Proportional band and gain converter
Proportional band and gain describe the same thing from opposite ends. Gain is how much output you get per unit of error; proportional band is how much error it takes to move the output across its full range.
They are reciprocally related, so increasing one is decreasing the other. That inversion is behind a large share of loops that were made worse by a change intended to improve them.
| Gain | Proportional band |
|---|---|
| 0.1 | 1000% |
| 0.25 | 400% |
| 0.5 | 200% |
| 1 | 100% |
| 2 | 50% |
| 5 | 20% |
| 10 | 10% |
The relationship
Proportional band as a percentage is one hundred divided by the gain, and gain is one hundred divided by the band. A gain of one is a band of 100%; a gain of two is a band of 50%; a gain of one half is a band of 200%.
The direction is what matters day to day. To make proportional action stronger you raise the gain — or lower the band.
Questions that come up
Can proportional band be more than 100%?
Yes, and it very often is. A band of 200% corresponds to a gain of one half, which is entirely normal on a flow loop. It means the error would have to exceed the full measurement range to drive the output across its whole span.
Related
Last reviewed 2026-08-01.