Prentice’s rule gives the prism a lens induces when the line of sight does not pass through the optical centre: the prism in prism dioptres equals the decentration in centimetres times the lens power. Enter the lens power and the decentration and this calculator returns the induced prism, or enter any two of prism, power and decentration and it solves for the third. Useful for optician students checking their understanding of the rule, technicians verifying a centration job, and dispensers troubleshooting a symptomatic frame.
The Formula
P = c × F, where P is the prism in prism dioptres (Δ), c is the decentration in centimetres, and F is the lens power in dioptres.
Because decentration is usually noted in millimetres, the bench form is P = (decentration in mm × power) ÷ 10. Rearranged, the decentration that produces a target prism is c = P ÷ F, and the power that produces a given prism at a known decentration is F = P ÷ c.
Worked Examples
- A +5.00 D lens with the line of sight 4 mm from the optical centre: 0.4 cm × 5.00 = 2.0 Δ.
- A −4.00 D lens decentred 2 mm: 0.2 cm × 4.00 = 0.8 Δ per eye.
- To build 1.0 Δ into a +2.50 D lens, decentre it 1.0 ÷ 2.50 = 0.4 cm, or 4 mm.
Use the power in the meridian along which the decentration occurs: vertical decentration uses the vertical-meridian power, horizontal uses the horizontal-meridian power. As the StatPearls optics reference defines it, one prism dioptre deviates light 1 centimetre at a distance of 1 metre.
Which Way the Base Points
Plus lens: the base points toward the optical centre. Minus lens: the base points away from it.
A plus lens is thick in the middle and bends light toward that centre; a minus lens is thin in the middle and bends it toward the edge. So a plus lens whose centre sits above the pupil induces base-up prism, while a minus lens in the same position induces base-down.
Why It Matters at the Desk
A horizontal PD error and a misplaced optical centre are the same thing: the visual axis falls a few millimetres off centre, and the wearer looks through prism. That is why every centration tolerance traces back to this equation. A 3 mm PD error on a −5.00 D lens already induces 1.5 Δ per eye, and the effect scales with power, so the same error matters far more in a strong prescription. The full derivation, base directions, and the vertical imbalance anisometropia produces are covered in the guide to Prentice’s rule and induced prism, and the manufacturing limits it feeds in eyeglass prescription tolerances. A correct centration starts with an accurate monocular PD and fitting height, which Optogrid measures from a photo of the patient in the chosen frame.
Frequently Asked Questions
What is Prentice’s rule?
Prentice’s rule gives the prism a lens induces away from its optical centre: P = c × F, where P is the prism in prism dioptres, c is the decentration in centimetres, and F is the lens power in dioptres. In millimetres it is P = (decentration in mm × power) ÷ 10.
How do you calculate induced prism from a PD error?
Convert the PD error to centimetres and multiply by the lens power. A 3 mm error on a −5.00 D lens gives 0.3 cm × 5.00 = 1.5 Δ per eye. Because the effect scales with power, the same error matters far more in a strong prescription.
Which way does the induced prism base point?
For a plus lens the base points toward the optical centre; for a minus lens it points away. A plus lens with its centre above the pupil induces base-up; a minus lens in the same spot induces base-down.
What is a prism dioptre?
A prism dioptre (Δ) deviates a ray of light 1 centimetre measured at a distance of 1 metre. It is the unit for both prescribed prism and the unwanted prism Prentice’s rule calculates.
How do you decentre a lens to create prism?
Rearrange the rule to c = P ÷ F. To create 1.0 Δ in a +2.50 D lens, decentre it 0.4 cm (4 mm). Decentring a plus lens inward gives base-in prism, a common way to add a small amount of prescribed prism without grinding it.
I am a seasoned software engineer with over two decades of experience and a deep-rooted background in the optical industry, thanks to a family business. Driven by a passion for developing impactful software solutions, I pride myself on being a dedicated problem solver who strives to transform challenges into opportunities for innovation.