Polar coordinates describe a point by distance from the origin and angle from the positive x-axis. The rectangular form uses cosine and sine to split that distance into x and y components.
⚠Angle is entered in degrees. Radius should be nonnegative for this standard coordinate conversion.
How Polar to Rectangular Conversion Works
The radius acts like a hypotenuse. Cosine gives the horizontal component, and sine gives the vertical component of the point.
Radius r
Distance from the origin.
Angle θ
Direction from the positive x-axis.
x Coordinate
x = r cos θ.
y Coordinate
y = r sin θ.
💡 Example: For r=10 and θ=30°, x=8.660254 and y=5.
Applications of Polar to Rectangular
VectorsComplex NumbersNavigationPhysics
Frequently Asked Questions
What is a polar to rectangular calculator?▼
It converts coordinates from radius and angle form into x and y coordinates.
What is the polar to rectangular formula?▼
The formulas are x = r cos θ and y = r sin θ.
How do I use this calculator?▼
Enter radius r and angle θ in degrees, then click Calculate.
Can radius be negative?▼
This calculator expects a nonnegative radius for the standard conversion.
Where is polar conversion used?▼
It is used in vectors, complex numbers, navigation, physics, and coordinate geometry.
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