Cross-Cylinder Calculator
Toric refinement, Rx combination, and power cross
Combine two crossed cylinders at different axes into a single sphere, cylinder and axis: the oblique-cylinder maths done for you.
Mode
Sphero-cylinder
What each mode does
Power cross: Shows the two principal meridian powers (axis meridian = sphere; meridian 90° away = sphere + cylinder). Useful to verify axis and cylinder effect.
Rx combination: Returns the single sphero-cylinder equivalent to stacking two prescriptions (dioptric power sum). Helpful for trial-lens math.
Toric refinement: Combines trial lens Rx, observed rotation, and over-refraction to suggest an on-eye lens power. LARS: Left Add, Right Subtract from clinician’s view.
Combining crossed cylinders
Sometimes two astigmatic corrections at different axes need to be combined into a single sphere-cylinder result, for example when accounting for residual astigmatism over a lens, stacking a refraction over an existing correction, or reconciling obliquely crossed cylinders. Doing this by hand involves oblique-cylinder trigonometry that is easy to get wrong; this calculator performs the combination for you.
Enter each cylinder with its power and axis, and the tool returns the equivalent single sphere, cylinder and axis.
When would I combine crossed cylinders?
Common cases include over-refraction on top of a toric lens, combining a spectacle correction with residual astigmatism, and resolving obliquely oriented cylinders into one prescription.
Why can't I just add the cylinders?
Cylinders only add directly when their axes are parallel. At different axes they must be combined vectorially, which is what this tool does.
For background on cylinder and axis, see Toric lenses & astigmatism basics. Verify results clinically. See our disclaimer.