# Polynomial Regression Calculator Fit a polynomial least-squares curve to paired numeric data and inspect coefficients, R squared, and predictions > Canonical page: https://elysiatools.com/en/tools/polynomial-regression-calculator - **Category:** Math & Numbers - **Keywords:** polynomial regression, curve fitting, least squares, coefficients, r squared, calculator ## Overview The Polynomial Regression Calculator is a mathematical tool designed to fit a least-squares curve to sets of paired numeric data. It allows users to determine the best-fit polynomial equation of a specific degree, calculate the R-squared value for goodness-of-fit, and generate predictions for specific X-values. ## Inputs - **Data Pairs** (textarea): One pair per line, e.g. 0, 1 1, 4 2, 9 3, 16 - **Polynomial Degree** (number) - **Prediction X (Optional)** (text): e.g. 5 - **Decimal Places** (number) ## When to use - When you need to model non-linear relationships between two variables using a polynomial equation. - When you want to find the coefficients of a trend line for a dataset to understand its mathematical behavior. - When you need to predict future or intermediate values based on historical data points that follow a curved path. ## How it works - Input your paired numeric data points, entering one X and Y pair per line separated by a comma. - Select the desired polynomial degree, from 1 for linear to 6 for complex curves, to define the model's complexity. - The tool applies the least-squares method to minimize the sum of the squares of the vertical deviations between each data point and the curve. - The calculator outputs the resulting coefficients, the R-squared value, and an optional prediction for a specified X-value. ## Use cases - Analyzing growth rates in biological or economic datasets where trends are not strictly linear. - Calibrating scientific instruments by fitting a curve to known reference points and their measured outputs. - Forecasting resource demand or sales trends that exhibit seasonal or accelerating patterns. ## Frequently asked questions ### What is the maximum polynomial degree supported? The calculator supports polynomial degrees from 1 (linear) up to 6. ### How should I format my input data? Enter data as pairs of numbers separated by a comma, with each pair on a new line (e.g., 1, 5). ### What does the R-squared value indicate? R-squared measures how well the polynomial curve fits your data points, with 1 representing a perfect fit. ### Can I predict a Y-value for a specific X? Yes, enter a value in the 'Prediction X' field to calculate the corresponding Y-value based on the fitted model. ### How many decimal places can I specify? You can set the precision of the output coefficients and results from 0 to 10 decimal places. ## Related tools - [Three-Phase Short-Circuit Current Calculator (IEC 60909)](https://elysiatools.com/en/tools/short-circuit-current-calculator): Estimate the three-phase symmetric short-circuit current using the IEC 60909 far-from-generator method: I"_k = c·U_n/(√3·|Z|) and i_p = κ·√2·I"_k with κ = 1.02 + 0.98·e^(−3R/X). 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