More than most people expect. The download is roughly 6 to 10 GB, and sources recommend 15 to 20 GB of free space to install. Afterwards, iOS plus System Data can temporarily grow past 20 GB, especially on iPhones with Apple Intelligence. Before updating, it helps to decide which iPhone essentials, meaning the apps and photos used every week, should stay on the phone, and which can be offloaded. The current figures are visible at Settings > General > iPhone Storage.
Numbers vary by model and library, so any single figure should be treated with caution. One iPhone 15 Pro Max owner on Apple's German community forum reported about 22 GB shown for iOS, including roughly 6.6 GB for Apple Intelligence, and 15.7 GB for System Data after updating. Other users in the same thread posted very different figures of their own, which shows how much the numbers depend on the device and what is installed on it.
System Data also keeps changing and often shrinks once background work finishes. If space is tight, offload unused apps, clear browser data and turn on iCloud Photos optimisation. Low free space also causes failed installs, so it is wise to clear room before the update starts and not after.
