The spherical equivalent formula
An astigmatic lens forms two focal lines instead of a point. Halfway between them, in dioptres, lies the circle of least confusion. The spherical equivalent (SE) is the sphere power that puts that circle on the retina.
SE = SPH + CYL ÷ 2
- SPH
- Sphere power in dioptres, with its sign.
- CYL
- Cylinder power in dioptres, with its sign. Plus or minus cylinder form gives the same SE.
- Axis
- Not used. The midpoint between the two focal lines does not depend on which way they point.
Take SPH and CYL exactly as written, signs included. If the columns on a prescription are new to you, see how to read an eye prescription.
Worked examples
| Eye | Prescription | Working | Calculator shows |
|---|---|---|---|
| OD | −4.00 / −0.50 × 180 | −4.00 + (−0.50 ÷ 2) | -4.25 D |
| OS | +2.50 / −1.00 × 90 | +2.50 + (−1.00 ÷ 2) | +2.00 D |
| Plus cyl | +1.00 / +1.50 × 90 | +1.00 + (+1.50 ÷ 2) | +1.75 D |
Rounding to a quarter dioptre
Lenses are made in 0.25 D steps, so an SE that ends in .125 has to be rounded. The calculator shows the exact value: −3.00 / −0.25 gives -3.13 D, which is ordered as −3.00 or −3.25.
Which way to go is a clinical choice. A common rule is the less minus option for a presbyope, who gains nothing from extra minus, and the more minus option for a young myope who wants the sharpest distance vision. Check it with the wearer.
Where opticians use it
- Spherical soft contact lenses for low astigmatism, commonly 0.75 D of cylinder or less. Above about ±4.00 D, take the SE to the corneal plane with the vertex distance calculator.
- Spherical-only lenses such as some safety inserts, swimming goggles and ready-made readers.
- Comparing refractions, for example following a child's myopia from one visit to the next with one number per eye.
What the SE does not do
An SE lens does not correct astigmatism; it spreads the blur evenly. With −6.00 / −2.50 the calculator gives -7.25 D, and the 2.50 D of cylinder left uncorrected is more than most wearers accept. When the cylinder is above about 0.75 D, or large compared with the sphere, a toric lens is usually needed. It is a calculation, not a clinical decision; see the medical disclaimer.
Questions
Does the cylinder axis change the spherical equivalent?
No. The SE depends only on the sphere and half the cylinder. The axis tells you which way the two focal lines lie, not how far apart they are.
Can the spherical equivalent be used for spectacles?
Only when the lens has to be spherical, such as ready-made readers or some safety and sports inserts. Spectacle lenses can carry the cylinder at little extra cost, so the full prescription is normally used.