Developed by Shivani Malvi & Satyajit Puhan Free for research & teaching · no sign-up · nothing to install
Curve Fit Bench
Documentation

Using the bench.

Everything you need for a first fit in five minutes. The full manual, with every model in the library, is a 162-page PDF.

Quick start

  1. Open the bench. It loads with a sample dataset already fitted.
  2. Drop your CSV or TXT file on the data panel, or paste x y pairs, one per line.
  3. Read the best fit: the formula, parameters with uncertainties, reduced χ² and the region strip. Click any row in the ranking to see another model.

Data format

Two columns are x and y. A third column is read as the uncertainty σy — the bench asks before assuming — and a header row names the axes. Commas, tabs and spaces all work, and instrument files with a few text lines at the top are handled.

# temperature (K), resistivity (µΩ cm), sigma
T, rho, sigma
2.0, 1.842, 0.004
4.0, 1.843, 0.004
6.0, 1.847, 0.004

Fitting modes

Best form searches every enabled family and ranks them. My equations fits only what you type, and still shows the automatic pick as a dashed comparison. Under Model families you can switch groups on and off — the materials-science library is off by default.

Writing equations

Every letter that is not x becomes a parameter. After a semicolon give starting values, bounds and fixed values:

A*exp(-x/tau) + c ; A=2, tau=5, tau>0
# fixed parameter with !
rho0 + a*x^n ; n=2, !rho0=1.84
# several equations, one per line, are fitted and compared
A/(1+((x-x0)/g)^2) + b ; g>0

Functions include exp log sqrt sin cos tanh erf erfc gamma voigt digamma brillouin lambertw and more — 65 in all.

Reading the result

Reduced χ² (χ²/ν) is near 1 for a correct model when σ is given. Without σ, look at the misfit: how far the curve sits from the points in units of the point-to-point noise. The runs z flags residuals in long same-sign stretches, and the by region strip shows χ²/N in up to ten parts of the x range.

A green headline with an orange or red region means the model is right on average and wrong somewhere specific — look there first.

Adaptive decomposition

It runs only when nothing else comes within the noise. The result is listed as Adaptive decomposition: … with its components; switch on components to draw them. Use it to read positions, widths and frequencies, then fit the named model that matches your mechanism. The Best named physics model card always shows the best library model alongside.

Parameter explorer

Below the ranking, pick a parameter, choose multiples of the fitted value or absolute values (0.5, 1, 2 or from:to:count) and compare curves and χ²/ν. Edit this plot opens its own styling panel.

Figures & export

Edit plot controls titles, ranges, ticks, fonts, colours and the statistics box. Only selected curve hides everything but the model chosen in the ranking. PNG and PDF save at 3× resolution; copy fitted y puts the curve on your clipboard.

Citing

If the bench helped your work, please cite it — citations are how we justify the time to keep improving it. See About for BibTeX.