Calculator Form
Enter paired calibration readings. Separate each number with commas, spaces, or new lines.
Example Data Table
This sample shows a nearly linear calibration response for a pressure sensor.
| Calibration Point | Input (kPa) | Output (V) |
|---|---|---|
| 1 | 0 | 0.12 |
| 2 | 2 | 1.08 |
| 3 | 4 | 2.14 |
| 4 | 6 | 3.07 |
| 5 | 8 | 4.11 |
| 6 | 10 | 5.09 |
Formula Used
Average sensitivity from regression slope:
S = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²)
Zero offset from regression intercept:
b = ȳ - Sx̄
Predicted output at any input:
ŷ = Sx + b
Point-to-point sensitivity:
Spp = (ylast - yfirst) / (xlast - xfirst)
Full-scale sensitivity:
Sfs = Output Span / Input Span
Sensitivity error relative to full scale:
Error % = ((S - Sfs) / Sfs) × 100
Coefficient of determination:
R² = 1 - (SSres / SStot)
How to Use This Calculator
- Enter the instrument name for easier result tracking.
- Provide input and output units.
- Add paired calibration inputs and outputs in matching order.
- Enter a reference input to estimate output near a target operating point.
- Optionally provide full-scale spans to compare measured and rated sensitivity.
- Add instrument resolution if you want minimum detectable input change.
- Click Calculate Sensitivity to show results above the form.
- Review the chart, computed table, and interval sensitivity values.
- Download the result summary using the CSV or PDF buttons.
FAQs
1. What is calibration sensitivity?
Calibration sensitivity shows how much output changes for each unit of input. It is commonly expressed as slope, such as volts per kilopascal or millivolts per degree.
2. Why use regression instead of only two points?
Regression uses all calibration points together. That reduces the effect of random noise and gives a better estimate of average sensitivity, offset, and overall fit quality.
3. What does zero offset mean?
Zero offset is the output value predicted when the input is zero. A nonzero intercept often indicates baseline drift, sensor bias, or electronics offset.
4. What does R² tell me?
R² measures how well the fitted line explains the calibration data. Values closer to 1 usually indicate stronger linear behavior and smaller unexplained variation.
5. Can I use this for nonlinear sensors?
Yes, but interpret results carefully. The slope here represents an average linear sensitivity. For strongly nonlinear devices, compare interval sensitivity values or use a nonlinear calibration model.
6. What is local sensitivity near the reference input?
Local sensitivity uses the nearby calibration segment around your chosen reference input. It helps when sensitivity changes slightly across the operating range.
7. Why include instrument resolution?
Resolution helps estimate the smallest input change the instrument can reliably reflect. This is useful when checking whether fine changes are practically measurable.
8. How often should calibration sensitivity be checked?
Check it after installation, repair, overload, harsh environmental exposure, or scheduled maintenance. Critical instruments may require tighter verification intervals based on standards or process risk.