Correction Formula

Correction formulae are used to correct consistent length measurement errors in roll forming control systems, but they are handy in other areas related to manufacturing.  They can be used to correct error in closed loop servo resolution, and even when importing drawings into CAD software when the imported drawing isn’t at the same scale as the current drawing.

Length error is always expressed as a percentage.  Thus, if you have 1% of error in a 120″ part, you will have 1% of error in a 48″ part.  While the specific length error is different for both part lengths (1.2″ and 0.48″, respectively), the percentage of error is the same.

Often, the length control system will have an on-board length correction function where the system will calculate it’s own correction percentage.  If not, or if you just want to verify the value, the formula is:

ddes ÷ dmeas = Correction Percentage


ddes = desired distance (length)

dmeas = measured length

Correction Percentage = % by which to multiply the measured length to achieve the desired length


A roll former is run by a length control system connected to an encoder and measuring wheel.  After quadrature, the system is counting 4,000 pulses per revolution from the encoder, and the measuring wheel is 12″ in circumference.  Based on these values, the resolution in the length control system is programmed to 0.003″ per pulse.

The control system is programmed to run a 120″ part.  From the system’s perspective, that’s 40,000 pulses (120″ ÷ 0.003″ per pulse).  After a few parts, it’s clear the parts are consistently coming out at 120.25″.

ddes ÷ dmeas = Correction Percentage = 120″ ÷ 120.25″ = 0.998 or 99.8%

99.8% · 40,000 pulses = 39,917 pulses

The length control system will now cut the part after fewer encoder pulses are accumulated, thus, shortening the overall length of the part by the appropriate percentage.  The error measured in the part length is likely due to an imperfect circumference, or rounding error by the technician who originally setup the system, or even by a misalignment of the encoder bracket.  Regardless of where the error originated, a consistent length error can be corrected using Correction Percentage.  Variance is almost always due to physical problems on the machine, and not to parameters related to the length control system.  Correction Percentage cannot fix variance.  It can only shift the window of variance up or down the length of the part.