The cluster numbers are linear but - as has been previously mentioned - are relative to the data area, with cluster 2 being the first cluster of the data area. Reads from the disk, however, are in terms of disk sectors, and each FAT cluster may contain multiple sectors - this is what the conversion to LBA is for - to convert from a cluster number to a sector number (so, subtract 2 from the required cluster number - to account for cluster 2 being the first cluster of the data area, then multiply by the number of disk sectors per cluster, and then add the number of disk sectors in use before the data area, to come up with the absolute disk sector(s) where our data is stored.
The older BIOS int 0x13 functions didn't read from the disk in terms of absolute sectors though - they read a specifc sector, by a specific head, on a specific cylinder (http://en.wikipedia.org/wiki/Cylinder-head-sector). Therefore if you use these functions you need to take the added step of working out which cylinder/head/sector corresponds to the absolute sector you want to read. An alternative is - if available - to use the extended read int 0x13 function, which takes absolute sector (LBA) addresses directly.