Exponential and Power Curve Fit Calculator
Fit positive y data to y=A exp(Bx) or y=A x^B by least squares after a logarithmic transformation. Inspect predictions and residuals on the original scale.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Transform y to its natural logarithm. For the power model, transform x as well. Fit a straight line in the transformed coordinates and exponentiate the intercept and fitted values.
Exponential: ln y=ln A+Bx; power: ln y=ln A+B ln x
Worked example
The points (0,2), (1,4), (2,8) give y=2 exp(ln(2)x), predicting 16 at x=3. The points (1,3), (2,12), (3,27) give the power model y=3x².
Assumptions and input details
Use 2–100 observations with numeric magnitude up to 1e12. Every y must be positive; power fits require positive observed and prediction x. Transformed x values must not all be equal. The fit minimizes squared log residuals, not squared original-scale errors. Exponentiated fitted values have no lognormal bias correction and are not automatically arithmetic-mean predictions. R² on the original scale may be negative and is undefined when observed y is constant. This tool does not provide inference, confidence intervals, causal claims or a guarantee outside the observed x range. Extremely large coefficients/predictions are rejected if outside finite numeric limits.
References: NIST least-squares regression · Log transformation and interpretation
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Fit y=a+bx to 2–100 entered coordinate pairs. Inspect the regression equation, correlation, R², predictions, residuals and a scatter plot.
Apply an entered constant growth or decay rate to an initial quantity. Compare periodic and continuous models, view a time curve and find doubling time or half-life.
Integrate tabulated measurements using trapezoids or composite Simpson 1/3. Keep interval contributions, signed accumulation and the entered unit labels visible.
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