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Spherical equivalent calculator

Turn a sphere + cylinder prescription into one sphere power: sphere + half the cylinder.

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Spherical equivalent

Turn a sphere + cylinder prescription into the single sphere power that is closest to it: sphere + half the cylinder.

Number line: the two powers of the lens and the spherical equivalent halfway between them The spherical equivalent is the sphere plus half the cylinder, which lands halfway between the two powers of the lens. more minus more plus
The spherical equivalent sits exactly halfway between the two powers of the lens.
The axis is not needed: it does not change the spherical equivalent.
Words used here
Spherical equivalent (SE)
One sphere power that gives the best single focus for a sphere + cylinder prescription. Used, for example, when choosing a spherical contact lens or checking a prescription quickly.
Circle of least confusion
An astigmatic lens focuses light into two lines instead of a point. Halfway between them the blur is a small round patch: that is where the spherical equivalent puts the focus.

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How to find the spherical equivalent

Spherical equivalent (SE) = sphere + (cylinder ÷ 2). The axis does not matter.

  • −2.00 −1.00 × 180: −2.00 + (−0.50) = −2.50 D.
  • +1.00 −2.00 × 090: +1.00 + (−1.00) = plano.
  • +3.00 +1.50 × 090: +3.00 + 0.75 = +3.75 D (the same answer as its minus-cylinder form, +4.50 −1.50 × 180).

Why it works: a sphero-cylinder lens focuses light into two lines. The spherical equivalent puts a single focus halfway between them, where the blur is smallest (the circle of least confusion).

References

  • Brooks CW, Borish IM. System for Ophthalmic Dispensing. Butterworth-Heinemann (spherical equivalent).
  • Schwartz SH. Geometrical and Visual Optics: A Clinical Introduction. McGraw-Hill (astigmatism, the conoid of Sturm and the circle of least confusion).

Calculators are study aids. Always verify finished eyewear with your instruments and follow your practice's procedures. More optical calculators.

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