Ampere Hour, meaning and formula

What is ampere hour?

As clear from the name “Ampere Hour” is the amount of current that flows for an hour. It is further explained that for a battery to discharge, how much time it will take.

Actually the ampere-hour “Ah” tells us about the capacity of the battery. And how long it will feed a load of a specific current.

To understand and learn more about the term Ampere hour we have to discuss the working principles of a battery.

Working of a battery

We know that battery current is produced by the movement of ionic chemicals. While the movement takes place due to chemical reaction. The number of molecules in a charged battery is limited and once the molecule reacts with each other the number of charges decreases and when it reaches a specific level, we will need to charge the battery again.

The capacity of the Battery is actually the total number of electrons, but the number of these electrons will be more. The current is the movement of electrons. Therefore one ampere of current is the flow of one coulomb of electrons in one second.

One hour has 3600 sec therefore due to the direct proportion/therefore 1 amp-hour = 3600 coulombs. It shows the capacity of a battery.

So, here is a clear definition. A battery of 1 Ah will supply 1-ampere current for one hour to a DC load (like DC motor). If we double the number of loads, i.e double the value of supplied current, then the time value will be half an hour.

Similarly, if we increase the load value to be 3 Amp DC load, then amount of current will be three-time, and then the time will be reduced three times (i.e 20 minutes).

What does it mean by 100 Ah on the battery?

100 Ah on a battery means that this battery can provide 100 amperes to a load for 1 hours continuously. And a load of 50 A for two hours, and so on.

  • While we know that not all the loads need 100 amperes. So, if we have a load of 20 Amperes, the battery will be to supply energy for 5 hours.
  • Similarly, a load of 10 amperes will be entertained for 10 hours and a load of 1 ampere can be (theoretically) work use this battery for 100 hours.

To better get into the concept of these calculation, an engineer must recall the definition of ampere-hour (Ah) before using a battery.

“The amount of current (in amperes) that a battery can provide in 1 hour is called an Ampere-hour”

So, if we have a load of more than 100 amperes current requirement, a battery of 100 amperes-hour will not be able to even turn the load ON or in a worst-case scenario, the battery will melt down. So, we must match the ampere-hour rating to the load required before using the battery as a power supply to the load.

Is battery capacity measured in Kwh or Ah?

Battery capacity is usually measured in Ah not in Kwh, Some types of Li-Io batteries have both Ah and Kwh listed on its body. We can always convert Ah to Kwh. as in the example below of this post.

The Ah is listed on the battery is to make it easier for consumer to know how long will the battery run his device with out using a formulas. All the consumer needs is his device ampere.

A simple example to show the difference is:

Ah is like capacity of a bucket. No matter what, the bucket has always a fixed capacity. You cannot fill it more than that.

But the Kwh is different. It is like you are filling the bucket with a garden pipe, where the current is water flow and voltage is water flow rate per unit time (seconds, etc.). You want to fill the bucket, your water flow and water flow rate both should be a high value.

So, to map our analogy on the battery scenario is like battery needs to charge. The charging is an energy transfer process. In this energy transfer kwh tells the amount of energy being stored in battery per hour while Ah rating of the battery is referring to the total energy that is stored in battery.

What is the difference between kwh and Ah?

Kwh and Ah, both are energy units. These units are used for measurement of power of electrical systems. Both these units are relative to time. To understand the difference let us go through the definition of these units first.

“If 6.24×1018 number of electrons pass through a certain in one second, then the amount power transfer is called 1 Ampere.”

So, when 3600(60×60) times 6.24×1018 number of electrons pass through a certain point in 1 hour time, the power transfer is called “Ampere-hour”.1 ampere-hour battery means that this battery can support a rated load of 1 ampere for 1 hour (60 minutes) without interruption.

Kwh is also an energy unit.

“If 1 joule of energy is used/ supplied by an electric component/ power supply respectively, in 1 sec, the energy that is transferred is called 1 watt.”

So, if a power supply supplies 1 kilo watt energy in the time units of 1 hour, the power transferred in this time is called 1 Kwh.

Ampere-hours is used to determine the battery capacity. The value of ampere-hour tells how much time depending upon the load requirements of amperes the battery can run the load. While the Kwh is the measure of energy used in one hour no matter what is the rating of power supply or the requirement of load is.

So, if we want to calculate energy transfer without being relative to requirement and supply but relative to Volts and Amperes, we must use Kwh. But for choosing a battery for our car or machine, we must go for the Ampere-hour ratings.

