# Decibels made ultra-simple: Part 1

## What is a decibel?

If you know one end of a logarithm from the other, this page is NOT for you so please leave now!

But, if you've ever wondered what decibels actually are, but mathematical equations don't mean much to you, this page *is* for you.

You will need a scientific calculator to do the examples, but don't worry if you haven't got one, we will provide one at the right time.

The first thing to realise is that the decibel is not like other units such as the foot, kilogram or second. If you know now many feet something measures, then you know its length, full stop. You could convert that length into any other measure, such as metres. But the decibel is, fundamentally, a way of comparing two amounts. Rather like a percentage, it doesn't tell you the absolute quantity unless you know what you're comparing it with.

## How much energy have you got?

Decibels can be used to compare various different things, such as sound, or electricity. But fundamentally, what is being compared is always related to some form of power or energy.

What is power? Well, you know what it means when you say that one car, or one electric heater, is more powerful than another. That's the meaning we need - it tells you how hard something is working. A machine that can do the work in half the time is twice as powerful (in simple theory anyway).

Unfortunately there is a completely separate meaning of power that we will also use. That's when we say that numbers such as 100 (10 times 10) and 1000 (10 times 10 times 10) are *powers* of 10.

Energy (used as a technical word, not the everyday meaning) is simply power added up over a period of time. Energy, not power, is what you pay for in your electricity bill. It depends both on the power (of your heater, for example) and the length of time that it was switched on.

## Why bother?

So why use decibels? If we had two heaters, the first of one kilowatt and the second of 10 kilowatts, we would simply say that one was 10 times the power of the other. Why complicate it?

There are several reasons. One is that we often use decibels when the range of comparison is huge. With sound, we have to deal with a range of power with ratios of billions to one. Using decibels allows us to deal with these big numbers in a handy way. The other main reason is that using decibels makes certain calculations, that would otherwise be quite fiddly, extremely easy. And with sound, using decibels is the norm, because it relates well to the way we hear things.