage percentage (for lead acid batteries usually 0.5, for lithium batteries at least 0.8), before you divide the result by the power consumption in watts. The result is the operating time in hours.

The C-rate is a current that is expressed as a multiple of the capacity and used to either charge or discharge. A 1C rate means the current is equal to the capacity, so the battery will last for one hour. At a 2C rate it lasts half an hour while at a 0.5C rate it lasts two hours. The discharge current is the result of multiplying the capacity (in ampere-hours) by the C-rate.

Can a power bank that says "20000mAh" actually store 20000mAh?

A cell can store 20,000mAh (equivalent to 20 Ah). The cell voltage is usually about 3.7V, which equates to approximately 74Wh of power. A mobile phone charges at around 5V and due to energy losses during the charging process, the actual amount of energy delivered will be significantly less than 20,000mAh (calculated at 5V). Therefore a 20,000mAh portable battery cannot fully charge a 4,000mAh mobile phone five times.

Why doesn't the battery reach its nominal capacity?

The nominal capacity is measured under mild and standardized conditions. In reality the battery usually does not reach the number stated on the label because high discharge currents, internal resistance, low temperatures and ageing mean that less energy can be drawn from it.

Battery Capacity Calculator

Battery capacity calculator

What do you want to work out?

Battery capacity (Wh & Ah)

Runtime / backup time

Charge time

C-rate & discharge current

Capacity (charge)

Voltage

Energy (capacity)

Please input values into the fields

The battery capacity calculator tool links the numbers printed on a battery to the values you actually want to know. It converts between amp-hour and watt-hour ratings, calculates how long a load can run from a battery, how long it will take to charge, and what current will flow at a given C-rate.

By selecting a mode at the top, the items shown change accordingly. The capacity mode works both ways: if you leave blank the value that you want to calculate, the tool will compute it from the other values.

Ampere hours, watt hours, voltage

The function of a battery is to store energy and this is measured in watt hours. However the capacity is usually quoted in ampere hours which represents charge not energy. Both quantities are related by the voltage of the battery.

E = Q \times V

In this formula E is the energy in watt-hours, Q is the capacity in ampere-hours and V is the voltage. When you multiply the voltage by the ampere-hours, you get the watt-hours. This relationship is at the core of this tool. Since there are three elements involved, if two of them are known, then you can calculate the missing value.

Let's take a battery with a nominal capacity of 12 Volts and 100 Ampere-hours. Its energy is 100 times 12, i.e. 1200 Watt-hours, which corresponds to 1.2 Kilowatt-hours. Conversely, if a drone uses a battery with a storage capacity of 97.7 Watt-hours and an operating voltage of 22.2 Volts, the capacity is approximately 97.7 divided by 22.2, i.e. about 4.4 Ampere-hours.

Battery	Voltage	Capacity	Energy
AA NiMH cell	1.2 V	2 Ah	2.4 Wh
Phone battery	3.7 V	4 Ah	14.8 Wh
Car battery	12 V	50 Ah	600 Wh
Solar / leisure bank	12 V	100 Ah	1200 Wh

Watch out for the milli-prefix. The capacity of a phone battery display that shows "4000 mAh" is equivalent to 4 Ah. The energy stored by a mobile battery marked with "5 V" and "20000 mAh" is approximately equal to 20 Ah multiplied by 5 V, which is 100 Wh, not 20.

How long does the battery last?

The battery runtime is the quotient of the available energy in the battery and the power consumed by the connected device. Not the entire rated capacity can be used. It is rare that a battery will be fully discharged, and when operating an AC device with an inverter additional energy losses occur.

\text{Runtime (h)} = \frac{Q \times V \times \text{usable \%} \times \text{efficiency}}{\text{load (W)}}

A battery operating at 12 Volts and 100 Ampere-hours stores 1200 Watt-hours. If only 80% of that is used to supply a load of 50 Watts, the runtime will be approximately 1200 multiplied by 0.8, divided by 50, or about 19 hours. As real batteries generally deliver less power than their nominal values at high currents, low temperatures and due to ageing, these results are not guaranteed but should be considered as optimistic estimates.

