# Percentages in Sheldon Brown's Gear Calculators

## by Sheldon "Gain Ratio" Brown

My gear calculators provide not only values for the individual gears, but also show the percentage difference between adjacent gears. There has been some confusion about this, so here's the skinny:

The percentages are mainly of use with derailer or hybrid gearing, where they help the rider determine the most efficient shift pattern, where there are two or three different shifters to be considered.

The algorithm is pretty simple. Look at two adjacent gears, then express the higher one as a percentage _increase_ over the lower of the two.

For instance, if one gear is 80 inches and the next gear up is 88 inches, that's a 10% increase. The higher gear is 110% of the lower gear, but the increment is only 10%.

Manufacturers of internal gear hubs tend to tout the total gear range of their hubs, but they commonly calculate it in a different way.

For instance, if there was an internal-gear hub "Hub A" that only covered a range from 80 inches to 88 inches, the manufacturer could say this was a range of 110%.

This is a legitimate way to represent the overall range of a gear system, though I prefer the incremental approach, and would call it 10%.

The range of another hub, lets' call it "Hub B", 40 inches to 100 inches, could be called either 250% or 150% , depending on which system you use.

However, for purposes of comparison, if you use the bigger numbers, it appears that Hub B has little more than twice as wide a range as Hub A, but in reality, Hub B has 15 times the range of Hub A!

If you carry this to the extreme, the hub manufacturers' system would consider a singlespeed bike to have a gear "range" of 100%!