By February 2017, Microsoft should have Windows 10 on more than 440 million personal computers, according to a new analysis of user share data and upgrade tempo.

More than eight out of every 10 PCs now running Windows 8 or 8.1 will migrate to Windows 10 in the first 20 months of Windows 10's life. Meanwhile, approximately one in four systems now running Windows 7 will also make the move to Windows 10 in that same timeframe, adding even more machines to the tally.

Those calculations are based on the upgrade performance of Windows 8.1 and a conservative estimate of how quickly consumers with Windows 7 PCs will make the switch.

According to California-based metrics firm Net Applications, which measures operating system user share, 82% of all the PCs running either Windows 8.1 or Windows 8 ran the former last month, a 12-percentage-point increase from 6 months ago and up almost 30 points compared to 12 months prior.

Computerworld used Windows 8.1 adoption because it was the best yardstick available: In the same way that Windows 10 will be a free upgrade from Windows 8.1 or 7, Windows 8.1 was gratis to users of Windows 8.

So it's a good bet that 82% of all Windows 8 and 8.1 PCs will run Windows 10 within 20 months, or by the end of February 2017. Using Microsoft's oft-stated figure of 1.5 billion PCs now on Windows, that translates into 217 million machines worldwide (17.6% user share for Windows 8/8.1 at the end of June x 82% = about 14.4% x 1.5 billion).

Estimates of Windows 7's adoption of Windows 10 are fuzzier.

IDC says that approximately 55% of all PCs are in the hands of consumers, the remainder in businesses, governments or other organizations. Apply that ratio to Windows 7 -- which accounted for 67% of all Windows PCs at June's end -- and it means 37% of all Windows 7 machines are consumer-owned.

Computerworld has discarded commercial PCs from its series of forecasts because while businesses must eventually upgrade to Windows 10, analysts have said it's unlikely that their migrations will ramp up until 2017.

Likewise, it would be reckless to count on consumers owning Windows 7 PCs to upgrade to Windows 10 at the same rate as those running Windows 8 or 8.1. For one thing, Windows 7 runs on more than half a billion consumer PCs, about twice as many as 8/8.1, and moving such a large number will be time consuming. For another, Windows 10 is largely a course correction for Windows 8 and 8.1, as it restores many of the UI (user interface) elements Microsoft ditched, like the Start menu, that exist in even-more-familiar forms in Windows 7.

Many users of the latter may be satisfied staying with that they know.

Say consumers upgrade Windows 7 to Windows 10 at half the rate of Windows 8/8.1.... Under that scenario, 15% of all Windows 7 machines would have migrated to the new OS within 20 months (67% x 55% for consumers' part of the total, x 41% upgrade rate, or half the 82% of Windows 8.1).

The 15% would represent another 227 million Windows PCs.

Together, the Windows 8/8.1 and Windows 7 upgrades would total 443 million, and represent almost 30% of all Windows PCs.

But the projection is conservative for one simple reason: Windows 7 did better than that in its first 20 months. And people paid for a Windows 7 upgrade if they didn't get the new OS on a new PC. They paid $50 for the consumer-grade Windows 7 Home Premium upgrade, $100 for Windows 7 Professional during a very short discount period, then twice that under the regular pricing scheme.

True, Windows 7 debuted during the run towards 2011's "peak PC," as PC shipments surged 14% in 2010, virtually all of them Windows systems, virtually all of those equipped with the then-new OS. But if a free upgrade deal can't beat one priced between $50 and $100, even with computer shipments down 19% from 2010, then Microsoft should just go back to charging for its software.

Other factors that point to a better-than-30% adoption of Windows 10 include Microsoft's marketing, which has thumped the upgrade-to-Windows-10 drum much louder, much longer than it did the one for Windows 8.1.

For proof of Microsoft's target audience, one has only to look at the first Web advertisement unveiled earlier this week. Aimed directly at Windows 7 users, it touted the familiarity of the new OS. "With the best of Windows 7 ... and the best of Windows 8," the ad trumpeted, then highlighted "the desktop you know and love, only better."

Microsoft has also lit the urgency fuse by putting a one-year time limit on the free upgrade offer (it told Windows 8 users that they had two years to move to 8.1) to push people off the fence. And it's taken unprecedented steps to make customers, especially consumers, aware of the upgrade, using a nag-and-notification system fed to their devices that let them reserve a copy of Windows 10. It didn't do that for either Windows 7 or 8.1.

Most important, the Redmond, Wash. company has serious skin in this game, and not just because it's stamped a goal of 1 billion instances by mid-2018 on Windows 10.

The company is betting big that Windows 10 can restore the OS to, if not glory, then a turn-around. "I do believe that Windows 10 will broaden our economic opportunity and return Windows to growth," CEO Satya Nadella said Tuesday.

Nothing would cripple that restoration of growth more than a sluggish start to Windows 10's adoption. Fortunately for Microsoft, the numbers point to the opposite, a quick take-off.