Polar Coordinates in Rectangular Form
Polar coordinates describe a point by distance and direction. The distance is called radius. The direction is the angle from the positive x axis. Rectangular coordinates describe the same point with horizontal and vertical distances. These values are usually written as x and y.
Why Conversion Matters
Many Maths problems move between both systems. Polar form is helpful for rotation, circular motion, spirals, and trigonometric curves. Rectangular form is easier for graphing on a standard grid. It is also useful for slope, distance, intercepts, and algebraic equations. This calculator connects both views in one step.
Advanced Inputs
The calculator accepts degrees, radians, gradians, and turns. It can normalize angles before conversion. This keeps large angles easier to read. You can add an origin shift when the polar axis starts at another point. You can also use a scale factor for drawings, maps, or model layouts. Precision control helps you round answers for homework, reports, or checking work.
Reading the Result
The x value tells how far the point moves left or right. A positive x moves right. A negative x moves left. The y value tells how far the point moves up or down. A positive y moves up. A negative y moves down. The quadrant note helps confirm the sign pattern. Axis points are also identified.
Batch Work
Use the batch box when several points are needed. Enter one point per line. You may use radius and angle only. You may also add a label before them. The same angle unit, scale, origin, and rounding settings apply to all rows. This makes tables fast and consistent.
Good Practice
Always check the angle unit first. A degree angle entered as radians gives a very different answer. Keep the radius sign in mind. A negative radius points in the opposite direction. Use enough decimals when the result will be reused in another calculation. Round only at the final step when possible. Use the export buttons after checking the table. The CSV file works well in spreadsheets. The PDF file is useful for printed notes. Save the sample table as a guide when testing your own polar coordinate entries. It also supports class demonstration checks during lessons.