Transposition Calculator Glasses

Optical Transposition Calculator

Convert eyeglass prescriptions between Plus-Cylinder and Minus-Cylinder forms.

Transposed Result:

New Sphere

New Cylinder

New Axis

function calculateTransposition() { var s = parseFloat(document.getElementById('inputSphere').value); var c = parseFloat(document.getElementById('inputCylinder').value); var a = parseInt(document.getElementById('inputAxis').value); if (isNaN(s) || isNaN(c) || isNaN(a)) { alert("Please enter valid numbers for Sphere, Cylinder, and Axis."); return; } if (a 180) { alert("Axis must be between 1 and 180."); return; } // 1. New Sphere = S + C var newSphere = s + c; // 2. New Cylinder = Change sign of C var newCylinder = c * -1; // 3. New Axis = Change by 90 degrees var newAxis; if (a = 0 ? "+" : "") + newSphere.toFixed(2); var fc = (newCylinder >= 0 ? "+" : "") + newCylinder.toFixed(2); var fa = newAxis; document.getElementById('resSphere').innerText = fs; document.getElementById('resCylinder').innerText = fc; document.getElementById('resAxis').innerText = fa + "°"; document.getElementById('stringFormat').innerText = fs + " / " + fc + " x " + fa; document.getElementById('resultDisplay').style.display = 'block'; }

Understanding Lens Transposition in Optometry

In optometry and ophthalmology, an eyeglass prescription can be written in two different but mathematically equivalent formats: plus-cylinder form and minus-cylinder form. While ophthalmologists historically favored plus-cylinder, most modern optometrists and lens laboratories use minus-cylinder form. This transposition calculator allows you to switch between the two seamlessly.

The Three Golden Rules of Transposition

To manually transpose a prescription, you must follow three specific steps. Our tool automates these calculations to ensure accuracy:

1. Sum the Sphere and Cylinder: Algebraically add the current Sphere power and Cylinder power together to determine the new Sphere power.
2. Change the Cylinder Sign: Simply switch the sign of the Cylinder value. If it was negative, make it positive; if it was positive, make it negative. The numeric power remains the same.
3. Rotate the Axis: Move the axis by 90 degrees. If the original axis is 90 or less, add 90. If it is greater than 90, subtract 90. The resulting axis must always be between 1 and 180.

Practical Examples

Example 1: Converting Minus-Cyl to Plus-Cyl
Input: -2.00 SPH / -1.00 CYL x 180
1. New Sphere: -2.00 + (-1.00) = -3.00
2. New Cylinder: -1.00 becomes +1.00
3. New Axis: 180 – 90 = 90
Result: -3.00 / +1.00 x 90

Example 2: Converting Plus-Cyl to Minus-Cyl
Input: +1.50 SPH / +0.50 CYL x 45
1. New Sphere: +1.50 + 0.50 = +2.00
2. New Cylinder: +0.50 becomes -0.50
3. New Axis: 45 + 90 = 135
Result: +2.00 / -0.50 x 135

Why Is Transposition Necessary?

Lens transposition is essential for manufacturing and verification. Optical labs often require prescriptions in minus-cylinder form because surfacing machines and lens blanks are typically designed for minus-cyl geometry. Additionally, transposing allows practitioners to check if two different-looking prescriptions are actually providing the same vision correction to the patient.

Note: While the mathematical result of transposition is identical, always ensure the final axis is written correctly (e.g., 180 instead of 0) to comply with standard clinical notation.