At Microsoft Corp.’s (NASDAQ: MSFT) 2015 Build developer conference on Wednesday, the head of the company’s operating systems group predicted that the company’s Windows 10 operating system (OS) will be installed on 1 billion devices within two to three years. The company did not say exactly when Windows 10 would ship to customers, but late this summer is the working target.

One billion is a big number, but exactly how big, and in what universe?

As of March, about 91% of all desktop PCs are running some version of the Windows OS. At the same time, only about 2.5% of mobile devices are using some version of Windows Phone.

The number of personal computers (PCs) in use around the world likely tops 2 billion. In 2008, Gartner reported that PCs in use around the world exceeded a billion and the firm predicted that number would pass 2 billion in 2014. Even though sales have slowed, a global total of 2 billion is a cinch by now.

The total number of smartphones in use around the world is forecast at 1.9 billion in 2015, and will top 2 billion in 2016, according to research firm eMarketer.

By 2018 — the long end of Microsoft’s prediction for Windows 10 penetration — there could be as many as 2.5 billion PCs and a roughly equal number of smartphones in use. That means that Microsoft is predicting that it will run on 20% of all those devices.

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Windows 7 and Windows 8.1 are currently running on about 68.6% of the world’s PCs, or about 1.37 billion boxes, if we assume 2 billion PCs in use. Of the 1.64 billion smartphones in use at the end of 2014, Microsoft will be the OS on about 41 million.

Getting Windows 10 on a billion devices should be a slam dunk. What is trickier is getting the new OS — in all its various flavors — running on the right 1 billion devices. Microsoft has already said it will offer the new OS free to consumers and small businesses running Windows 7, 8.1 and Windows Phone 8.1. If Windows 10 cannot reach a billion devices in two to three years, Microsoft is really in trouble.

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