At ±4.00 D and above, a lens needs a different ordered power when it is worn at a different distance from the eye than where it was refracted. This calculator applies the vertex formula to make that adjustment. Enter the refracted power, the refraction vertex and the as-worn vertex, and it returns the compensated power to order. Useful for optician students learning when vertex distance matters, and for opticians and prescribers working with high-power lenses who want to verify the adjustment.
The Formula
F_c = F / (1 − d × F), where F is the refracted power in dioptres, d is the change in vertex distance in metres (positive when the lens is worn closer to the eye than at refraction), and F_c is the power to order.
A lens worn closer to the eye than the phoropter shifts toward plus (less minus, more plus); worn farther, it shifts toward minus (more minus, less plus).
Worked Examples
- −10.00 D refracted at 12 mm, worn at 14 mm (2 mm farther, d = −0.002): −10.00 / (1 − (−0.002) × −10.00) = −10.00 / 0.980 = −10.25 D. Worn farther, it needs more minus.
- +8.00 D refracted at 12 mm, worn at 8 mm (4 mm closer, d = +0.004): +8.00 / (1 − 0.004 × 8.00) = +8.00 / 0.968 = +8.25 D. Worn closer, it needs more plus.
When to Compensate
Two conditions both have to be true: the power is ±4.00 D or more in the meridian, and the as-worn vertex differs from the refraction vertex by more than 2 mm. Below that, the shift stays under a single 0.25 D step. The vertex distance compensation guide covers measurement technique, the distometer, and a full reference table. To convert a spectacle Rx all the way to the cornea, which is the special case of moving the lens onto the eye, use the glasses-to-contacts converter. For toric prescriptions, compensate each meridian separately; the cylinder axis does not change. Accurate as-worn geometry is part of what Optogrid captures from a photo of the patient in the chosen frame.
Frequently Asked Questions
What is the vertex distance formula?
F_c = F / (1 − d × F), where F is the refracted power, d is the change in vertex distance in metres (positive when the lens is worn closer to the eye than at refraction), and F_c is the power to order. Round to the nearest 0.25 D.
When do you compensate for vertex distance?
When the power is ±4.00 D or more in the meridian and the as-worn vertex differs from the refraction vertex by more than 2 mm. Below that, the shift is under 0.25 D.
Which way does the power change?
A lens worn closer to the eye than it was refracted needs a shift toward plus (less minus, more plus). Worn farther, it needs a shift toward minus (more minus, less plus).
Is the refraction vertex 12 or 13.75 mm?
Both are used. Phoropters are often calibrated to 13.75 mm, while 12 mm is the common working assumption. What matters is the difference between the refraction vertex and the as-worn vertex, not either value alone.
How do you compensate an astigmatic prescription?
Apply the formula to each principal meridian separately (the sphere, and the sphere plus the cylinder). The cylinder axis does not change.
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