it is often recommended to have ~50 GB free to perform an upgrade. while the download itself is only ~13 GB, the Mac needs to have room to expand the upgrade as well as moving things around while performing the upgrade.
if you are running low on space, you can purchase an external HDD or SSD of sufficient capacity and move your larger files (videos, pictures, documents, etc...) to it. once they are on the EHD, you can simply erase the same files from your internal drive. and, if it's just going to be used for storage, you can use an HDD and save a few bucks over the cost of an SSD. FWIW, i personally keep very little on my internal drive.
also, you may want to read these two articles:
Optimize storage space on your Mac
How to free up storage space on your Mac
additionally, you want to keep ~ 20% of your local drive as free space for proper operation of macOS.