Astigmatism vector change

About this calculator

Comparing two prescriptions by eye is hard when both the amount and the axis of astigmatism change. Power vectors turn each prescription into three numbers that can be compared directly.

What you need

• Two glasses prescriptions for the same eye, earlier and later: SPH, CYL and AXIS

How it is calculated

M = S + C ÷ 2, J0 = −(C ÷ 2) × cos(2 × axis) and J45 = −(C ÷ 2) × sin(2 × axis), with the axis in degrees converted to radians and 180° treated as 0°. Each change is later − earlier. Cylinder vector difference = 2 × √(ΔJ0² + ΔJ45²).

What the result can and cannot tell you

The same prescription written in plus or minus cylinder gives the same result. Power vectors describe regular astigmatism corrected by glasses; irregular astigmatism, for example from keratoconus, needs corneal imaging and an eye exam.

References

1. Thibos, Wheeler and Horner: Power vectors. Optometry and Vision Science 1997
2. Netra Eye Institute: Astigmatism

Related

• Visual acuity converter
• Glasses prescription reader
• Glasses to contact lens converter
• Astigmatism guide
• All eye calculators

For information only. These tools explain numbers and do not replace an eye examination or your eye doctor’s advice. Values you enter stay in your browser.