What is the formula used?

x = r·cos(θ) and y = r·sin(θ). These come directly from the definition of cosine and sine on the unit circle extended to radius r.

Can I enter a negative radius?

Yes. A negative r reflects the point through the origin — equivalent to (|r|, θ + 180°).

When should I use degrees vs. radians?

Use degrees for everyday geometry (bearings, compass angles). Use radians for calculus, signal processing, and most programming math libraries where Math.cos() expects radians.

How many decimal places are shown?

Results are shown to 6 significant figures. Very small values near zero (< 1e-10) are displayed as 0 to avoid floating-point noise.

What is the difference between polar and Cartesian coordinates?

Polar coordinates describe a point by how far it is from the origin (r) and in what direction (θ). Cartesian coordinates use two perpendicular distances (x horizontal, y vertical). Both systems describe the same 2D plane.

Polar To Cartesian Calculator

Name: Polar To Cartesian Calculator
Availability: InStock
Author: Nham Vu

Enter radius r and angle θ (in degrees or radians) to instantly get the equivalent Cartesian x and y coordinates.

Polar Input

Radius (r)

Angle (θ)

Angle unit:

Cartesian Result

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Coordinate Plane

Formula: x = r·cos(θ) y = r·sin(θ)

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Summary

Enter radius r and angle θ (in degrees or radians) to instantly get the equivalent Cartesian x and y coordinates.

How it works

Enter the radius r (distance from the origin). Negative values are accepted.
Enter the angle θ — choose degrees (0–360) or radians (0–2π) from the toggle.
The calculator applies x = r·cos(θ) and y = r·sin(θ) as you type.
Results are displayed with up to 6 significant figures and copied with one click.
A coordinate-plane diagram updates live so you can visually verify the point position.

Use cases

Convert sensor or radar data from polar to Cartesian form for plotting.
Check manual calculations for physics or engineering problems.
Understand trigonometry visually through the live coordinate diagram.
Convert robotics/navigation angles from (r, θ) to (x, y) reference frames.
Quickly verify vector decomposition into horizontal and vertical components.
Prepare data for spreadsheets or code that requires (x, y) pairs.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu