# Battery size calculator

The battery size calculator calculates the battery size in ampere-hour (Ah).

## Parameters

• Load type (ampere or watt): Select the unit in which the load will be specified, ampere or watt.
• Load (watt): If the load type is watt, specify the load in watt, for example 100 W. Use and average value if its a cyclical load.
• Load (ampere): If the load type is ampere, specify the current in ampere, for example 10 A.
• Voltage (Vdc): Specify the battery voltage in volts DC, if the load type is watt.
• Required duration (hours): Specify the duration that the load must be supplied for.
• Battery type: Select the battery type. Lead-acid or lithium-ion.
• Remaining charge (%): Specify the required remaining charged. To prolong the life of a battery, a lead-acid battery should not frequently be discharged below 50 %, and Lithium-ion battery not below 20%. Note that 0% is a flat battery and 100% if a full battery.

## How to calculate battery current?

If the load is specified in watt, the current I is calculated as:

$$I=\dfrac{P}{V_{dc}}$$

Where:

• P is the power in watts.
• Vdc is the voltage in volts DC.
• ## How to calculate the size of a battery?

The required battery size B is calculated as:

$$B =\dfrac {100 \cdot I \cdot t}{100 - Q}$$

Where:

• I is current in ampere.
• t is the duration in hours.
• Q is the required remaining charge in percentage (%).

## Battery discharge rate

The calculated C-rate rate for the battery to discharge to 0%.

It is measured in % charge per hour

A discharge rate of 1C, meanse that the battery will fully discharge in 1 hour.

A discharge rate of 0.5C, meanse that the battery will fully discharge in 2 hours.

It is calculated as:

$$C_{rate} =\dfrac {100 - Q}{100 \cdot t}$$

Where:

• t is the duration in hours.
• Q is the required remaining charge in percentage (%).

For example, if you specified a "Duration" of 20h with a "Remaining charge" of 50%. Then the theoretical discharge rate is 0.025C (40h).

The calculated discharge rate must be lower than the the battery discharge rate specification

## Battery discharge rate specification

A battery's maximum discharge rate is specified my the manufacturer as the C-Rate.

The C-rate measured as % charge per hour. And indicated with a letter C.

For example, a C-Rate of 1C means the battery should not be discharged in less than 1 hour.

In other words, 10 Ah battery with a discharge rating of 1C can deliver 10 A for 1 hour.

Note that a 10 Ah battery with a discharge rate of 1C (1h), cannot deliver 20 A in 0.5h.

Because, when a 1C rated battery is discharged faster than 1 hour, the losses becomes high, and the Ampere-hour ratio is not maintained.

Lead Acid batteries are typically rated at 0.05C (20h). Which means they should be discharged over 20 hours or longer.

The table below shows typical battery discharge rate specifications.

C-rate Discharge time
5C 12 min
2C 30 min
1C 1h
0.5C or C/2 2h
0.2C or C/5 5h
0.1C or C/10 10h
0.05C or C/20 20h