Everyday Tools

Cartesian to Polar Calculator

Convert 2D Cartesian coordinates into polar form with radius and angle.

Updated April 17, 2026
Free online tool
Planning and research use

Why this page exists

Coordinate conversion gets easier when a point can be translated into radius and angle directly instead of rebuilding the trig each time. This calculator helps users convert 2D Cartesian coordinates into polar form and clearly shows the radius, angle, and original point used.

Interactive tool

Run the estimate

Enter your numbers and read the result first, then use the sections below to understand what affects the outcome.

Calculator

Cartesian to polar calculator

Convert 2D Cartesian coordinates into polar coordinates using radius and angle.

Result

r = 5.000000, θ = 53.130102 degrees

Estimated polar coordinates from the Cartesian point entered using the standard radius and atan2 angle conversion.

Radius5.000000

Angle53.130102 degrees

Original x and y used(3, 4)

Angle unit usedDegrees

(3, 4) converts to a radius of about 5.000000 and an angle of about 53.130102 degrees.
The radius comes from the distance from the origin, and the angle comes from the point direction measured with atan2.
Use the result as a quick coordinate-conversion check for geometry, trig, and vector problems.

This is a standard 2D coordinate-conversion estimate. At the origin, the radius is zero and the angle is shown as 0 by convention because direction is undefined there.

Planning note

Last updated April 17, 2026. Use this tool to compare scenarios and plan ahead, then confirm important details with the lender, employer, insurer, contractor, or other qualified provider involved in the final decision.

How it works

What the calculator is doing

Enter the x and y coordinates of the point you want to convert.

Choose whether you want the angle displayed in degrees or radians.

The calculator uses the standard radius and atan2 relationships to estimate the polar coordinates.

Understanding your result

This is standard 2D coordinate-conversion math. At the origin, the radius is zero and the angle is shown as 0 by convention because the point has no single direction.

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Examples

Ways people use this tool

Example scenarios help turn a quick estimate into a more useful comparison or planning step.

Translate a Cartesian point into polar form

A quick radius-and-angle view can make trig or vector problems easier to understand.

Compare degree and radian angle output

Switching the angle unit makes it easier to match a class, calculator, or engineering reference.

Use it with inverse coordinate conversion

The result fits naturally beside a polar-to-Cartesian tool when you want to move between both forms.

When to use it

Good times to run this calculator

Use this when you want a quick polar-form conversion from a 2D Cartesian point.

It is especially useful for geometry, trigonometry, and vector problems where radius and angle are easier to work with than x and y alone.

Assumptions and limitations

The calculator assumes a standard 2D coordinate system and numeric x and y inputs.

It does not handle 3D coordinate conversion or alternate angular conventions beyond degrees and radians.

Common mistakes

Avoid the usual input mistakes

Using basic arctangent instead of atan2 by hand can place the angle in the wrong quadrant, which is why the conversion is helpful.

Treating the origin like an ordinary directional point can be confusing because the angle there is conventional rather than uniquely defined.

Practical tips

Match the angle unit to the class, calculator, or reference you are using so the converted value stays easy to compare.

Use the polar-to-Cartesian tool next if you want to verify the conversion by moving back into x and y form.

Worked example

Walk through a realistic scenario

A worked example shows how the estimate behaves when the inputs resemble a real planning decision.

Convert a point to polar form

A student wants the polar form of the point (3, 4) and needs the angle in degrees.

1. Enter x and y for the point.

2. Calculate radius from the distance to the origin.

3. Use atan2 to estimate the angle in the display unit selected.

Takeaway: The result gives a fast polar-form check without rebuilding the coordinate conversion manually.

FAQ

Common questions

How is radius calculated here?

The calculator uses the standard distance-from-origin formula, which is the square root of x squared plus y squared.

How is the angle found?

It uses the standard atan2 relationship so the angle stays in the correct quadrant for the point entered.

What happens at the origin?

The radius is zero, and the angle is shown as 0 by convention because the point does not point in one defined direction.

Related tools

Keep comparing

Polar-to-Cartesian, distance, angle-conversion, and vector-magnitude tools help place the conversion inside the broader coordinate workflow.

Unit-vector and dot-product tools can add context when the point conversion is only one part of a larger vector or trig problem.

Everyday ToolsUpdated April 17, 2026