How much free space do I need to install an app update?

Apps are submitted as .ipa files which is really just a zipped container of a .app file. In fact, you can simply unzip a .ipa file to see its true size.

Apps in the App Store are listed by their compressed size, and will need to be uncompressed after installing.

As of iOS 6, updates to apps only include files that have been changed. As of iOS 7, updates to apps only include changes to changed files.

So, I guess to answer the question directly, for any given app you would need: Free space to store the compressed app update file, free space to store the uncompressed app update file, and space currently being used by the app and all its data/caches.

https://developer.apple.com/library/ios/qa/qa1779/_index.html