To find the spherical equivalent, take the sphere plus half the cylinder, keeping signs, and drop the cylinder. It sits halfway, in diopters, between the two meridian powers. The answer comes out the same whether written with plus or with minus cylinder, and it also equals the power 45° from the axis. A worked set follows.
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Formula
SE = sphere + (cylinder ÷ 2), signs included. The result has no cylinder or axis. It is the midpoint between the two principal meridian powers.
- +3.25 −0.75 × 045: +3.25 + (−0.375) = +2.875 D.
- −2.00 −1.00 × 180: −2.00 + (−0.50) = −2.50 D.
Same in both cylinder forms
Transposing changes how the prescription is written, not the lens. Take +1.50 −3.00 × 090. Its plus-cylinder form is −1.50 +3.00 × 180. SE: +1.50 − 1.50 = 0.00, and −1.50 + 1.50 = 0.00. Check transpositions in the transposition calculator and SE in the spherical equivalent calculator.
Where it’s used
The formula also shows how to keep SE fixed if a cylinder changes: move the sphere by half the change, the opposite way. Example: from −3.00 −1.00 × 180, adding −0.50 D of cylinder calls for +0.25 D of sphere: −2.75 −1.50 × 180. SE before: −3.50; after: −2.75 − 0.75 = −3.50.
Relation to power at 45°
Using the sin² method in oblique meridian power, a meridian 45° from the axis has power sphere + cylinder × sin²45° = sphere + cylinder ÷ 2. The same number, a different meaning.
Practice set
Original problems.
Find the SE of −1.25 −1.50 × 010.
Show answer
−1.25 + (−0.75) = −2.00 D.
Find the SE of +0.75 −1.50 × 170.
Show answer
+0.75 − 0.75 = 0.00 D.
Transpose +2.00 −1.00 × 090 and find SE in both forms.
Show answer
Plus form +1.00 +1.00 × 180. SE: 2.00 − 0.50 = +1.50; 1.00 + 0.50 = +1.50.
From −1.00 −0.50 × 090, the cylinder becomes −1.00. What sphere keeps the same SE?
Show answer
Move the sphere +0.25: −0.75 −1.00 × 090 (SE −1.25 before and after).
Find the SE of +4.00 +1.00 × 060.
Show answer
+4.00 + 0.50 = +4.50 D.
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Standard text used for this page: Brooks CW, Borish IM. System for Ophthalmic Dispensing, 3rd ed. Butterworth-Heinemann, ch. 12 (spherical equivalent); Ledford JK. Certified Ophthalmic Assistant Exam Review Manual, 3rd ed. SLACK, contact lens chapter answers (SE method). The Iowa optics review is linked under sources.
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Frequently asked questions
How do you calculate spherical equivalent?
Take the sphere plus half the cylinder, keeping signs; the result is a sphere with no axis. For −2.00 −1.00 × 180: −2.00 + (−0.50) = −2.50 D.
Sources: Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 12, pp. 300–301 (spherical equivalent) (opens in a new tab) ; Ledford, Certified Ophthalmic Assistant Exam Review Manual, 3rd ed. (textbook), ch. 3 answers, printed pp. 34, 37 (opens in a new tab)
Is spherical equivalent the same as the power at 45 degrees from the axis?
The numbers match: 45° from the axis, the sin² formula gives sphere + half the cylinder. They mean different things, though. The spherical equivalent is a stand-in sphere for the whole lens; the 45° value is the power along one line.
Sources: Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 12, pp. 300–301 (spherical equivalent) (opens in a new tab) ; University of Iowa EyeRounds — Wilkinson & Shahid, Optics Review (PDF), pp. 42–43 (opens in a new tab)
Can spherical equivalent be zero with cylinder present?
Yes. If the sphere is exactly minus half the cylinder, they cancel. +1.50 −3.00 × 090 has a spherical equivalent of 0.00, though it is far from a plano lens.
Sources: Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 12, pp. 300–301 (spherical equivalent) (opens in a new tab) ; Ledford, Certified Ophthalmic Assistant Exam Review Manual, 3rd ed. (textbook), ch. 3 answers, printed pp. 34, 37 (opens in a new tab)
Official sources
- Brooks & Borish, System for Ophthalmic Dispensing, 3rd ed. (textbook), ch. 12, pp. 300–301 (spherical equivalent) (opens in a new tab)
- University of Iowa EyeRounds — Wilkinson & Shahid, Optics Review (PDF), pp. 42–43 (opens in a new tab)
- Ledford, Certified Ophthalmic Assistant Exam Review Manual, 3rd ed. (textbook), ch. 3 answers, printed pp. 34, 37 (opens in a new tab)
Last reviewed . Requirements, fees, and dates change — always confirm with the official source before you register or apply. ABO-NCLE and IJCAHPO are the only authorities for their own exam facts, so those facts rest on a single source.