Ampere-hours formula and calculations

Ampere hours formula of a battery if the multiply of the current and its discharge time, Ampere Hour (Ah) = Current (I) × Discharge time(T). Where, I is the current in amps and T is the discharge time in hours.

From the above-mentioned formula, we can also calculate how long the battery will provide charge. But as we know that the discharging of the battery is exponential. For this purpose, we will assume everything ideal.

The discharging of the battery is exponential because there exist a lot of factors such as the number of charging /discharging cycles, age, and temperature of the battery. The other reason is that when a battery discharge voltage decreases and resistance increases.

Battery ampere-hours example

If we have a battery of 50 Ah, this means we can use this battery to feed a load of:

  • 50 A for about 1 hour.
  • 25 A for about 2 hours.
  • 12.5 A for about 4 hours.

Equipment ampere-hours calculation step by step example

Say, we have a vacuum cleaner with ratings 200 watts, 150 V (DC). The efficiency of the system is 90%. We want to run the system using a battery for 7 hours.

  • First of all, convert Watts into Watt-hour:

Watt-hour= 200 x 7=1400 Watt-hour

  • Consider the efficiency:

Watt-hour= 1400 / (90%) = 1400 / 0.90 = 1555.55 watt-hours.

This means the cleaner will consume 1555.55 watt each hour of working.

  • From the Ampere-Hours formula:

P = I x V

Where :

P is power in [watt-hours]

I is current in [ampere hours]

V is voltage in [volts]

  • For Ampere- hours we must divide both sides with volts. So,

Ampere-hours= Watt-hours /Volts

  • Putting in values.

I = 1555.55 / 150 = 10.370 Ah

Watt-hours calculation example

Say, we have a computer with ratings 300 watts, 130 V (DC value). The efficiency of the system is 90%. We want to run the system using a battery for 4 hours.

  • First of all, convert Watts into Watts-hour:

Watt-hours= 300×4=1200 Watt-hours

  • Consider the efficiency:

Watt-hour= 1200/ (90%) = 1200/0.90 = 1333.33 watt-hours.

  • From the formula:

P[watt-hours] = I[ampere hours]x V[volts]

  • For Ampere- hours we must divide both sides with volts. So,

Ampere-hours= Watt-hours /Volts

  • Putting in values.

Ampere-hours= 1333.33/130 = 10.256 Ah.

Calculating in terms of watt hours, we can calculate the battery rating as follows.

So, now we have a computer with ratings 10.2567Ah, 130 V (Ac value). The efficiency of the system is 90%. We want to run the system using a battery for 4 hours. What is the power rating in watt-hour for the battery to be used?

  • From the formula:

P[watt-hours] = I[ampere hours]x V[volts]

P=10.2567x 130

P=1333.33 watts-hour

Now let’s move to another ampere-hours calculation, converting it to watts.

How do I convert ampere-hours to watts?

We can easily convert ampere-hours to watts using the formula P [watts] = ((I [Ah] x V [V]) x efficiency) / T (hours). We follow the steps below to convert ampere-hours to watt.

  • Multiply ampere-hours by rated voltage of machine.
  • Then multiply the answer with the efficiency of the system.
  • At the end, divide the answer calculated in last step by the number of hours to convert unit of time to 1 hour.

Here is an example to understand:

If we have an electric equipment of the following data, I [Ah] = 10 Ah, V [volts] = 250V, Efficiency= 0.80, Number of hours – T =3.

  • P [watts] = ((I [Ah] x V [V])x efficiency)/ T.
  • P [watts] = ((10 x 250) x 0.80) / 3
  • P = ((2500) x 0.80 / 3)
  • P = (2000 / 3)
  • P= 666.66 Watts

How many coulombs does one ampere-hour equal?

There are 3600 coulombs in one ampere hour. Because, in one ampere the number of coulombs is 1.

Theoretically,in 1 ampere-minute, number of coulombs are 60. And in 1 ampere-hour number of coulombs are 3600.

How to double a battery ampere hour capacity?

Connecting two batteries in parallel will produce double the AH with the same voltage, this method is used in power-banks and laptop batteries manufacturing, if you have laptop old battery you can carefully open it and you will discover that it is a set of batteries connected to each others.

On the other hand connecting two batteries in series will give the same current with double the voltage.
For example, let’s say we have three 12 V, 7 A batteries, then connecting the in parallel will produce one 12V 21A battery, while connecting them in series will give you one 36V, 7 A battery.

But you should only connect same type, age, voltage and current batteries to connect together in series or parallel. Connecting different batteries together will affect life time and output power of them, this is because the lower current battery in case of charging will be charged faster and then will over charge, and in case of discharging it will discharge faster and this will over load the larger one.

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