How do you convert polar to Cartesian coordinates?

Use x = r · cos(θ) and y = r · sin(θ). Make sure θ is in radians if you are using a calculator in radian mode. If θ is in degrees, first convert to radians by multiplying by π/180.

Can I use degrees instead of radians?

Yes. This tool lets you choose degrees or radians. It will internally convert degrees to radians before applying the formulas.

What if r is negative?

A negative radius means the point is in the opposite direction of the angle. The calculator will still produce the correct (x, y).

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Polar to Cartesian Converter

Enter polar coordinates (r, θ) and get the corresponding Cartesian point (x, y). Choose degrees or radians, see the formulas, and learn how to handle angles beyond 360° / 2π.

Convert coordinates

r (radius) distance

θ (angle)

Angle measured from +x axis counterclockwise.

Angle unit

Result (Cartesian)

x: –

y: –

Tip: to go the other way, use our Cartesian to Polar converter.

If θ is negative or > 360° (or 2π), the tool still gives a correct (x, y).

Formulas and theory

In the polar coordinate system, a point is represented by its distance from the origin (r) and an angle (θ) measured from the positive x-axis.

Polar → Cartesian formulas

x = r · cos(θ)
y = r · sin(θ)

These formulas are valid for any real θ. If your angle is in degrees, first convert:

θ_rad = θ_deg × π / 180

Angle direction

By convention, θ is measured counterclockwise from the positive x-axis. So θ = 0° → (r, 0), θ = 90° → (0, r), etc.

Negative radius?

Sometimes in math problems, r can be negative. The point is then in the opposite direction of the angle. This tool will compute the correct x and y even if r < 0.

FAQ

What is polar vs Cartesian?

Cartesian (x, y) describes a point by horizontal and vertical distances. Polar (r, θ) describes a point by how far it is from the origin and at what angle.

When should I use polar coordinates?

Polar coordinates are great for circular motion, waves, phasors, or any system with natural radial symmetry (electromagnetics, signal processing, robotics, game dev with radial patterns).

Why are my results negative?

Perfectly normal. If the point lies in Quadrant II, III, or IV, one or both of x and y will be negative.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

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Formula (extracted text)

x = r · cos(θ) y = r · sin(θ)

Formula (extracted text)

θrad = θdeg × π / 180

Variables and units

No variables provided in audit spec.

Sources (authoritative):

Cartesian to Polar — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/cartesian-to-polar

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
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