SC QUALITY GUILDInterpolation from a calibration table
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Enter the corrections, errors or true values a calibration certificate gives at a few points. Get the correction and the corrected value at any reading by straight-line interpolation, with the slope and intercept of each segment, a least-squares line through the table, and a flag on any reading outside it.
ON THE EXAM · CCT IV.D.4, IV.D.7 · FREE · NOTHING YOU TYPE LEAVES YOUR BROWSER
Q-BotClick for an explanation of this tool.For educational use. This page is a study aid. The method behind it has far more depth and detail than one page and one tool can cover, and what you see here is not everything the method offers or everything this site offers. For full understanding and application, use the governing standards and texts, and seek further education, training or qualified advice. Results depend on the data you enter, so check them before relying on them.
Using a calibration table
A calibration certificate reports what was found at a few test points: the error, the correction, or the true value at each one. To use the instrument between those points you need values in between. The simplest assumption, and the usual one, is that the instrument behaves in a straight line from one calibrated point to the next.
Linear interpolation
For a reading x between two table points (x1, y1) and (x2, y2):
- slope m = (y2 − y1) / (x2 − x1)
- intercept b = y1 − m·x1
- y = y1 + (x − x1)·m, which is the same as y = m·x + b
In the worked example the correction is +0.25 psi at 100 psi and +0.30 psi at 150 psi, so at 120 psi it is 0.25 + 20 × (0.05 / 50) = +0.27 psi, and the corrected value is 120.27 psi.
Correction, error or true value
Get the sign right. The error is reading minus true value, so true = reading − error. The correction is the error with its sign reversed, so true = reading + correction. Some certificates give the true (reference) value at each nominal reading instead. Say which one the table holds and the tool applies it the right way round.
Extrapolation
Outside the table there is no calibrated point on one side. Extending the end segment gives a number, but nothing on the certificate supports it: the instrument may bend away from the line beyond the last point tested. Treat an extrapolated value as unverified, and calibrate over the range you actually use.
Slope, intercept and linearity
The least-squares line through the whole table summarizes it with one slope (a gain error) and one intercept (an offset error). The largest departure of the table from that line is a measure of the instrument's nonlinearity. If it is small, a single line would do; if not, as in the worked example where the correction rises and then falls, point-to-point interpolation follows the instrument better. Spanning and zeroing adjust the slope and intercept; linearization deals with the departure from the line.
On the exam
CCT IV.D.4 asks you to interpret tables and graphs to find intermediate and extrapolated values, and to illustrate slope, intercept and linearity of data sets. IV.D.7 covers solving algebraic equations for the unknown, as in rearranging y = m·x + b. Expect to interpolate a correction from a short table by hand, and to recognize when an answer depends on extrapolating beyond the data.