Adding mod 2*pi to atan2 should work just fine z = mod(atan2(y,x),2*pi);

The atan function simply computes the inverse tangens of a value. The atan2 function takes two values (y and x). This function is used to convert from cartesian coordinates (x,y) to polar coordinates (r,phi), where phi=atan(y,x).

It seems the answers provided so far are missing the point. If we want to see a 4 quadrant atan2 version, that works for complex X and Y, can we use what Alpha suggests? Thus atan2(U,V) = -i*log(U+i*V)./sqrt(U.^2 + V.^2) I'll modify what @Stephen23 did to see what happens, for complex U and V. A serious problem is I would need to have a hyper-dimensional monitor to show the complete behavior. (My own personal holodeck is broken, awaiting parts. But shipping is very slow, coming from the future.) I would need to display essentially 6 dimensional behavior, and a regular monitor is just not up to snuff there. Nor are my eyes or my brain. So I can only do my best to look at what happens. fun = @(V,U) -1i*log((U+1i*V)./sqrt(U.^2+V.^2)); First, what happens for real U and V? utest = randn(3);vtest = randn(3); fun(vtest,utest) And that is clearly a problem, since for real U and V, we want the result to return a purely real result. We need to patch it for that case. function Z = atan2alt(V,U) % extension of atan2(V,U) into the complex plane Z = -1i*log((U+1i*V)./sqrt(U.^2+V.^2)); % check for purely real input. if so, zero out the imaginary part. realInputs = (imag(U) == 0) & (imag(V) == 0); Z(realInputs) = real(Z(realInputs)); end atan2alt(vtest,utest) so atan2alt now returns purely real output for purely real inputs. Next, is it consistent with atan2? norm(atan2(vtest,utest) - atan2alt(vtest,utest)) And that is (as we sometimes said in the deep past) good enough for government work. The difference is down into the realm of floating point trash. Now I am at least a little happy, since the two are consistent for real input. Next is this a 4 quadrant result? Again, that will be difficult to show in detail. But perhaps we can do a little, by plotting the result along a simple path in the complex plane. V = (-10:10); U = V(:); v = V - 0.1i; u = U + 0.2i; So u and v both now each live along lines in the complex plane, where the imaginary part is constant, and non-zero. Z = atan2alt(v,u); And of course, since atan2alt will now return a complex result, we need to look at both the real and imaginary part. surf(U,V,real(Z)) xlabel "Real(U)" ylabel "Real(V)" zlabel "Real(Z)" surf(U,V,imag(Z)) xlabel "Real(U)" ylabel "Real(V)" zlabel "imag(Z)" The result is a 4 quadrant version. Here we see the imaginary component is indeed non-zero. surf(U,V,abs(Z)) xlabel "Real(U)" ylabel "Real(V)" zlabel "abs(Z)" Of course, this would need a great deal more thought, to see if there were additional problems other than the need for a real result. What happens when one or both of the arguments are zero? Again, unless the two are consistent, we have a problem. atan2([0 1],[0;1]) atan2alt([0 1],[0;1]) Hey, that worked. I was actually just a little surprised. I was going to guess the code would fail when U==V==0, and perhaps return a NaN. But as it turns out, the result from the formula is then 0+infi, with an infinite imaginary part. But since it has a zero real part, the check at the end of atan2alt saved me. I noticed that @M A wanted to see it work also for symbolic inputs. Again, I was wondering for just a second if it would survive here, but it did. syms u v atan2alt(v,u) Some might suggest plots I generated do not form a very strong test, since they presumed constant imaginary part. And, while it is not too difficult to conjure up a pair of paths for U and V that are more complicated, this seems a good point to stop. 'nuff said.

Since it will be periodic, just add 360 if the value is less than 0. This will suffice to correct the negative angles. winddir = winddir + (winddir < 0)*360; You can use atan2d if you prefer to work in degrees, but it will map to the same range, [-180,180], so you will still need to correct for the negative angles. If you wanted a simple expression that works in one line of code, this should do: winddir = atan2d(Vi,Ui) + 360*(Vi<0);

Your question is not very clear, but I guess you are searching for the function unwrap. This will correct all the 2 pi jumps you get when your vector rotates through the negative x-axis. You use it like so:

t = linspace(0,3,1000);
x = cos(2*pi*t);
y = sin(2*pi*t);
phi = atan2(y,x);
unwrapped_phi = unwrap(phi);
plot(t, phi, t, unwrapped_phi)
xlabel('time (s)')
ylabel('angle (rad)')
legend('wrapped angle','unwrapped angle')