Polar to Cartesian Calculator - Convert Radius & Angle to Coordinates

Convert Polar Coordinates to Cartesian Form in Seconds

Understanding the relationship between polar and Cartesian coordinates is essential in mathematics, physics, and engineering. Our Polar to Cartesian Calculator is a free and accurate online tool designed to help you quickly convert values from polar form (r, θ) into Cartesian coordinates (x, y).

Whether you're working on a geometry assignment or designing a physics simulation, this tool gives you instant, reliable results.

What Are Polar and Cartesian Coordinates?

• Polar Coordinates represent a point using a radius (r) and an angle (\(\theta\)) from the origin.
• Cartesian Coordinates express the same point using horizontal (x) and vertical (y) distances from the origin.

The conversion formulas are:

\(x = r \times \cos(\theta)\) \(y = r \times \sin(\theta)\)

Where \(\theta\) is the angle in degrees or radians, and r is the distance from the origin.

How to Use the Calculator

1. Enter the radius (r) - the ditance from the origin.
2. Input the angle (\(\theta)\) - in degrees.
3. Click the "Convert to Cartesian" button.
4. Instantly get your x and y coordinates displayed below.

Example:

If r = 5 and \((\theta)= = 60^\circ \) ,

\(x = 5 \times \cos(60^\circ) = 2.5) \(y = 5 \times \sin(60^\circ) \approx 4.33)

So, Cartesian Coordinates: (2.5, 4.33)

Why Use This Tool?

• Free and fast - Instant conversion at your fingertips
• Student-friendly - Great for math, physics, and engineering homework
• Mobile optimized - Use it on the go from any device
• Accurate results - Handles precise angles and decimal values

Applications

• Trigonometry and coordinate geometry
• Robotics and navigation systems
• Electrical engineering (phasor analysis)
• Physics simulations
• Graphing and plotting polar equations

Learn Better With Visuals

Understanding how polar and Cartesian systems relate geometrically enhances your learning. Use this calculator alongside graphing tools or coordinate plane diagrams to visualize the transformation from a circular system to a rectangular one.

Try the Polar to Cartesian Calculator Now!

Whether you're a student, engineer, or hobbyist, our Polar to Cartesian Coordinate Converter is a must-have utility. Try it now and convert with confidence.