Calibration Curve Calculator

An r squared of 0.999 says the line is straight, not that it is the right line — read the intercept.

Clear
Concentration of the unknown4.87771read back off the fitted line
Slope0.100857signal per unit concentration — the sensitivity
Intercept0.013048small, as a clean blank should give
r squared0.999972how straight the line is — not how accurate it is
Residual standard error0.002231
Standards used6
Calibrated range0 to 10
An r squared near one only says the points lie on a line. It cannot detect a systematic error that shifts every standard equally — for that, look at the intercept and at a blank you trust.

The formula

least-squares fit of signal against concentration, then read the unknown back off the line

An ordinary regression with a chemical name

A calibration curve is a straight-line least-squares fit of instrument response against known concentration. Once the slope and intercept are known, an unknown sample's reading inverts through the same line. Everything that is true of linear regression is true here.

Read the intercept, not just the r squared

An r squared of 0.999 is easy to obtain and says almost nothing about accuracy — it measures how straight the line is, not whether it is the right line. A large intercept where the chemistry says there should be none points to a contaminated blank or a baseline problem, and it will bias every result systematically without ever disturbing the correlation.

Do not extrapolate

An unknown reading above the highest standard is outside the range that was actually demonstrated to be linear. Detectors saturate; chemistry changes. The remedy is to dilute the sample back into the calibrated range and multiply, not to extend the line.

Where these models stop

Michaelis-Menten assumes a single substrate and a steady state; Langmuir assumes one layer on identical sites with no interaction between them; Stokes-Einstein assumes a hard sphere much larger than the solvent molecules around it. Each is an idealisation that happens to describe real systems well over a useful range, and each fails predictably outside it. Knowing which assumption a number rests on is usually more valuable than the number.