# How do I plot a circle with a given radius and center?

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MathWorks Support Team on 26 Jul 2010
Answered: Steven Lord on 25 Dec 2020 at 5:29
I would like to plot a circle with a given radius and center.

MathWorks Support Team on 3 Jan 2019
Here is a MATLAB function that plots a circle with radius 'r' and locates the center at the coordinates 'x' and 'y':
function h = circle(x,y,r)
hold on
th = 0:pi/50:2*pi;
xunit = r * cos(th) + x;
yunit = r * sin(th) + y;
h = plot(xunit, yunit);
hold off
An alternative method is to use the 'rectangle' function:
function h = circle2(x,y,r)
d = r*2;
px = x-r;
py = y-r;
h = rectangle('Position',[px py d d],'Curvature',[1,1]);
daspect([1,1,1])
If you are using version R2012a or later and have Image Processing Toolbox, then you can use the 'viscircles' function to draw circles:

Walter Roberson on 23 Dec 2020 at 0:48
r * cos(th) is part of polar to cartesian coordinate conversion. For a given theta, for a circle of radius r centered on the origin, then the x coordinate is r multiplied by cos(theta) and the y coordinate is r multiplied by sin(theta). And then you add the actual center of the circle, x and y, to those coordinates.
A more common mathematical notation would be and for a circle of radius r centered on and Tey Yi Hua on 25 Dec 2020 at 2:05
Okayyyy thank you very much...this help a lot!!!
Walter Roberson on 25 Dec 2020 at 4:47
r*cos(theta) is used because of the definition of cos. cos(theta) = y/r where r = sqrt(x^2 + y^2) so y = r*cos(theta)

serwan Bamerni on 17 Feb 2016

Walter Roberson on 17 Oct 2016
This is part of the Image Processing Toolbox
ceethal piyus on 16 May 2019
I've applied circular hough tranform for identifing the circlular objects in an image and i got the results . But when i used the code into an app designer, insted of ploting the circles into the image where the centers are marked its ploting the circle in a different figure. How can i get both circles and center points into the same axes ( named "app.segmented" ) error How to add the axes name to viscircles function in an app designer. I tired
viscircles(centres,radii,'color','b','parent','app.segemented'); which is giving the following error. Walter Roberson on 25 Dec 2020 at 4:49

Supoj Choachaicharoenkul on 2 Oct 2019
plot(x, y, 'bo', 'MarkerSize', 50);

#### 1 Comment

wagenaartje on 7 Dec 2020
This is the best solution by far if you want to highlight some part in the figure

amine bouabid on 23 Jul 2018
Edited: amine bouabid on 23 Jul 2018
hello
you can plot a circle simply by writing :
syms x; syms y;
ezplot((x-xi).^2+(y-yi).^2-r.^2)
where xi and yi are the coordinates of the center and r is the radius

Devin Marcheselli on 17 Jan 2020
how do i plot a circle using the equation: (x-h).^2+(y-k).^2 = r.^2

