# Convert Watt-Hours to Amp-Hours and Amp-Hours to Watt-Hours

Watt-hours (Wh) and Amp-hours (Ah) are two very common units in electrical engineering - simplified, Watt-hours is the unit of energy, while Amp-hours is the unit of battery capacity.

Direct conversion from Watt-hours to Amp-hours and from Amp-hours to Watt-hours is not possible without introducing the third unit - nominal and/or actual voltage of the electricity source, mostly battery.

Published: December 13, 2021. ## How to Convert Watt-Hours to Amp-Hours and Amp-Hours to Watt-Hours

Before diving into math and physics, it is important to know which unit is used for what:

- 'I': current strength, given in Amps (A),

- 'P': power, given in Watts (W),

- 'U': potential difference, given in Volts (V),

- 'E': energy, given in Joules (J) and sometimes in Wh (Watt-Hours) - 1 Wh equals 3600 J,

- 'C': battery capacity, given in Amp-Hours (Ah),

- 'T': time, measured in seconds (s) and sometimes in hours (h).

Also, battery capacity is often defined as the ability of the battery to provide a certain current for a certain period of time - for lead-acid batteries, the standard discharge time is 20h, but for other batteries, various discharging conditions may be used.

In order to convert Watt-hours to Amp-hours and Amp-hours to Watt-hours one must use the following formulas:

E(Wh) = I(A) * T(h) * U(V)

E(Wh) = C(Ah) * U(V)

C(Ah) = E(Wh) / U(V)

## Watt-Hours to Amp-Hours and Amp-Hours to Watt-Hours Conversion Examples

Here are several Watt-Hours to Amp-Hours and Amp-Hours to Watt-Hours conversion examples:

Example 1: The battery features capacity of 100Ah and a constant output voltage of 24V.  How many Watt-hours of energy is the battery able to provide?

In order to calculate this, we use the following formula:

E(Wh) = C(Ah) * U(V) = 100Ah * 24V = 2400 Wh

Example 2: If the sump pump backup battery must provide 1800Wh without recharging, what is its minimum required capacity if the nominal battery voltage is 12 volts?

In order to calculate battery's required capacity, we use the following formula:

C(Ah) = E(Wh) / U(V) = 1800Wh / 12V = 150 Ah

Example 3: If the power bank features an internal 3.7V 20000 mAh battery, how many Watt-hours is it able to provide at 5V?

This is a trick question - in order to calculate watt-hours of the battery, we use the following formula:

E(Wh) = C(Ah) * U/V) = 20Ah * 3.7V = 74Wh

The output voltage of 5V in this example is of absolutely no importance.

In real-life we use the same formulas to calculate Watt-Hours to Amp-Hours and Amp-Hours to Watt-Hours, but in order to get as accurate results as possible, one should use constant current and constant power discharge charts of the batteries being used - more on that later.

## Watt-Hours to Amp-Hours and Amp-Hours to Watt-Hours Conversion Calculators In order to convert Watt-Hours to Amp-Hours and Amp-Hours to Watt-Hours, feel free to use these conversion calculators - write the values that You have and click 'Calculate' to convert them.

 Watt-Hours to Amp-Hours Amp-Hours to Watt-Hours Watt-Hours: Volts: Amp-Hours: Amp-Hours: Volts: Watt-Hours:

## Watt-Hours to Amp-Hours Chart

The following Watt-Hours to Amp-Hours chart lists the required capacity (given in Amp-hours) of specific energy sources, depending on their nominal voltage:

 Energy (Wh) Required Capacity (Ah) @ Nominal Voltage 12 Volts 24 Volts 36 Volts 120 Volts 230 Volts 250 Wh 20.83 Ah 10.41 Ah 6.94 Ah 2.083 Ah 1.087 Ah 500 Wh 41.67 Ah 20.83 Ah 13.89 Ah 4.167 Ah 2.174 Ah 746 Wh 62.16 Ah 31.08 Ah 20.72 Ah 6.216 Ah 3.243 Ah 1000 Wh 83.33 Ah 41.66 Ah 27.78 Ah 8.333 Ah 4.238 Ah 1492 Wh 124.3 Ah 62.16 Ah 41.44 Ah 12.43 Ah 6.487 Ah 2000 Wh 166.6 Ah 83.3 Ah 55.5 Ah 16.66 Ah 8.695 Ah 2238 Wh 186.5 Ah 93.25 Ah 62.16 Ah 18.65 Ah 9.730 Ah 2984 Wh 248.6 Ah 124.3 Ah 82.88 Ah 24.86 Ah 12.97 Ah 3730 Wh 310.8 Ah 155.4 Ah 103.6 Ah 31.08 Ah 16.21 Ah 5000 Wh (5 kWh) 416.6 Ah 208.3 Ah 138.8 Ah 41.6 Ah 21.74 Ah 10 kWh 833.3 Ah 416.6 Ah 277.8 Ah 83.3 Ah 43.48 Ah

For example: If Your 36V system needs at least 2000Wh of energy, what is the minimum required capacity of the battery pack?

C(Ah) = E(Wh) / U(V) = 2000Wh / 36V = 55.5 Ah

Note that some electric cars feature batteries being able to store 80-100 or even more kWh (80000-100000 Wh) of energy. ## Amp-Hours to Watt-Hours Chart

The following Amp-Hours to Watt-Hours chart lists the energy values (given in Watt-hours), depending on the specific capacity (given in Ah) and nominal voltage (given in V):

 Capacity (Amp-Hours) Energy (Wh) @ Nominal Voltage 12 Volts 24 Volts 36 Volts 120 Volts 230 Volts 1 Ah 12 Wh 24 Wh 36 Wh 120 Wh 230 Wh 2 Ah 24 Wh 48 Wh 72 Wh 240 Wh 460 Wh 5 Ah 60 Wh 120 Wh 180 Wh 600 Wh 1150 Wh 10 Ah 120 Wh 240 Wh 360 Wh 1200 Wh 2300 Wh 25 Ah 300 Wh 600 Wh 900 Wh 3000 Wh 5750 Wh 50 Ah 600 Wh 1200 Wh 1800 Wh 6000 Wh 11500 Wh 100 Ah 1.2 kWh 2.4 kWh 3.6 kWh 12 kWh 23 kWh 200 Ah 2.4 kWh 4.8 kWh 7.2 kWh 24 kWh 46 kWh 500 Ah 6 kWh 12 kWh 18 kWh 60 kWh 115 kWh 1000 Ah 12 kWh 24 kWh 36 kWh 120 kWh 230 kWh

For example: If You have 10 (ten) 12V 100Ah batteries connected in series, how much energy that battery-pack would be able to store?

E(Wh) = C(Ah) * U(V) = 100Ah * 10 * 12V = 12000 Wh = 12 kWh

Long Story Short: When calculating watt-hours (energy), one must know Amps (current), hours (time), and Volts (voltage), or capacity (Ah) and Volts (voltage) - when converting Wh (again, the energy given in watt-hours) to Ah (again, capacity given in Amp-hours) and back, one must know the nominal voltage of the system.

If the power source of the electric system is a lead-acid battery, and the discharge time is relatively short, the effective capacity of the battery decreases, requiring the users to check the constant current and constant power discharge tables of the batteries in question.