About the Spherical Equivalent Calculator
A glasses prescription has a sphere (SPH), a cylinder (CYL) for astigmatism and an axis. The spherical equivalent is a single number that sums up the overall power of the lens, the sphere plus half the cylinder. It is used to compare prescriptions and in research. This calculator gives it and also writes the same prescription in the transposed form, with the cylinder sign changed. Type the sphere, the cylinder and, optionally, the axis and the spherical equivalent appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Spherical Equivalent Calculator
- 1Enter the sphere, the cylinder and, optionally, the axis.
- 2Pick the units or options from the menus if the spherical equivalent tool offers them.
- 3Read the spherical equivalent in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the spherical equivalent
Opticians use transposition to move between minus-cylinder and plus-cylinder notation. Students and researchers use the spherical equivalent to describe how short- or long-sighted an eye is in one number.
A spherical equivalent of zero does not mean perfect vision: a prescription of +1.00 −2.00 has a spherical equivalent of zero but still needs correction for astigmatism. It is only a summary.
How the spherical equivalent is worked out
Spherical equivalent = sphere + cylinder ÷ 2. Transposition: new sphere = sphere + cylinder, new cylinder = −cylinder, new axis = axis ± 90 degrees. A prescription of −2.00 −1.00 × 90 has a spherical equivalent of −2.50 D. Transposed it reads −3.00 +1.00 × 180. Both give the eye exactly the same correction. A prescription of +1.00 −2.00 × 45 has an equivalent of 0.00 and transposes to −1.00 +2.00 × 135.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Spherical equivalent
- Transposed prescription
- Axis adjusted
Mistakes to avoid with spherical equivalent
This tool is for information and education; it cannot replace an eye test or a prescription written by a professional. The axis, in degrees from 1 to 180, is optional. The numbers should be entered as they are written, including their sign.
On phone and computer
On a phone, type into the boxes one after another and read the spherical equivalent underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the spherical equivalent move. The spherical equivalent calculator works the same on both. A prescription has several numbers, and a few helpers make the units clearer. Convert units with the Unit Converter, check angles with the Angle Converter, and look at a general health number with the BMI Calculator.
Features
- Equivalent zero is not perfect vision
- Keep the signs
- Use your optician's prescription
- Clear messages when the spherical equivalent inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate spherical equivalent?
Spherical equivalent = sphere + cylinder ÷ 2. Transposition: new sphere = sphere + cylinder, new cylinder = −cylinder, new axis = axis ± 90 degrees. A prescription of −2.00 −1.00 × 90 has a spherical equivalent of −2.50 D. Transposed it reads −3.00 +1.00 × 180. Both give the eye exactly the same correction. A prescription of +1.00 −2.00 × 45 has an equivalent of 0.00 and transposes to −1.00 +2.00 × 135.
What is the formula for spherical equivalent?
Spherical equivalent = sphere + cylinder ÷ 2. Transposition: new sphere = sphere + cylinder, new cylinder = −cylinder, new axis = axis ± 90 degrees. The spherical equivalent calculator applies it exactly and rounds only the displayed answer to six significant figures.
What does the axis show?
The direction of the astigmatism, in degrees from 1 to 180.
Why transpose a prescription?
Some practitioners write the cylinder as minus, others as plus. The two forms describe the same lens.
Can I order glasses from this?
No. Always use the prescription given by your optician.
Is this spherical equivalent calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.