Yeah, that 'Estimating time remaining' screen is the worst kind of patience test. You wait ten minutes, nothing moves. Here's how you actually get out of it.
The Fix That Works 90% of the Time
Do a force restart. Not the normal swipe-to-power-off, the physical button combo. On an iPhone with Face ID or an iPad without a Home button, quickly press and release Volume Up, then Volume Down, then press and hold the Side button until you see the Apple logo. On an iPhone with a Home button (SE, 8 or earlier), hold the Home and Side (or Top) buttons together for about ten seconds.
When the phone comes back, go to Settings > General > Software Update again. The download will resume, and more often than not, the estimate actually turns into a real progress bar.
Why This Works
The 'Estimating time remaining' text is a symptom, not the disease. What's actually happening is that the update daemon (mobileassetd if you want to get picky) is stuck in a state where it's trying to reach Apple's servers but the connection got dropped or the cryptographic handshake stalled. The UI thread is waiting on a callback that never fires, so you get an infinite spinner with a shrug.
A force restart kills that daemon cold. It doesn't clear the partially downloaded update, which is a good thing — you don't want to re-download a 2GB file if you don't have to. When the system boots back up, it checks the existing download, verifies the signature, and continues from where it left off. That's why the fix is almost always this simple, and why you should skip the 'reset network settings' advice you'll see on forums — that's for a different problem entirely.
When the Force Restart Isn't Enough
If you're back to the same stuck screen after a reboot, you've got one of the less common variations. Here's what to check, in order:
1. The Download Is Corrupted
Sometimes the partial download gets a bad block, and the verifier keeps failing silently. The fix here is to delete the update and start fresh. Go to Settings > General > iPhone Storage, find the iOS update file (it's listed as a separate item, usually labeled with the iOS version), tap it, and hit Delete. Then go back to Software Update and try again. This forces a clean download. Yes, it costs you bandwidth, but a corrupted 2GB file is useless anyway.
2. Storage Is Too Tight
iOS needs roughly twice the size of the update to unpack and install it — the download plus the installed system. If you're under 5GB of free space, the update will sit at 'Estimating' forever because the system can't allocate space for the extraction step. Check your storage in Settings > General > iPhone Storage. If it's low, delete videos or offload an app you haven't used in months. Then force restart again and retry.
3. Apple's Servers Are Flaky
Rare, but happens during a major release (iOS 17.0.1 day, for example). The update keeps stalling because the CDN is rate-limiting or sending bad responses. You can check Apple's system status page (apple.com/support/systemstatus) from your computer. If Software Update shows a yellow or red dot, your phone isn't the problem — wait an hour and try again.
4. The Real Edge Case: Corrupted System Cache
I've seen this on older devices (iPhone 7 era) after months of incremental updates. The update cache partition itself is borked, and no amount of deleting or restarting helps. The only reliable cure is a full restore through a computer. Attach your iPhone to a Mac or PC, open Finder (or iTunes on Windows), put the device in recovery mode (press Volume Up, Volume Down, then hold Side until the recovery mode screen appears), and select Update. That reinstalls the OS while keeping your data. It's the nuclear option, but it's also the only thing that clears the bad cache.
Prevention: Don't Let It Happen Again
You can't avoid the 'Estimating' screen entirely, but you can make it less likely to hang.
Update when you have a solid Wi-Fi connection. Not 2 bars on the edge of your router. The worst failures happen when the connection drops mid-handshake, and iOS doesn't always recover gracefully. Move closer to the router or plug into Ethernet if you're on a Mac with iPhone mirroring.
Keep 10–15GB free. I know, it feels wasteful, but iOS uses that headroom for swap and the update staging area. If you're chronically at 2GB free, you're going to hit this again.
Don't update on release day. Apple's servers are hammered, and the error rate spikes. Wait two or three days. The update isn't going anywhere, and the first point release (like 17.0.1) is usually worth having anyway.
One more thing: if you're on an Apple Silicon Mac, updating your iPhone via Finder over a USB-C cable bypasses Wi-Fi entirely and is more reliable. But that only works if your iOS device is supported by your Mac's OS version, so check that first.
That's it. Force restart, check storage, and if all else fails, restore. You'll be back on the new iOS sooner than you think.