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

Name: Prism Diopter Calculator
Availability: InStock
Author: Nham Vu

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