About This Calculator
A Cartesian equation describes a curve with x and y. A polar equation describes the same curve with r and θ. This calculator changes the form by using standard substitutions. It accepts a full second degree equation. That means it can handle lines, circles, parabolas, ellipses, hyperbolas, and many rotated forms.
Why Polar Form Helps
Polar form is useful when distance and direction matter. Many curves look simpler from an origin point. Circles through the origin often become short polar equations. Lines also convert neatly when written as r times a trigonometric expression. This makes graphing easier for many maths problems.
What The Tool Calculates
The calculator replaces x with r cos θ. It replaces y with r sin θ. Then it groups the equation by powers of r. The grouped result shows a quadratic style equation in r. When possible, the tool also gives a solved form for r. It checks a sample angle and reports possible radius values. This helps verify the conversion.
How To Read The Result
The first result line shows the original Cartesian equation. The next line shows the substituted polar equation. The compact line groups terms as r squared, r, and the constant. If the equation is linear, the solved form is usually direct. If it is quadratic, two branches may appear. A branch may be invalid when the discriminant is negative.
Good Input Practice
Enter zero for missing terms. Use decimals when needed. Keep signs with the coefficient. For example, use -4 for a negative x term. Select a precision that fits your work. Use degrees for classroom angles. Use radians for advanced calculus or physics work.
Practical Use Cases
Students can check homework steps. Teachers can prepare examples quickly. Designers can review radial patterns. Engineers can compare coordinate models. The export buttons help save work for notes, records, or reports. Always compare the result with a graph when accuracy matters.
Accuracy Notes
A conversion does not change the curve. It changes the language used to describe it. Some solved polar forms may have restrictions. Denominators cannot be zero. Square roots need nonnegative values. Review the notes before using values in proofs, or classroom worksheets and final written exams today.