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Key Features
Instant Calculation
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Every point on a 2D plane can be described two equivalent ways: Cartesian coordinates (x, y — how far along each axis) or polar coordinates (r, θ — distance from the origin and angle). This tool converts a point between the two forms in either direction.
How it works
Choose a conversion direction. Cartesian → Polar: enter x and y, and the tool computes r = √(x² + y²) and θ = atan2(y, x) in degrees. Polar → Cartesian: enter r and θ in degrees, and the tool computes x = r·cos(θ) and y = r·sin(θ).
- Enter conversion direction.
- Enter x (for Cartesian → Polar).
- Enter y (for Cartesian → Polar).
- Enter r (for Polar → Cartesian).
- Enter θ in degrees (for Polar → Cartesian).
- Click Calculate to see your results.
Examples
A simple 3-4-5 triangle
The point (3, 4) in Cartesian coordinates converts to r = 5, θ ≈ 53.13° in polar coordinates — a classic 3-4-5 right triangle relationship.
Who should use it
- Math, physics, and engineering coursework involving coordinate systems.
- Graphics, robotics, and navigation calculations that mix the two coordinate forms.
Industry applications
- Engineering and physics education
- Robotics, graphics, and navigation systems
Advantages
- Instant, exact conversion in either direction.
- Correctly handles all four quadrants via atan2.
Limitations
- Limited to 2D — use the Cartesian-Spherical Converter for 3D points.
Common mistakes to avoid
- Assuming a plain arctan(y/x) always gives the right angle — it doesn't account for quadrant, unlike atan2.
- Mixing degrees and radians when doing further math by hand after converting.
Best practices
- Keep track of which convention (degrees vs. radians) your next calculation expects, and convert accordingly.
- Use polar coordinates when a problem is naturally about distance-and-direction; use Cartesian when it's naturally about horizontal-and-vertical position.
Tips
- Converting a point to polar and back to Cartesian should return your original x and y — a handy way to sanity-check your own by-hand math.