Quickly convert coordinates between Cartesian (rectangular) and Polar systems. Understand the relationship between (x,y) and (r,θ) with our user-friendly online tool. Perfect for students and professionals in geometry, trigonometry, engineering, and physics. Achieve precise coordinate conversions effortlessly.
Formula:
Understanding Polar and Cartesian Coordinate Formulas
Our Polar Coordinates Calculator uses the following standard formulas for converting between Cartesian and Polar coordinate systems:
Cartesian (x, y) to Polar (r, θ):
- Radius (r):
r = √(x² + y²) - Angle (θ):
θ = atan2(y, x)(Theatan2function correctly determines the angle in all four quadrants, returning a value in radians, which is then converted to degrees if specified.)
Where:
- x represents the horizontal distance from the origin.
- y represents the vertical distance from the origin.
Polar (r, θ) to Cartesian (x, y):
- X-coordinate (x):
x = r cos(θ) - Y-coordinate (y):
y = r sin(θ)
Where:
- r is the radial distance from the origin.
- θ is the angular coordinate, measured counter-clockwise from the positive x-axis (must be in radians for direct calculation).