REDMOND, Wash. >> Microsoft on Wednesday took the wraps off a new version of Windows — and a new wearable 3D gadget it calls the HoloLens.

The company showed the new headset, which lets users view and interact with three-dimensional images, at an event where it also revealed new features coming to the company’s flagship operating software.

Executives said Windows 10 is designed to embrace the way people use computers today — offering a familiar experience as they switch back and forth from personal computers to tablets, smartphones and other gadgets such as gaming consoles or even holographic projectors.

While it’s designed to let apps work in similar fashion on all those devices, Windows 10 will also come with a new Web browser that will be closely integrated with Cortana, the company’s voice-activated answer to Siri. Microsoft is expanding Cortana to serve as a search engine and personal assistant, capable of answering questions and responding to commands such as “Play music” on desktop and laptop computers, as well as mobile devices.

And in a break from past practice, Microsoft announced that Windows 10 will be released later this year as a free upgrade for anyone owning a computer or gadget that’s currently running Windows 8.1 or 7, the two previous versions of the software.

Microsoft is making a big bet that Windows 10 will help it regain ground the company has lost to the mobile computing boom. Windows has long been the dominating operating software for desktop and laptop computers, but that business has suffered as more people have begun using smartphones and tablets. Microsoft tried to reach those users by emphasizing touch-screen features in its last update, Windows 8, but many traditional PC users found it jarring and difficult to navigate.

Hoping to win back a larger audience, Microsoft is promising Windows 10 will provide a familiar experience to users on across devices, and a common platform for software developers to create apps that work on all of them.

“Windows 10 is built for a world in which there are going to be more devices on the planet than people,” CEO Satya Nadella told reporters and industry analysts at Microsoft’s headquarters. He said Microsoft wants to “enable that seamless cross-over, across devices as you move around at home and at work.”

Rivals including Apple and Google have also been working toward that goal, by making apps that, for example, save files or photos created on a PC and let the user retrieve them on a smartphone. But analysts say new features in Windows 10 could give Microsoft an edge.

For example, Microsoft executives showed new versions of the company’s Word app, its Outlook email service and a photo-storage app that look and act similarly on different screen sizes. They also promise to synchronize files so that changes made on one device would appear when the app is opened on another gadget.

Windows 10 will be used in Microsoft’s Xbox gaming systems as well. A new Xbox app for computers running Windows 10 will give gamers one place to find messages, video clips and games they have played on multiple devices. Microsoft gaming executive Phil Spencer also suggested programmers may eventually use Windows 10 to create other apps for TVs tied to an Xbox console.

As for the company’s new hologram device, executives did not say when it will be available for sale. But they talked about using it for games as well as more serious purposes, such as helping a surgeon visualize a new operating technique or showing someone how to perform plumbing repairs. Nadella said it will be priced to appeal to both consumers and businesses.

And there won’t be a Windows 9. Microsoft has skipped ahead in naming the next version, from Windows 8 to Windows 10, as though to put more distance between them.