The limit of quantitation (LOQ) and limit of detection (LOD) are calculated by converting the standard deviation of the intensity of the calibration blank sample (σ BL) into concentration and multiplying it by 10 (10σ) and 3 (3σ), respectively. In general, the calibration blank sample is measured repeatedly (e.g., 10 consecutive measurements, n=10), and the values are calculated from the standard deviation of the intensity obtained in this way.

LOD = 3 × σ BL / k
(σ BL: Standard deviation of the blank sample, k: Slope of the calibration curve)

LOQ = 10 × σ BL / k
(σ BL: Standard deviation of the blank sample, k: Slope of the calibration curve)

If a test method or similar document specifies a method for calculating the LOQ, it should be calculated in accordance with that method (e.g., the Water Analysis Method, JIS  [Japanese Industrial Standards] General Rules for Emission Spectrochemical Analysis).

The Shimadzu ICP software (ICPEsolution) provides an automatic calculation function for the LOD and LOQ. For details on the settings, please refer to the following procedure.

1. On the [Calibration-Curve Standards] tab in the [Standard Registration] window, select the [Display Limit of Quantity] checkbox and then select a blank sample to use to calculate the LOQ.
   
    
2. The LOD (3s, equivalent to 3σ) and LOQ (10s, equivalent to 10σ)   are displayed in the [Calibration-Curve] window and [Calibration-Curve Enlarged] window. 
   
   
   

In ICPEsolution software, the relationship between the concentration and emission intensity of the calibration sample is expressed as follows:

Concentration = a × I³ + b × I² + c × I + d
(I: Emission intensity, a, b, c, d: Calibration coefficients)

Since the slope of a first-order calibration curve is c, 1/k=c.
The standard deviation (SD) value of the analytical results is used as the standard deviation σBL of the calibration blank sample intensity.
Accordingly, the calculation formulae for the LOD and LOQ in the software are as follows:

LOD = 3 × SD × c
LOQ = 10 × SD × c