Polar-Cartesian Coordinate Converter

This calculator converts inputs as polar coordinates to cartesian coordinates (and vice versa). A degree to radian converter (and vice versa) is also provided.
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CalculationPolar Coordinate to Cartesian Coordinate
InputsPolar Coordinate ﻿(r,θ)
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﻿﻿r
:200.0​
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﻿﻿θ
:222.0deg​
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OutputCartesian Coordinate ﻿(x,y)
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﻿﻿x-coordinate
:-148.6​
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﻿﻿y-coordinate
:-133.8​
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x=rcos⁡(θ),y=rsin⁡(θ)x = r \cos(\theta), \hspace{0.3cm} y=r\sin(\theta)x=rcos(θ),y=rsin(θ)
Output Graph
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Cartesian Coordinate to Polar Coordinate 
 InputsCartesian Coordinate ﻿(x,y)
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﻿﻿x-coordinate (1)
:5.0​
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﻿﻿y-coordinate (1)
:-8.0​
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OutputPolar Coordinate ﻿(r,θ)
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﻿﻿r (1)
:9.4​
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﻿﻿θ (1)
:-58.0deg​
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r=x2+y2,θ=tan−1(yx)r=\sqrt{x^2+y^2}, \hspace{0.3cm}\theta = tan^{-1}(\frac {y}{x})r=x2+y2​,θ=tan−1(xy​)
Output Graph
Can’t display the image because of an internal error. Our team is looking at the issue.
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Radian Degree Converter
Radians to Degrees:
﻿﻿Radians
:0.23rad​
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﻿﻿Degrees
:13.18deg​
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θ°=(θc)×(180π)\theta\degree = (\theta^c) \times (\frac {180}{\pi}) θ°=(θc)×(π180​)
 Degrees to Radians:
﻿﻿Degrees (1)
:114.59deg​
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﻿﻿Radians (1)
:2.00rad​
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θc=(θ°)×(π180)\theta^c= (\theta\degree)  \times (\frac {\pi}{180})θc=(θ°)×(180π​)
The symbol for radians is ﻿θc
 and the symbol for degrees is ﻿θ°
.
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ExplanationPolar and cartesian coordinates can be used to describe location, orientation or direction in a two-dimensional space at any time.
What is the polar coordinate system?The polar coordinate system describes the location of a point in a 2D plane by defining a fixed point away from the origin, called the pole, and an angle moving counter-clockwise from the positive x-axis. A polar coordinate is expressed as ﻿(r,θ)
 where ﻿r
 is the pole and ﻿θ
 is the direction of movement.
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Polar coordinate system
What is the cartesian coordinate system?The cartesian coordinate system, however, describes the location of a point in a 2D plane using a pair of numbers called an ordered pair. The ordered pair is expressed as ﻿(x,y)
 where ﻿x
 is the distance away from the origin along the horizontal axis and ﻿y
 is the distance away from the origin along the vertical axis. Direction in the cartesian coordinate system is expressed as a positive or a negative sign.
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Cartesian coordinate system
Converting between coordinate systemsDiscover how to convert between the two coordinate systems in the toggles below.
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Converting between polar and cartesian coordinates
Converting Polar Coordinates to Cartesian Coordinates
With the concept of right triangles and trigonometric equations, it is possible to convert polar coordinates ﻿(r,θ)
 to cartesian coordinates ﻿(x,y)
.
The relationship of the x-coordinate and y-coordinate is expressed as:
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x=r cos⁡(θ)x = r\ \cos(\theta)x=r cos(θ)
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y=r sin⁡(θ)y = r\ \sin(\theta)y=r sin(θ)
where ﻿θ
 is in radians.
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Converting Cartesian Coordinates to Polar Coordinates
The same concept can be used in converting cartesian coordinates to polar coordinates. Their relationship is expressed as:
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r=x2+y2r =\sqrt {x^2 + y^2}r=x2+y2​
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θ=tan−1(yx)\theta = tan^{-1} (\frac {y}{x})θ=tan−1(xy​)
where ﻿θ
 is in radians.
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Related ResourcesPythagorean Theorem Calculator
Poisson Distribution Calculator
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ReferencesStover, C. & Weisstein, E. "Polar Coordinates" Available at: Wolfram MathWorld Web Encylopedia.
Stover, C. & Weisstein, E. "Cartesian Coordinates" Available at: Wolfram MathWorld Web Encylopedia.
NASA. "Rectangular and Polar Coordinates" Available at: https://www.grc.nasa.gov/www/k-12/airplane/coords.html.
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