Proportional band and gain converter
This page converts. Gain is how much output you get per unit of error; the band is how much error it takes to move the output across its full range. They are reciprocals, 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. For what the band means, use the glossary.
| 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
These tools assume a self-regulating loop and a bump you have not shown us. Photograph the trend and the faceplate if you want a check against the loop in front of you, not a formula.
Written by PIDSnap control engineering. Published 2026-08-01, last reviewed 2026-09-11.