twitter-music-itunes-radioTonight, Apple CEO Tim Cook revealed some new stats on the company’s iTunes Radio music service during its iPad launch event.

““We now have had over 20m users listening to iTunes Radio, and this number continues to grow,” he says. “They’ve listened to over a billion songs, and this is just in the US in the last month. It’s absolutely fantastic.”

But is it? Time for some maths. 20m people listening to 1bn songs means – if you take four minutes as the average song length – 4bn minutes of listening time. Which is around 66.7m listening hours in iTunes Radio’s first month after launch, and so around 3.4 hours per user.

Compare that to Pandora, which announced recently that in September it had 72.7m active listeners who notched up 1.36bn listener hours. Which is around 18.7 hours per user – five and a half times the figure for iTunes Radio.

Bear in mind we’re talking about two services at very different stages of their development: Pandora is well established, while iTunes Radio is brand new – and so an unknown chunk of those 20m first listeners were sampling.

What’s more, they weren’t all using it for the entire month: Apple said on 23 September that 11m people had tried iTunes Radio in its first five days of availability, so the other 9m will have started using the service since then. We’ve also been hearing anecdotally that iTunes Radio IS performing above labels’ and Apple’s expectations in terms of the amount of iTunes song purchases it’s generating, although we don’t have any numbers on that yet.

That said, if those first 11m iTunes Radio users had shown similar engagement to Pandora’s active users, they’d have racked up 205.7m listener hours over the month, or just under 3.1bn song listens. So, it seems iTunes Radio has some way to go before it matches Pandora for engagement, even if it already has 27.5% of its active users.

Update: As a fun extra data point, UK radio body Rajar says the average UK radio listener – as in traditional radio – tunes in for 21.3 hours a week.