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Prentice's rule

Prentice's rule gives the prism induced when the line of sight misses the optical center: P = c x F, with c the decentration in centimeters and F the lens power in the meridian of the decentration. Three millimeters of decentration on a 4.00 D lens induces 0.3 x 4.00 = 1.2 prism diopters.

Prentice's rule calculator

Enter each eye and how far the optical center sits from the visual axis. The prism uses the lens power in the meridian of the decentration, not the sphere alone.

OD (right eye)
OS (left eye)
Direction of the decentration
Where the OC sits relative to the line of sight

OD result

Induced prism: 1.20 prism diopters, base up

  1. Power in the vertical (90 degree) meridian: F = S + C x sin^2(90 - axis) = +4.00 D.
  2. Decentration in centimeters: 3 mm = 0.30 cm.
  3. Prentice's rule: P = c x F = 0.30 x 4.00 = 1.20 prism diopters.
  4. A plus lens points its base toward the optical center, so the prism is base up.

OS result

Induced prism: 0.75 prism diopters, base down

  1. Power in the vertical (90 degree) meridian: F = S + C x sin^2(90 - axis) = -2.50 D.
  2. Decentration in centimeters: 3 mm = 0.30 cm.
  3. Prentice's rule: P = c x F = 0.30 x 2.50 = 0.75 prism diopters.
  4. A minus lens points its base away from the optical center, so the prism is base down.

Canonical check: 3 mm of decentration on a 4.00 D meridian induces 0.3 x 4.00 = 1.20 prism diopters.

Practice Prentice's rule

Unlimited generated problems with exact answers and worked steps.

Go deeper

The Prentice's rule guide explains the base direction convention and when the vertical meridian power replaces the sphere. For the anisometropic reading problem, see vertical imbalance.

Frequently asked questions

What is Prentice's rule?

Prentice's rule estimates the prism a wearer gets when the line of sight misses the optical center: prism diopters = decentration in centimeters times the lens power in that meridian. A 3 mm decentration on a 4.00 D lens induces 0.3 x 4.00 = 1.2 prism diopters.

Which direction is the prism base?

As a simplification, a plus lens acts like two prisms base to base at the optical center, so the base points toward the OC; a minus lens is apex to apex, so the base points away from the OC. A complete dispensing analysis considers both eyes and both meridians.

Do I use millimeters or centimeters in Prentice's rule?

The rule takes centimeters. Measurements are usually taken in millimeters, so divide by 10 first: 5 mm is 0.5 cm.

Which power goes into the formula for an astigmatic lens?

The power acting in the meridian of the decentration. For vertical decentration use the power in the vertical (90 degree) meridian, which you can read from the meridian power tool.