Curve Fitting Calculator

A curve of best fit (or best-fit curve) is the mathematical function that most closely follows the trend of your data points, minimizing the overall difference between observed and predicted values. It lets you summarize, interpolate, and extrapolate your data using a single equation.

Start by plotting your data and observing its shape. A straight-line trend suggests linear regression. A U-shaped or peak pattern suggests a polynomial (quadratic or cubic). Rapid growth or decay typically indicates an exponential model. Compare R² values across models — the higher the R², the better the fit.

R² (the coefficient of determination) measures how well the fitted curve explains the variance in your data. A value of 1.0 means a perfect fit, while 0 means the model explains none of the variation. Generally, R² above 0.95 indicates a very good fit for most engineering and science applications.

Beyond R², examine the residuals (the differences between observed and fitted values). If residuals appear random with no pattern, the model is a good fit. A systematic pattern in the residuals suggests the wrong model type has been chosen, and you should try a higher-degree polynomial or a different functional form.

Both are exponential models but with different parameterizations. In y = ae^(bx), the base is Euler's number e and b controls the growth rate. In y = ab^x, the base b is estimated directly from your data. They are mathematically equivalent since ab^x = a·e^(x·ln(b)), but the coefficient interpretation differs slightly.

You need at least as many data points as there are coefficients in your model — so 2 for linear, 3 for quadratic, 4 for cubic, and 2 for exponential. In practice, 6 or more data points are recommended to get a statistically meaningful and stable fit. More data generally improves reliability.

Enter each X, Y pair on a separate line, separated by a comma or a space. For example: '1, 2.5' on one line, '2, 4.8' on the next, and so on. The calculator will automatically parse your data, ignoring blank lines, and perform the selected regression.

Yes — enter any X value in the 'Predict Y at X' field and the calculator will apply your fitted equation to return the predicted Y. Keep in mind that extrapolating far beyond your data range can reduce accuracy, as the fitted model may not remain valid outside the observed region.