Rotate the cut plane and watch both views move together. Drag the point on the circle, or use the angle control below.
Stress element, rotated θ from the x-axis
Mohr's circle — shear plotted downward
A single point in a loaded body has one stress state, but the numbers you read off depend on how you cut it. Turn the cut by θ and the face stresses change; the circle traces every possible answer at once.
The factor of two is the whole trick. One full lap of the circle is only half a turn of the element, because a square repeats every 90°. Where the circle crosses the horizontal axis, shear vanishes — those are the principal planes. The top and bottom of the circle are the maximum shear planes, always 45° away from the principal ones, and they still carry normal stress equal to the centre of the circle.