How to use the limit of detection and quantitation calculator
- Choose where the noise comes from: a standard deviation you already have, or replicate readings that the page turns into one.
- Enter the standard deviation of the blank, or paste at least three readings of blanks or very low level samples.
- Enter the calibration slope, which is the signal per unit of concentration.
- Check the two multipliers. The page starts with 3.3 for the detection limit and 10 for the quantitation limit, and you can change them to what your method asks for.
Formula
LOD = k1 x sigma / S, with k1 = 3.3 as a common example
LOQ = k2 x sigma / S, with k2 = 10 as a common example
sigma is the standard deviation of the blank or of low level readings, in signal units
S is the slope of the calibration line, in signal per concentration unit
The limits come out in the concentration units of the calibration. With replicate readings, sigma is the sample standard deviation with n - 1 in the denominator.
A blank with a standard deviation of 0.02
With sigma = 0.02 and a calibration slope of 0.5 signal units per concentration unit, the detection limit is 3.3 x 0.02 / 0.5 = 0.132 and the quantitation limit is 10 x 0.02 / 0.5 = 0.4. The quantitation limit is about three times the detection limit with these multipliers.
Ten blank readings of 0.011, 0.014, 0.009, 0.012, 0.016, 0.010, 0.013, 0.012, 0.008 and 0.015 have a sample standard deviation of 0.002582. With a slope of 0.25, the detection limit is 0.034082 and the quantitation limit is 0.10328.
What the two limits mean
The limit of detection is the smallest amount that you can tell apart from a blank with reasonable confidence. The limit of quantitation is the smallest amount that you can measure with acceptable precision and accuracy. Because measuring takes more certainty than noticing, the quantitation limit is always higher.
To find the slope from your standards, use the linear regression calculator. For the spread of repeat readings, see the standard deviation calculator.
Several ways to define sigma
Guidelines allow more than one choice: the standard deviation of blanks, of low level samples, or of the residuals of the calibration line. The page takes sigma from what you enter, so it follows whichever definition your method uses. The multipliers 3.3 and 10 are widely used examples, and some methods use 3 and 10, or other factors.
After you compute a limit, confirm it by measuring samples near it. A calculated limit is a prediction, and a method validation shows whether it holds. To compare a measured value with a known one, use the percent error calculator.
Assumptions and limits
- The response is linear near zero, and the slope applies at the low end.
- Sigma is a standard deviation in the same signal units as the slope.
- The multipliers are those of your method. 3.3 and 10 are examples.
- Readings are independent and come from blanks or very low level samples.
Frequently asked questions
How do I calculate the limit of detection?
Multiply the standard deviation of the blank by 3.3 and divide by the calibration slope. A blank deviation of 0.02 with a slope of 0.5 gives 0.132.
What is the difference between LOD and LOQ?
The LOD is the lowest amount you can detect. The LOQ is the lowest amount you can measure with acceptable precision, and it is higher.
Why 3.3 and 10?
They are common conventions tied to the chance of false results and to a precision of about 10 percent. Your method may ask for other factors, and you can change them here.
Can I use readings instead of a standard deviation?
Yes. Choose replicate readings and paste at least three values. The page computes the sample standard deviation for you.