Find SPH and CYL
Take both values from the same eye’s prescription. A minus sign and a plus sign produce different calculations.
Sphere + half the cylinder · SE = SPH + CYL/2
Spherical Equivalent Calculator
Calculate spherical equivalent from sphere (SPH) and cylinder (CYL). Get the exact result, quarter-diopter rounding, and a clear breakdown of the formula.
Calculate Your Spherical Equivalent
One eye at a time. Use the plus or minus signs on your prescription.
SE summarizes optical power. It does not preserve the full astigmatism correction or issue a glasses or contact lens prescription.
Plus & minus CYL supportedExact value shown first
Understand the calculation
Spherical Equivalent Formula: SPH + CYL/2
Spherical equivalent (SE) combines sphere power and half the cylinder power into one value, measured in diopters (D). Keep each value’s original sign.
THE FORMULA
SE=SPH+CYL2
Sphere + half the cylinder
Divide CYL by two
For CYL −1.00 D, half is −0.50 D. For CYL +1.00 D, half is +0.50 D.
Add the sphere power
With SPH −3.00 D and CYL −1.00 D, the result is −3.00 + (−0.50) = −3.50 D.
The idea behind SE
What Does Spherical Equivalent Mean?
It is the average of the powers in the two principal meridians: SPH and SPH + CYL. It summarizes the prescription without retaining cylinder power or its axis.
Two meridian powers → one average
Same SE does not mean the same prescription
SPH −2.00 / CYL −2.00 and SPH −3.00 / CYL 0.00 both have an SE of −3.00 D. They have different cylinder corrections.
−2.00 / −2.00SE −3.00 D
−3.00 / 0.00SE −3.00 D
For astigmatism, a single spherical value cannot describe the full correction. This calculator does not decide whether a spherical lens is suitable.
Check the signs
Spherical Equivalent Calculation Examples
These examples show the exact result before rounding. Plus cylinder, minus cylinder and plano all use the same formula.
| Example / SPH | CYL | CYL ÷ 2 | Exact SE |
|---|---|---|---|
| Minus cylinderSPH −3.00 D | −1.00 | −0.50 | −3.50 D |
| Plus cylinderSPH +2.00 D | +1.00 | +0.50 | +2.50 D |
| Plano sphereSPH 0.00 D | −1.50 | −0.75 | −0.75 D |
| Between quarter-diopter stepsSPH −2.00 D | −0.25 | −0.125 | −2.125 D |
Exact calculation first. Rounded display second.
The tool also shows the nearest 0.25 D. At an exact midpoint, it rounds away from zero: −2.125 → −2.25 D and +2.125 → +2.25 D. This is a display convention, not a lens-selection rule.
Choose the right calculation
Spherical Equivalent vs Vertex Conversion
Spherical equivalent
Combines SPH and CYL into an average power at the same lens position. No vertex distance or axis is used.
Glasses ↔ contacts conversion
Adjusts theoretical optical power for the distance between glasses and the cornea. For astigmatism, our main tool converts both meridians.
Quick answers
Spherical Equivalent Calculator FAQ
Does axis affect spherical equivalent?
No. The formula uses sphere and cylinder power only. Axis remains important for describing the full astigmatic prescription, but it does not change this average.
Does the formula work with plus cylinder?
Yes. Preserve the sign: SPH +2.00 with CYL +1.00 gives SE +2.50 D. If a prescription is correctly transposed between plus- and minus-cylinder notation, its spherical equivalent stays the same. Use the plus/minus cylinder converter to check both notations.
What if my prescription says PL or has no cylinder?
PL or plano means zero sphere, which this calculator accepts. Enter 0 for a confirmed zero CYL. Do not guess an unreadable or missing cylinder value; check the prescription before calculating.
Why can the exact result have three decimal places?
Halving a cylinder such as −0.25 D produces −0.125 D. The exact result keeps that precision. Quarter-diopter rounding is shown separately so you can see the difference.
Can I use spherical equivalent to order contact lenses?
This result alone is not a contact lens prescription. It does not determine the lens product, fit, base curve or diameter, and it does not preserve full astigmatism correction. Use your fitted contact lens prescription.
Formula reference & method
The SPH + CYL/2 relationship is explained in the University of Iowa’s refraction teaching material (slide 18). Our implementation keeps the exact result separate from its rounded display. Calculations run in your browser; entered values are not sent by this tool.
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