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Vertex distance compensation
When a lens moves closer to or farther from the eye its effective power changes. The compensated power is F' = F / (1 - d x F), where d is the distance moved in meters, positive when the lens moves closer. Moving +10.00 D from a 12 mm vertex to the corneal plane gives +11.36 D; moving -10.00 D the same way gives -8.93 D. Compensation is usually considered from about 4.00 D up.
Vertex compensation calculator
Works in both directions: spectacle plane to corneal plane (set the new vertex to 0 mm for a contact lens power) or cornea back out to a spectacle plane. Cylinder is handled by compensating both principal meridians.
OD result
Compensated: +11.36 sph (nearest quarter: +11.25 sph)
- d = (12 - 0) / 1000 = 0.012 m (positive when the lens moves closer to the eye).
- Each principal meridian compensates with F' = F / (1 - d x F).
- First meridian: +10.00 / (1 - 0.012 x 10.00) = +11.36 D.
OS result
Compensated: -8.93 sph (nearest quarter: -9.00 sph)
- d = (12 - 0) / 1000 = 0.012 m (positive when the lens moves closer to the eye).
- Each principal meridian compensates with F' = F / (1 - d x F).
- First meridian: -10.00 / (1 - 0.012 x -10.00) = -8.93 D.
Canonical checks: +10.00 D at 12 mm becomes +11.36 D at the corneal plane; -10.00 D becomes -8.93 D. Compensation is usually considered for powers of about 4.00 D and above.
Effective power at the eye
The power the eye actually experiences from a lens fitted at a given vertex distance: the same compensation with the new plane at the cornea.
Effective power at the cornea: +11.36 D (+10.00 / (1 - 0.012 x +10.00))
Practice vertex compensation
Unlimited generated problems with exact answers and worked steps.
Go deeper
The vertex distance guide derives the formula and covers the sign convention in both directions. Common fitting distances live in the vertex distance reference.
Frequently asked questions
What is vertex distance compensation?
When a lens moves closer to or farther from the eye its effective power changes. The compensated power is F' = F / (1 - d x F), where d is the distance moved in meters (positive when moving closer to the eye). Moving +10.00 D from a 12 mm vertex to the corneal plane gives +11.36 D; -10.00 D gives -8.93 D.
When does vertex distance matter clinically?
A common rule of thumb is powers of about 4.00 D and above, where a normal change in fitting distance shifts the effective power by an eighth diopter or more. For contact lens conversions from high-power spectacles it always matters.
Why do plus and minus lenses compensate in opposite directions?
Moving a plus lens closer to the eye weakens its effect, so the compensated lens must be stronger. Moving a minus lens closer strengthens its effect, so the compensated lens can be weaker in magnitude.
What does effective power at near mean?
It is the same formula applied at a specific working geometry: the power the eye actually experiences at its corneal plane given the lens sitting at the fitted vertex distance. The calculator reports it whenever you set the new vertex to 0 mm.