Understanding Cartesian and Rectangular Coordinates
Cartesian and rectangular coordinates usually mean the same coordinate style. A point is described by distances along straight axes. In two dimensions, the point uses x and y. In three dimensions, the point uses x, y, and z. This calculator keeps that meaning clear. It also helps when data comes from polar, cylindrical, or spherical form.
Why Conversion Matters
Many formulas in geometry, physics, graphics, robotics, navigation, and engineering need rectangular components. A force may be given by length and angle. A sensor may report range and direction. A model may store spherical distance. Rectangular form makes addition, subtraction, scaling, plotting, and vector analysis easier. It breaks one direction-based value into axis-based parts.
What Rectangular Output Shows
The main output is the ordered coordinate. For two dimensional work, that is usually written as (x, y). For three dimensional work, it is written as (x, y, z). The calculator also reports vector magnitude. This value is the straight-line distance from the origin to the point. The XY radius shows the distance from the z-axis. The angle from the positive x-axis helps confirm direction. The quadrant label helps check signs.
Polar and Cylindrical Inputs
Polar coordinates use radius and angle. The radius gives distance from the origin. The angle gives rotation from the positive x-axis. Cylindrical coordinates extend polar form by adding height. They are useful for pipes, tanks, circular paths, antennas, and rotating systems. Both systems use cosine for x and sine for y. The z value in cylindrical form stays unchanged.
Spherical Inputs
Spherical coordinates describe a point by radius, azimuth, and inclination. The radius gives total distance from the origin. The azimuth turns around the xy-plane. The inclination drops down from the positive z-axis. This convention is common in mathematics and many engineering texts. Some fields use elevation instead of inclination, so always check the angle definition before entering values.
Advanced Options
The scale factor multiplies every computed component. Translation then shifts the final point along each axis. This is useful when converting local coordinates into a larger map or model. The screen orientation option flips the y direction. That helps when matching image or canvas coordinates. Decimal control keeps answers readable. Scientific notation supports very large or very small values.
Checking the Result
A good conversion should match the expected signs and direction. Positive x points right in standard math. Positive y points upward in standard math. A point in Quadrant II has negative x and positive y. A point in Quadrant III has both x and y negative. If the quadrant looks wrong, check the angle unit and orientation setting first.
Using Exports
The CSV file is useful for spreadsheets and logs. The PDF file is useful for reports, homework notes, and engineering records. Both exports use the same submitted values. Recalculate after changing inputs before saving. This keeps downloaded results aligned with the visible answer.