Polar to Rectangular Calculator
Convert back and forth between polar coordinates (r, θ) and rectangular coordinates (x, y) with angles in degrees or radians.
Category: Mathematics
About this tool
What Is the connection between the two systems? Polar to Rectangular Calculator. This converter changes coordinates between the polar form (r, θ) and the rectangular form (x, y). It is extremely common in physics, navigation, and electrical engineering work. Rectangular coordinates place a point by its horizontal and vertical distances x and y. Polar coordinates place the same point by its distance from the origin r and the angle θ measured from the positive x-axis. The relationships are x = r cos θ, y = r sin θ for the forward direction, and r = √(x² + y²), θ = atan2(y, x) for the reverse. Angles are handled in degrees here, matching the way most people read a compass or a protractor. x = r cos θ, y = r sin θ · r = √(x² + y²), θ = atan2(y, x). How to Use Choose the conversion direction from the dropdown. For polar → rectangular, enter r and the angle θ in degrees; the x and y values appear at once. For rectangular → polar, enter x and y to get r and θ back. Worked Example Convert r = 5, θ = 36.87° to rectangular form: the tool computes x = 4 and y = 3, giving the point (4, 3). Reversing with x = 4, y = 3 returns r = 5 and θ = 36.87°. Common Use Cases force and vector decomposition in physics radar and GPS position reporting phasor math in AC circuits graphing polar curves Important Notes Enter θ in degrees — the tool converts internally to radians. Negative angles and angles b