How long does it take to charge?

The charge time is the capacity divided by the charging current, with additional losses due to the efficiency of the charger. Charging a 100 amp hour battery with a 10 amp charger will take at least about 10 hours. At an efficiency of 90% the charge time would be approximately 11 hours. As the charger reduces the current gradually as the battery nears full, it takes longer than if estimated using constant current.

\text{Charge time (h)} = \frac{Q}{I_\text{charge} \times \text{efficiency}}

C-rate and discharge current

The C-rate indicates the rate of charge or discharge relative to the capacity of the battery. At a value of 1C, the current is equal to the capacity and the battery will be discharged in one hour. At a value of 2C, the current is twice as high and the discharge takes half an hour. At a value of 0.5C, the current is half as high and the discharge takes two hours.

I = \text{C-rate} \times Q \qquad \text{Runtime to full (h)} = \frac{1}{\text{C-rate}}

So a 100 amp hour battery will deliver 1C at 100 amps and 50 amps for two hours at 0.5C. The data sheet of any given battery gives the maximum continuous C rate. If this is exceeded, then the pack heats up and its life is reduced. The time it takes to fully discharge depends only on the C rate and not on the size of the battery.

Measuring Actual Capacity

The values stated on the label are nominal values. To determine the actual capacity of a battery, it must first be fully charged, then discharged with a steady, moderate current and the discharge time recorded. The capacity is the product of this current and the time. Energy is the product of this capacity and average voltage. High discharge currents, high internal resistance, low temperatures, and aging can all reduce actual capacity.

Frequently asked questions

How do you convert amp hours to watt hours?: When expressed in ampere-hours, the voltage of the battery is taken into account. When expressed in watt-hours, the result is obtained by multiplying the ampere-hours with volts. A 100 Ah and 12 V battery therefore stores 1200 Wh. Conversely, if you divide the watt-hours by the voltage, you obtain the ampere-hours.
How long does a battery last?: You divide the available energy by the power consumption of the device. You multiply the capacity in ampere hours with the voltage to get watt hours, and then again with the actual usage percentage (for lead acid batteries usually 0.5, for lithium batteries at least 0.8), before you divide the result by the power consumption in watts. The result is the operating time in hours.
What is the C-value?: The C-rate is a current that is expressed as a multiple of the capacity and used to either charge or discharge. A 1C rate means the current is equal to the capacity, so the battery will last for one hour. At a 2C rate it lasts half an hour while at a 0.5C rate it lasts two hours. The discharge current is the result of multiplying the capacity (in ampere-hours) by the C-rate.
Can a power bank that says "20000mAh" actually store 20000mAh?: A cell can store 20,000mAh (equivalent to 20 Ah). The cell voltage is usually about 3.7V, which equates to approximately 74Wh of power. A mobile phone charges at around 5V and due to energy losses during the charging process, the actual amount of energy delivered will be significantly less than 20,000mAh (calculated at 5V). Therefore a 20,000mAh portable battery cannot fully charge a 4,000mAh mobile phone five times.
Why doesn't the battery reach its nominal capacity?: The nominal capacity is measured under mild and standardized conditions. In reality the battery usually does not reach the number stated on the label because high discharge currents, internal resistance, low temperatures and ageing mean that less energy can be drawn from it.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Ampere hour — Wikipedia
The amp-hour as a unit of electric charge and its relation to coulombs.
Watt-hour and electrical energy — Wikipedia
Watt-hours and kilowatt-hours as units of energy.
C-rate (battery) — Wikipedia
Definition of C-rate and its link to charge and discharge current.
Electric battery — Wikipedia
Battery capacity, energy, voltage, and the factors that affect real capacity.