Mark Rzewnicki on 20 Jan 2020
Hey there, I've been playing around with this as it relates to complex-valued functions.
It turns out that this is a very nontrivial question. There are several issues you run into along the way - you need to make some arbitrary choices about how to define your circle. I will share with you the way I found to be most natural.
Assuming y is the indpendent variable, expand the x term in the circle equation: Bring these expanded term to the right-hand side of the equation: Take the square root of both sides and bring k to the right-hand side: This is the equation you can use to plot the circle. The code I came up with is a little messy (was intended for personal use in another context) but I will throw some comments in and hopefully you find it as interesting as I did.
***The big takeaway from all of this: We can deal with circles in rectangular coordinates, but it is much more natural to use polar coordinates and think of the circle as the locus of points with distance r from the center.
% Circle equation: (x-h)^2 + (y-k)^2 = r^2
h = 1;
k = 1;
r = 1;
%% In x-coordinates, the circle "starts" at h-r & "ends" at h+r
%% x_res = resolution spacing between points
xmin = h - r;
xmax = h + r;
x_res = 1e-3;
X = xmin:x_res:xmax;
%% There are 2 y-coordinates on the circle for most x-coordinates.
%% We need to duplicate every x-coordinate so we can match each x with
%% its pair of y-values.
%% Method chosen: repeat the x-coordinates as the circle "wraps around"
%% e.g.: x = [0 0.1 0.2 ... end end ... 0.2 0.1 0]
N = length(X);
x = [X flip(X)];
%% ytemp1: vector of y-values as we sweep along the circle left-to-right
%% ytemp2: vector of y-values as we sweep along the circle right-to-left
%% Whether we take positive or negative values first is arbitrary
ytemp1 = zeros(1,N);
ytemp2 = zeros(1,N);
for i = 1:1:N
square = sqrt(r^2 - X(i)^2 + 2*X(i)*h - h^2);
ytemp1(i) = k - square;
ytemp2(N+1-i) = k + square;
end
y = [ytemp1 ytemp2];
%% plot the (x,y) points
%% axis scaling coefficient c: how far past the radius should the graph go?
c = 1.5;
figure(1)
plot(x,y)
axis([h-c*r h+c*r k-c*r k+c*r]);
Ashly Tom on 5 Mar 2020
Thank you so much.
Can you please tell how to plot 2 circles in same figure, using your code ?
Mark Rzewnicki on 17 Mar 2020
Sadly I just saw this now, sorry.
The easiest way to do this would have been to write the original code twice (renaming the variables the second time) and plot both circles using a "hold on" statement.
This makes the code look brutally ugly - you really should vectorize things and define functions when scaling up code like this - but it will get the job done in a pinch. The result would look something like this (5-minute edit of my original code):
% Circle equation: (x-h)^2 + (y-k)^2 = r^2
h = 1;
k = 1;
r = 1;
h1 = 2;
k1 = 2;
r1 = 2;
%% In x-coordinates, the circle "starts" at h-r & "ends" at h+r
%% x_res = resolution spacing between points
xmin = h - r;
xmax = h + r;
x_res = 1e-3;
X = xmin:x_res:xmax;
xmin1 = h1 - r1;
xmax1 = h1 + r1;
X1 = xmin1:x_res:xmax1;
%% There are 2 y-coordinates on the circle for most x-coordinates.
%% We need to duplicate every x-coordinate so we can match each x with
%% its pair of y-values.
%% Method chosen: repeat the x-coordinates as the circle "wraps around"
%% e.g.: x = [0 0.1 0.2 ... end end ... 0.2 0.1 0]
N = length(X);
x = [X flip(X)];
N1 = length(X1);
x1 = [X1 flip(X1)];
%% ytemp1: vector of y-values as we sweep along the circle left-to-right
%% ytemp2: vector of y-values as we sweep along the circle right-to-left
%% Whether we take positive or negative values first is arbitrary
ytemp1 = zeros(1,N);
ytemp2 = zeros(1,N);
ytemp11 = zeros(1,N1);
ytemp22 = zeros(1,N1);
for i = 1:1:N
square = sqrt(r^2 - X(i)^2 + 2*X(i)*h - h^2);
ytemp1(i) = k - square;
ytemp2(N+1-i) = k + square;
end
for i = 1:1:N1
square1 = sqrt(r1^2-X1(i)^2 + 2*X1(i)*h1 - h1^2);
ytemp11(i) = k1 - square1;
ytemp22(i) = k1 + square1;
end
y = [ytemp1 ytemp2];
y1 = [ytemp11 ytemp22];
%% plot the (x,y) points
figure(1)
plot(x,y)
hold on
plot(x1,y1)
axis([-5 5 -5 5]);

Steven Lord on 25 Dec 2020 at 5:29
Another possibility is to approximate the circle using a polyshape with a large number of sides and plot that polyshape.
p = nsidedpoly(1000, 'Center', [2 3], 'Radius', 5);
plot(p, 'FaceColor', 'r')
axis equal 