Input Data and Options
Use comma, space, or line-separated values. Keep X values strictly increasing.
Example Data Table
This sample resembles a small absorbance peak measured across evenly spaced wavelengths.
| Wavelength (nm) | Absorbance |
|---|---|
| 200 | 0.12 |
| 202 | 0.15 |
| 204 | 0.18 |
| 206 | 0.30 |
| 208 | 0.55 |
| 210 | 0.88 |
| 212 | 1.24 |
| 214 | 1.51 |
| 216 | 1.42 |
| 218 | 1.10 |
| 220 | 0.79 |
| 222 | 0.52 |
| 224 | 0.33 |
Formula Used
For each center point, the method fits a polynomial within a moving window by least squares. It preserves local peak shape better than a simple moving average.
ŷ(z) = a0 + a1z + a2z2 + ... + apzp
For smoothing, the reported value at the center is ŷ(0) = a0.
For derivatives, the calculator uses:
dmy / dxm = m! · am / (Δx)m
The coefficient form is:
c = m! · emT(ATA)-1AT / (Δx)m
Where A is the local Vandermonde matrix, m is derivative order, p is polynomial order, and the window length is odd.
How to Use This Calculator
- Paste evenly spaced X values and matching Y values into the input boxes.
- Choose an odd window length. Larger windows smooth more strongly.
- Select a polynomial order smaller than the window length.
- Keep derivative order at zero for smoothing, or raise it for derivative estimation.
- Leave Delta X blank to use average X spacing automatically.
- Pick a padding mode to control edge behavior.
- Press Smooth Data to generate the result summary, graph, coefficients, and output table.
- Use the CSV or PDF buttons to export your calculated values.
Frequently Asked Questions
1. What does Savitzky-Golay smoothing do?
It fits a small polynomial inside a moving window and reports the center estimate. This smooths noise while preserving peak height, width, and shape better than many simple averages.
2. Why must the window length be odd?
An odd window provides a true center point. The fitted polynomial then produces a centered estimate, which is essential for stable smoothing and derivative calculations.
3. How do I choose the window length?
Start small, such as 5 or 7 points. Increase it when noise is strong, but avoid windows so large that narrow peaks flatten or important inflection details disappear.
4. What polynomial order should I use?
Second or third order works well for many chemistry signals. Higher orders can follow curvature more closely, but they may also amplify noise or overfit short windows.
5. Can this calculator estimate derivatives?
Yes. Set derivative order above zero. The calculator scales the fitted coefficient by factorial and Delta X, giving a numerical derivative for evenly spaced chemistry data.
6. Why does evenly spaced X data matter?
The standard coefficient construction assumes constant spacing. Mild irregularity can still be explored, but strongly uneven spacing may reduce accuracy and distort derivative estimates.
7. What do the residual values show?
Residuals equal raw minus filtered values. They help you inspect removed noise, identify local mismatches, and judge whether the smoothing settings are too weak or too aggressive.
8. Which chemistry data types fit this method?
It is useful for spectroscopy, chromatography, electrochemical traces, sensor signals, and calibration curves whenever you need cleaner trends without severely damaging peak structure.