Polar to Rectangular Converter
Convert a polar coordinate given by a radius and angle into its rectangular (Cartesian) x and y components.
Angle unit
x-coordinate; y is shown below
- 1
Convert angle to radians
53.13 × π ÷ 180 = 0.927293 - 2
y = r · sin(θ)
5 × sin(0.927293 rad) = 4 - 3
x = r · cos(θ)
5 × cos(0.927293 rad) = 3
How does this calculator work?
To convert polar coordinates to rectangular, compute x = r · cos(θ) and y = r · sin(θ). Convert the angle to radians first if it is given in degrees (θ_rad = θ × π / 180). The radius is the distance from the origin and θ is measured from the positive x-axis, giving the point (x, y).
Formula
How this is calculated
A polar coordinate locates a point by its distance from the origin (the radius r) and the angle θ that the line to the point makes with the positive x-axis. This calculator takes r, the angle θ, and whether θ is measured in degrees or radians.
If the angle is in degrees it is first converted to radians using θ_rad = θ × π / 180, because the trigonometric functions operate on radians. The rectangular coordinates are then found with x = r · cos(θ) and y = r · sin(θ). These formulas come directly from the right triangle formed by the radius and its horizontal and vertical projections.
The radius may be negative, which points in the opposite direction (180° away), and the angle has no bounds since it wraps periodically every 360° (2π radians). The output x and y are in the same length units as the input radius. The plot draws the radius vector from the origin to the resulting point so you can see the angle and quadrant.
Frequently asked questions
Both measure the same angle. Degrees split a full turn into 360 parts; radians use 2π. Choose the unit that matches your input — the calculator converts degrees to radians internally before applying cosine and sine.
Yes. A negative radius reflects the point through the origin, equivalent to adding 180° to the angle. The formulas x = r·cos(θ) and y = r·sin(θ) handle this automatically.
Use r = √(x² + y²) and θ = atan2(y, x). The angle from atan2 already accounts for the correct quadrant of the point.
Also known as
TG we-Calculate Editorial Team. (2026). Polar to Rectangular Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/polar-to-rectangular-calculator
TG we-Calculate Editorial Team. "Polar to Rectangular Converter." TG we-Calculate. 2026. https://we-calculate.com/calculator/polar-to-rectangular-calculator.
TG we-Calculate Editorial Team, "Polar to Rectangular Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/polar-to-rectangular-calculator
@misc{wecalculate_polar_to_rectangular_calculator, title = {Polar to Rectangular Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/polar-to-rectangular-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?