There are plenty of impressive stats in Apple’s December quarter earnings report, such as 37 million iPhones shipped, $46 billion of overall sales, and $13 billion of profit.

But Apple’s most impressive stat continues to be its growth rate: Apple is not only huge, but it is growing at a rate far greater than its peers. And, even more incredible, its growth rate is accelerating.

As a company gets bigger, or as a market matures, its growth rate typically falls. It’s only natural: The numbers get bigger, so the percentage of change eventually shrinks. But for Apple, during the Christmas quarter — its busiest time of the year — that hasn’t happened yet.

Specifically, last quarter, Apple’s overall sales totaled $46.3 billion, an increase of 73% over the previous December quarter. That’s an acceleration over Apple’s growth rate from the December 2010 quarter, when it posted 71% growth. And that was better than the year before, when it grew 32%. That, too, was faster than the year before, when Apple posted a 6% growth rate in the bowels of the recession. So for the third year in a row, Apple has accelerated its Christmas quarter sales growth.

Why is this so impressive? Because maintaining your growth rate when you’re Apple’s size — never mind increasing it — takes a lot of work!

This past Christmas, Apple needed to add an extra $20 billion in new sales to grow by 73%. The year before, it “only” needed to generate an additional $11 billion in new business to grow by 71%. It’s pretty astounding, especially considering that Apple’s product lineup didn’t even change that much last year.

The reason it happened, of course, was the iPhone 4S “perfect storm.” Not only was it a new iPhone, but it launched during what is already Apple’s busiest time of the year, the holiday quarter. And it expanded Apple’s footprint to new carriers, such as Sprint. Add pent-up demand to the mix, and Apple was easily able to shatter its iPhone sales record. Then consider that the iPhone is Apple’s biggest business by revenue and profits, and the big numbers fall into place.

Can it happen again? It’s only going to get harder. To match this year’s growth — 73% — Apple’s December 2012 quarter would have to beat $80 billion in sales. That’s a lot of iPhones. The way the smartphone market is growing, and the way the iPad looks like it’s going to do, anything’s possible. But it’s not going to be easy.

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