The flat or neutral side of the cylinder is called the axis. The curvature is in the opposite direction of the axis. Thus, if a water pipe is set vertically, up and down, the axis is 90 degrees. If set horizontally, the axis would be 180 degrees. A cylinder lens is, in reality, a small piece of the outer portion of a cylinder.
Cylinder lenses also are either minus or plus. They have plus or minus curvature in one direction with the axis in the opposite direction. Thus, if a cylinder lens is set in your frame with the axis at 90 degrees, the curvature of the lens will be in the opposite direction. Cylinder lenses, like water pipes, are sometimes set at an angle. The axis is then given by degrees.
If a cylinder lens is prescribed, it must be designated as plus or minus and also the axis of the cylinder must be stated. Thus a cylinder prescription is written in symbol, +0.50 x 90, or -0.50 x 90. Likewise, +0.5. x 120, or -0.5. x 120, or any other given axis.
Many lenses are prescribed with both the sphere and the cylinder in the same lens. They are called compound lenses. They have a certain spherical curvature and a cylinder curvature added to the spherical. They are egg-shaped but not noticeably so. They are written as follows: plus 1.00 sph. combined with plus 0.50 cl. axis 90 -- in symbol it is +1.00==+0.50x90. They are written in many variations.