How this calculation works
Regress each standard integrated transform against the same increasing time series. Convert fitted values back to concentration, report original-scale residuals and compare models without claiming a reaction mechanism from R².
Fit C = a+bt, ln(C) = a+bt and 1/C = a+bt; k is −b for zero/first order and b for second orderA worked example
The illustrated concentrations follow C = 10 exp(−0.5 t). The selected first-order transform is linear with slope −0.5, so its fitted rate constant is 0.5 per entered time unit.
Good to know
Descriptive unweighted transformed regressions, not mechanistic proof. No replicate times, uncertainty weights, background concentration or nonlinear regression. Rate units depend on concentration/time basis and order.
Reference: OpenStax: integrated rate laws (opens in a new tab) ↗
Transforming changes the error emphasis
A least-squares line in concentration, logarithm and reciprocal concentration minimizes three different residual definitions. Their R² values are therefore not interchangeable measures of fit on the original concentration scale.
The page also calculates original-scale residuals and SSE where predictions remain positive and finite. Constant transformed responses have undefined centered R² rather than a claimed perfect fit.
Rate constants carry order-dependent units
For first order, k has reciprocal-time units. Zero order uses concentration per time, while second order uses reciprocal concentration per time.
The software does not silently convert the input’s unit conventions. Keep time and concentration units consistent when comparing a fitted constant with another source.
A linear pattern is not a unique mechanism
Several integrated models can look similar over a short or noisy interval. A high transformed R² alone does not identify an elementary step or demonstrate a causal chemical pathway.
Negative fitted k is retained and is not labeled ordinary decay. Nonphysical transformed predictions are exposed rather than silently clipped into positive concentration values.
Use the result with the next measurement
The Arrhenius two temperature rate calculator compares compatible rate constants at different temperatures. Establishing a consistent reaction-order and unit convention comes before that temperature comparison.
Descriptive unweighted transformed regressions, not mechanistic proof. No replicate times, uncertainty weights, background concentration or nonlinear regression. Rate units depend on concentration/time basis and order.
A few questions, answered
Can I choose order just by the largest transformed R²?
Not reliably; transforms change error weighting and do not prove mechanism.
Are constant responses given R² = 1?
No, centered R² is undefined for constant response.
Are negative fitted rate constants clipped?
No, their sign is retained and explained.