Coordinate Geometry Calculators

Free coordinate geometry calculators: irregular polygon area, sphere equation, least squares regression line, and more. Fast, accurate, and free online tools.

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Equation of a Sphere Calculator
Calculate the equation of a sphere from its center coordinates and radius. Convert between standard and expanded forms. Free 3D math calculator.
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Least Squares Regression Line Calculator
Calculate the least squares regression line y = mx + b from any data set. Shows slope, intercept, r, R², residuals table, and predictions. Free.
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Irregular Polygon Area Calculator
Calculate the area and perimeter of any irregular polygon from its vertex coordinates using the Shoelace formula. Free, instant, shows side lengths.

Coordinate Geometry Calculators

Coordinate geometry (analytic geometry) bridges algebra and geometry by describing shapes through numerical coordinates on a Cartesian plane. These calculators solve real coordinate geometry problems instantly using rigorous formulas.

Three Coordinate Geometry Calculators

Irregular Polygon Area Calculator - Find the exact area and perimeter of any polygon (3 to 8 vertices) by entering its vertex coordinates. Uses the Shoelace formula (Gauss’s area formula) and shows a full side-length breakdown table.

Equation of a Sphere Calculator - Find the standard form equation (x−h)²+(y−k)²+(z−l)²=r² from center and radius, or decode the general form x²+y²+z²+Dx+Ey+Fz+G=0 to extract center, radius, surface area, and volume. Two modes with full expanded form output.

Least Squares Regression Line Calculator - Compute the best-fit line ŷ = mx + b from any paired x, y data set. Shows slope, intercept, Pearson correlation r, R² (coefficient of determination), mean x and y, and a full residuals table. Predict mode forecasts y for any x value.

What is the Shoelace formula for polygon area?+
The Shoelace formula computes the area of any simple (non-self-intersecting) polygon from its vertex coordinates. Given vertices (x1, y1) through (xn, yn), the area equals one half of the absolute value of the sum of (xi times y(i+1) minus x(i+1) times yi) for all i, cycling back to vertex 1 after the last vertex. It works for any number of vertices and any shape, regular or irregular.