Enrichment · Passion Projects · Lab science

How little can your
method really see?

Paste the calibration standards and a set of blank readings. The calculator fits the line, measures the noise, and turns it into the smallest concentration you can detect and the smallest you can report.

Find the limitsWhat you get

The detection limit calculator

The worked example is made up: a blue dye measured by absorbance, six standards and ten blanks. Nothing you type leaves this browser.

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What you get

Enrichment · Passion ProjectsFree

What you finish with
The limit of detection and limit of quantitation, the calibration slope, intercept and R², the σ used, each standard’s residual and a lowest-standard check. It prints as a summary and downloads as a spreadsheet.
Who it is for
Chemistry students in high school and college, science fair and research students, and teachers running instrument labs.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The Passion Projects space in Caveat Enrichment.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Run your standards and type their concentrations and responses in order.
  2. Run a blank at least seven times and paste the readings.
  3. Choose blanks or residuals as the source of σ.
  4. Read the LOD and LOQ and check the lowest standard.
  5. Print the summary for the lab notebook.

Find the limits

How the limits are found

Noise, turned into concentration.

The worked example: a dye by absorbanceBlank noise σ0.0011510 blank readings÷ slope0.0232 mg/Lslope 0.0497 per mg/L× 3.3 = LOD0.077 mg/Lpresent or not× 10 = LOQ0.232 mg/La number you can reportThe worked example: a dye by absorbanceBlank noise σ0.0011510 blank readings÷ slope0.0232 mg/Lslope 0.0497 per mg/L× 3.3 = LOD0.077 mg/Lpresent or not× 10 = LOQ0.232 mg/La number you can report
The limits turn the instrument’s noise into a concentration: the slope says how much signal one mg/L gives, so noise divided by slope is noise in mg/L.

The formulas

The ICH guideline on validating analytical procedures gives LOD = 3.3σ ÷ S and LOQ = 10σ ÷ S, where S is the calibration slope and σ the standard deviation of the response at zero. σ can come from repeated blanks or from how far the standards scatter around the line. At the LOD a signal is unlikely to be noise; at the LOQ the noise is a tenth of the signal, so the number is worth reporting.

Doing it well

Use at least seven blank readings, prepared and measured like real samples. Keep standards close to the expected limit, since a line fitted only to high standards can misjudge the low end. Check the residuals: a pattern means the response curves. Then confirm by measuring a sample spiked near the LOQ.

Sources

  1. International Council for Harmonisation. ICH Q2(R1), Validation of Analytical Procedures: Text and Methodology (2005), and Q2(R2) (2023), detection and quantitation limits (ich.org).
  2. U.S. Environmental Protection Agency. Definition and procedure for the determination of the method detection limit, revision 2, 40 CFR part 136 appendix B (epa.gov).
  3. Harris, D. C., and Lucy, C. A. (2020). Quantitative Chemical Analysis (10th ed.). Macmillan: chapter 5, calibration methods and detection limits.
  4. NIST/SEMATECH e-Handbook of Statistical Methods, section 4.1.4.1, linear least squares regression (itl.nist.gov).

The worked example is made up. Follow your lab’s safety rules and its own validation procedure. Your data stay in this browser. Support: team@caveatacademic.com.