# Does a full battery weigh more than an empty battery?

It sounds logical: a full battery is heavier than an empty battery. Just think of a car: a car with a full tank is heavier than one with an empty tank. But is it true that a full battery is heavier than an empty battery and can we observe the difference? So we started calculating.

## How does a battery work?

A battery provides energy by allowing electrons to run from the negative terminal back to the positive terminal of the battery via a wire from the device in question. The electrons are not consumed and do not disappear: they only move and end up back in the battery. So that would mean that the mass of the battery doesn’t change and the battery doesn’t get lighter.

## E=mc2

To make it a little more difficult, we go back to Albert Einstein’s theory of relativity. In the original publication of the world-famous formula, Einstein describes E=mc ^ 2. The E stands for energy, the m for mass, and the c for the speed of light squared ( ^ 2). The speed of light is often rounded to 300,000,000 meters per second, so 300,000 kilometers per second or 1.08 billion kilometers per hour.

Also read: How far can I get with a full bicycle battery?

In addition to the theory, Einstein writes that an object gives off an amount of energy in the form of radiation. If there is no change in speed, the object becomes lighter. In principle, this applies to all forms of energy, according to Einstein.

The Einstein Society explains it a little more clearly: ‘ An object can lose its energy through heat conduction, through expansion (a gas), through an electric field or what not so that loss of any form of energy for an object means loss of mass.

## Just calculate

A battery loses its energy through an electric field and, with the above theorem, also mass. To calculate the difference between a full and an empty battery, we need to know the mass (m) of the energy in a full battery.

For an AA Alkaline (long life) battery, the stored energy is 9360 Joules.
Fill this value into the formula E=mc ^ 2 and you get 9360=mc ^ 2.
The formula for c ^ 2, the speed of light is (3*10^8)^2.
We plug this back into the formula: 9360 = m*((3*10^8)^2)
That is mass = Energy divided by c ^ 2.
If we plug that into the Omni calculator for the formula for convenience, then the answer is 0,000,000,000,104144 grams. In other words, 104.144 picograms. So the battery has become lighter. Eureka!

Also read: My bicycle battery has fallen. Can I still use it?

## What is the difference?

104.144 picograms, how much does that weigh? The number and weight is already difficult to comprehend because even with the best scales in the world it is impossible to measure. Perhaps the following comparison will help:
An AA alkaline battery weighs on average 15 grams. And for convenience let’s round the mass of the energy to 0.000,000,000.1 grams or 100 picograms.
To get 1 gram of the mass of the energy we need 10 billion (10,000,000,000) batteries.
And in this equation, 150 billion full batteries weigh the same as 150 billion + 1 empty battery.

In other words: 150,000,000,000 full batteries = 150,000,000,001 empty batteries .

## So how do you check whether your battery is full or empty?

No one has 15 trillion batteries to measure the difference. So to know if there is still energy in your battery, it is best to use a voltage meter. Handy, but maybe you don’t have them at home. Then you can of course also test your batteries by putting them in an electrical device, such as a flashlight. If the flashlight lights up, you know that the batteries are not empty yet.

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