Equatum

Find the formula behind your measurements.

Paste a table from your test bench or spreadsheet. Equatum searches closed-form equations, checks each one against data it has not seen, and points out the readings that don’t fit.

Analyse your data See a worked example

No installation. Works with CSV, tab-separated text and cells pasted from Excel, decimal commas included.

Measurements with the fitted equation; one reading that does not fit is ringed.012345510xline 21
fitted equation measurement does not fit the rest

What you get back

Three things, for every data set: an equation you can use, the evidence for choosing it, and a list of measurements to check.

The equation

A closed-form formula in your column names and units, with a standard error for every coefficient — and the same formula as Python, Excel or C code.

The evidence

Cross-validated error, R², AICc and the ten best alternatives, so you can see how clearly this equation beat the others — and whether it beats a plain polynomial at all.

The rows to check

Measurements that disagree with the rest, found with a studentised-residual test, then confirmed or cleared by the final equation. A typo in one cell no longer bends your fit.

How it works

Each analysis runs three stages on a dedicated compute server. A typical one-variable data set takes one to three minutes.

  1. Screen

    Polynomial response surfaces are fitted over subsets of your inputs and ranked by leave-one-out error. Every row is tested against the best surface for gross errors.

  2. Search

    Equation structures built from + − × ÷ ^ exp ln sin tan asin atan — up to 300,000 per search — plus classic laws such as logistic, Gompertz and damped sine, are fitted by Levenberg–Marquardt.

  3. Judge

    Candidates are ranked by cross-validated error, preferring fewer parameters when the difference is within noise. The winner re-examines every row the screen flagged.

Equations with one to five input variables; up to 20 inputs in the screen and 5,000 rows per data set.

Your data

Measurement data is often confidential. It is treated that way.

Hosted in Frankfurt, Germany (EU)The site, its database and the compute server all run in the same data centre.
Deleted when you say soDelete an analysis or your account and it is gone from the database at once. The compute server keeps nothing once it has returned a result.
No trackersNo analytics, advertising or third-party scripts and fonts. One cookie keeps you signed in.
Everything downloadableThe full result as JSON and your data as CSV with a verdict on every row.

Thirty years of turning measurements into equations

Equatum is made by Inzoner LTD, a team that has done mathematical modelling for industry for more than 30 years: hundreds of customer projects, across different industries, in which a measured curve had to become an equation that an engineer could defend and a device could compute.

That is why the site returns more than a best fit. You get the evidence for choosing the equation, the readings it cannot explain, and the formula in a form you can paste into your own code — the same things a modelling project would deliver.

Need more than a formula — a full model, or help with a difficult data set? Write to support@equatum.eu.

Have a curve you keep fitting by hand?

Paste it in. Results for a one-variable data set usually arrive within three minutes.

Analyse your data