Experimental data & uncertainty · SL/HL
Calibration curve
Fit standards and infer an unknown from its response.
Your values
Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
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Result & working
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Formula & example
The relationship
evaluates goodness of fit to the chosen linear trend
What the variables mean
| Symbol | Meaning |
|---|---|
| Known standard concentration. | |
| Instrument response such as absorbance when a linear calibration is justified. |
Worked example
- Standard concentrations x
- 0.00 0.20 0.40 0.60 0.80 1.00
- Measured responses y
- 0.02 0.18 0.35 0.53 0.69 0.87
- Unknown response y
- 0.44
- Concentration unit
- mol dm⁻³
- Response unit
- absorbance
0.5 mol dm⁻³
Follow the example steps
- OLS fit: y = 0.8514286x + 0.01428571
- R² = 0.9997073
- x_unknown = (y_unknown − c)/m = (0.44 − (0.01428571)) / 0.8514286 = 0.5 mol dm⁻³
Common mistakes
Use the intercept when converting a response to a concentration.
Incorrect approach
y = 2x + 1, y = 5: x = 5/2 = 2.5
Correct approach
x = (5 − 1)/2 = 2
More checks before you submit
- A calibration curve should use standards prepared and measured under conditions appropriate to the method.
Method notes
Check whether the unknown response lies within the calibrated range. Extrapolation beyond standards is less defensible and should be identified. A high R² alone does not prove the model or eliminate systematic error.