Custom formula syntax

Two places in Open Gauge let you enter a custom formula as a calibration model instead of a polynomial: model_direct's "Custom formula" option (a lab-supplied model with no raw data — see Alternative calibration data-entry modes) and raw data's "Custom Formula" Calibration method (fits the formula to your entered data). Both use the exact same formula input and syntax — they only differ in where the parameter values come from.

Writing a formula

A formula is a single-variable expression in x — x always means the measured/output value. Any other letter or word you use is treated as a free parameter, e.g.:

a*x + b

has two free parameters, a and b. Open Gauge detects them automatically as you type and shows one below the formula field:

• model_direct — enter a value for each parameter directly (from the certificate/datasheet that gave you the model).
• Raw data's Custom Formula method — no parameter inputs; Open Gauge fits a and b to your entered (reference, measured) points via nonlinear regression instead.

Either way, what's actually stored is the fully-resolved formula (parameters replaced with their values, e.g. 2.5 * x + 1.2) — that's what appears on the equation display, the fitted-curve chart, the Health tab's drift/curve comparison, and the certificate.

Allowed syntax

Nothing else is allowed — no assignment, no comparisons, no access to anything outside the expression itself. This is enforced independently on both the browser (expr-eval) and the server (simpleeval), each restricted to this exact same whitelist, since the formula you save is evaluated separately by each side.

^ means exponentiation (x^2 is "x squared"), not bitwise XOR — matching spreadsheet/calculator convention.

Worked examples

Quadratic — a*x^2 + b*x + c (3 parameters: a, b, c). A general-purpose curved correction when you don't want to commit to Open Gauge's own auto-degree-selected Polynomial Fit.

Exponential growth/decay — a*exp(b*x) (2 parameters: a, b). Common for sensors with a genuinely exponential response (e.g. some gas sensors, thermistors over a narrow range).

Damped/offset sine — a*sin(b*x) + c (3 parameters: a, b, c). For a periodic response — note that a nonlinear fit against a sine needs a reasonable initial guess to converge; Open Gauge always starts every parameter at 1.0 (see below), so a sine whose true period is very far from 2π may need the formula rewritten (e.g. pre-scaling x) to fit reliably.

When a fit doesn't converge

Raw data's Custom Formula method starts every free parameter's initial guess at 1.0 and runs a nonlinear least-squares solver (scipy.optimize.curve_fit). For most reasonably-scaled formulas against real calibration data this converges without any tuning — but a formula that's a poor match for the data's actual shape, or badly scaled (e.g. parameters that need to be in the thousands or the millionths to fit), can fail to converge. Open Gauge shows a clear error in that case rather than silently returning a wrong or misleading result — try simplifying the formula, double-checking the data, or switching to Polynomial Fit if the underlying shape doesn't need to be a specific known form.