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Prentice's Rule Calculator

Toric-aware meridional prism analysis — dual eye with binocular imbalance check

Δ = (d/10) × F(meridian)where d = decentration in mm, F = power at that meridian
Meridional power: F(θ) = Fsph + Fcyl × sin²(θ − axis)

OD (Right Eye)

Spectacle Rx
Decentration

+ = nasal/in

+ = superior

OS (Left Eye)

Spectacle Rx
Decentration

+ = nasal/in

+ = superior

Binocular Vertical Imbalance: 0.25Δ — PASS
ANSI Z80.1-2020 §5.3.2 allows ≤0.33Δ vertical imbalance between eyes.

OD — Right Eye Results

Horizontal Prism
1.80 Δ
Base Direction
Base IN
Meridian Power
-6.00D
ANSI Fail +1.13Δ over
Allowed:≤0.67Δ
Induced:1.80Δ
Over by:+1.13Δ
Why Base IN? Minus lens — base direction is opposite to decentration direction. Decentering in creates base in.

Significantly over tolerance by 1.13Δ. Must recut or regrind with compensating prism. Do not dispense.

Vertical Prism
0.75 Δ
Base Direction
Base DOWN
Meridian Power
-7.50D
ANSI Pass ≤1.88Δ
Allowed:≤1.88Δ
Induced:0.75Δ
Why Base DOWN? Minus lens — base direction is opposite to decentration direction. Decentering in creates base down.

Within ANSI tolerance. No correction required.

OD Vector Resultant
1.95 Δ
Resultant Angle
22.6°
Vector analysis: Total prism magnitude combining horizontal (1.80Δ) and vertical (0.75Δ) components. Resultant = √(H² + V²).

OS — Left Eye Results

Horizontal Prism
1.21 Δ
Base Direction
Base IN
Meridian Power
-4.03D
ANSI Fail +0.54Δ over
Allowed:≤0.67Δ
Induced:1.21Δ
Over by:+0.54Δ
Why Base IN? Minus lens — base direction is opposite to decentration direction. Decentering in creates base in.

Exceeds tolerance by 0.54Δ. Remount with corrected horizontal centering. Symptomatic risk moderate.

Vertical Prism
0.50 Δ
Base Direction
Base DOWN
Meridian Power
-4.97D
ANSI Fail +0.17Δ over
Allowed:≤0.33Δ
Induced:0.50Δ
Over by:+0.17Δ
Why Base DOWN? Minus lens — base direction is opposite to decentration direction. Decentering in creates base down.

Marginally over tolerance (0.17Δ). Re-verify seg height or OC placement. Patient may adapt.

OS Vector Resultant
1.31 Δ
Resultant Angle
22.3°
Vector analysis: Total prism magnitude combining horizontal (1.21Δ) and vertical (0.50Δ) components. Resultant = √(H² + V²).

ANSI Z80.1-2020 Prism Tolerance Reference

Horizontal (Monocular)

≤6.50D: ±0.67Δ

>6.50D: ±0.25Δ/D

Vertical (Monocular)

≤6.50D: ±0.33Δ

>6.50D: ±0.25Δ/D

Vertical (Binocular)

≤0.33Δ imbalance between eyes

Primary diplopia risk factor

Reference: ANSI Z80.1-2020 §5.3 — Prism Imbalance Tolerances. Tolerances apply to finished prescription lenses measured at the optical center. Toric lenses: tolerance applied per principal meridian.