On radio Shows how do they measure the amount of listeners?

Is the airwaves measured some how?

So how do the measure 8 million listeners and how come they know how many they have at certain parts of the show,

If it's the BBC, they probably make it up . . .

I think they measure how often and how much power they have to boost the signal through the transmitters and calculate it that way somehow, but I'm not sure.

its the same way for radio and tv
BARB, the Broadcasters' Audience Research Board, is the organisation that compiles television ratings in the United Kingdom. It was created to replace a previous system, where the BBC and ITV companies compiled their own ratings. It is owned by the BBC, the ITV companies, Channel 4, Five, BSkyB and the Institute of Practitioners in Advertising. Participating families have a box on top of their TV which tracks the programmes they watch. Currently, BARB have approximately 5,100 homes (equating to approximately 11,500 individuals) participating in the survey. The box records exactly what programmes they watch, which is then reported back to the TV stations and the advertisers. BARB numbers are extremely important to commercial television stations. The trading model that is used by television companies and advertising agencies depends on the number of people watching the shows. The advertising agency will pay the television station a certain amount of money based on the number of people watching a show. The BARB numbers are used to work this out. The higher the BARB numbers, the more money a television station will make. This leads to some interesting situations on the smaller channels. Since there are many television stations, and many hours in the day, there can be situations where BARB will record zero viewers for certain programmes.

here
http://www.rajar.co.uk/

Edit: good old fashioned paperwork !
http://www.rajar.co.uk/docs/about/RAJAR_...

its not as technical as people would believe.
but with web streaming a station can get a report of how many people are listening on the net. it is only beneficial to the station. but for selling ads they use rajar to get their rates for selling.

Arbitron, a ratings company, hands out a "diary" to random people of all nationalities and ages. kinda like when a organization measures circulation of a newspaper. Then, those people write down all sorts of info, like how long they were listening, to what station, could they recognize what station they were even listening to... stuff like that. it gets sent back and compiled... and stations get points for how many times they are mentioned in the diaries...

Well you've got differing systems and companies based on whether you are in the US or the UK - and whether it's TV or radio. There are some good answers posted.

I'll just add that in the US, Arbitron is gradually switching to the PPM (Portable People meter) for radio. This will be a big step forward in measurement for radio, as the device "listens" to anything you do and is carried like a pager then "docked" at night in a charging cradle that doubles as an online delivery device for that day's listening.

Pretty cool and way more accurate than the diary method.
-a guy named duh