How do you convert polar to Cartesian?
x = r cos θ and y = r sin θ.
Polar Coordinates Calculator
Switch between polar and rectangular form with a degrees/radians angle mode.
Choose conversion direction
Convert polar → Cartesian or Cartesian → polar.
About this calculator
How to use Polar Coordinates Calculator, plus the formulas and logic behind the results.
Tool description
Polar form stores distance from the origin and an angle from the positive x-axis. Cartesian form stores horizontal and vertical components.
How to use
- Select conversion direction and angle unit.
- Enter r and θ, or x and y.
- Select Calculate.
- Read the converted coordinates.
Formulas & reference
x = r cos θ, y = r sin θr = √(x² + y²)θ = atan2(y, x)
Examples
- r=5, θ=0° → (5,0)
- r=5, θ=90° → (0,5)
- (3,4) → r=5
- Origin has r=0; θ undefined conventionally shown as 0
Calculation logic
Uses cos/sin for polar→Cartesian and hypot/atan2 for Cartesian→polar. Degrees are converted with π/180.
θ from atan2 is returned in the selected unit, typically in (−180°, 180°] or (−π, π].
Polar Coordinates Calculator FAQ
Common questions about this calculator and how to use the results.
How do you convert Cartesian to polar?
r = √(x²+y²) and θ = atan2(y,x).
Should I use degrees or radians?
Match your problem statement; both are supported.
Can r be negative?
Negative r is allowed and interpreted by going opposite the angle direction.
What is atan2?
A two-argument arctangent that returns the correct quadrant.
What about the origin?
r = 0; angle is reported as 0 by convention here.