What is Prentice's rule?

Prentice's rule states that the prismatic effect (in prism diopters, Δ) at a point on a lens equals the lens power (in diopters) multiplied by the decentration (in centimeters) from the optical center: Δ = F × d(cm).

What is a prism diopter?

A prism diopter (Δ) is a unit of prism power that deflects a ray of light 1 cm at a distance of 1 meter. It equals approximately 0.573° of angular deviation.

How do I determine the base direction?

For a plus lens, when a point is nasal (decentration toward nose), the induced prism is base-in. For a minus lens with the same nasal decentration, the prism is base-out. This calculator shows the base direction automatically.

A centrad (%) is a unit where 1% equals 1 cm deflection at 100 cm (1 meter). It is numerically equivalent to a prism diopter.

What decentration is clinically significant?

Any induced prism above 0.5 Δ can cause symptoms in sensitive patients. Prescriptions with higher powers require tighter decentration tolerances because the induced prism grows proportionally.

Can this calculator handle oblique prisms?

This tool computes horizontal (base-in/out) and vertical (base-up/down) prismatic effects separately. Enter the horizontal and vertical decentrations in the respective fields to get each component.

Prism Diopter Calculator

Apply Prentice's rule to find the prismatic effect at any point on a spectacle lens, and convert prism diopters to prism angles.

Enter lens power and decentration to compute prismatic effect via P = F × d (Prentice's rule).

Lens Power (D)

Positive (+) for converging lens, negative (−) for diverging.

Horizontal Dec. (mm)

+ = temporal, − = nasal.

Vertical Dec. (mm)

+ = up, − = down.

Prentice's Rule

P = F × d

P
Prism effect (Δ)

F
Lens power (D)

d
Decentration (cm)

Decentration must be in centimeters. Enter millimeters above — the calculator converts automatically (÷ 10).

Base Direction Guide

Lens	Decentration	Prism Base
Plus (+)	Nasal (inward)	Base-In
Plus (+)	Temporal (outward)	Base-Out
Minus (−)	Nasal (inward)	Base-Out
Minus (−)	Temporal (outward)	Base-In

For vertical decentration: plus lens shifted down → base-down; shifted up → base-up. Minus lens: opposite direction.

Unit Reference

Prism Δ	Degrees (°)	Centrads (%)
1	0.573°	1.000%
2	1.146°	2.000%
5	2.862°	5.000%
10	5.711°	10.000%
20	11.310°	20.000%

Conversion: 1 Δ = arctan(0.01) ≈ 0.5729°. Centrads and prism diopters are numerically equal for clinical purposes.

Summary

This Prism Diopter Calculator applies Prentice's rule to determine the prismatic effect at any off-center point on a spectacle lens given its power and the decentration distance. It also converts between prism diopters, degrees, and centrads so optometrists and students can quickly switch between units used in clinical and academic settings.

How it works

Enter the lens power in diopters (D) — use a positive value for plus lenses and negative for minus lenses.
Enter the decentration in millimeters — the distance from the optical center to the point of interest.
The tool applies Prentice's rule: Prism (Δ) = Power (D) × Decentration (cm).
The direction of the prism base is shown: base-in or base-out depending on lens sign and decentration direction.
Use the unit converter tab to switch between prism diopters (Δ), degrees, and centrad (%).

Use cases

Verify induced prism when a frame is not centered on the optical axis.
Calculate prismatic demand for patients with binocular vision disorders.
Convert prescribed prism power between diopters, degrees, and centrads.
Check decentration limits before cutting spectacle lenses.
Teach or study optometry: quickly explore Prentice's rule with live feedback.
Estimate vertical or horizontal prism imbalance in anisometropic prescriptions.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu