Lens Decentration and Minimum Blank Size
Lens Decentration and Minimum Blank Size
Decentration per eye is (frame PD − patient PD) ÷ 2, and the blank is the effective diameter plus twice that plus a working allowance. A 67 mm frame PD on a 62 mm patient needs 2.5 mm per lens.
Frame and patient PD → blank size
Boxing systemA 50/17 frame (frame PD 67 mm) on a 62 mm patient PD, effective diameter 53 mm, 2 mm allowance, 4.00 D lens
Decentration, the blank it needs, and the prism it induces
- THE BRACKETS, which are the trap
- the source read prints the first formula as “Frame pupillary distance (PD) − Patient (Px) PD / 2”, with no brackets. Read literally on its own worked numbers that is 67 − 31 = 36 mm, which is absurd; the worked example alongside it gives “67 − 62/2 = 2.5” and says the centre moves 2.5 mm nasally on each lens. So the intended form is (frame PD − patient PD) ÷ 2 and this page states it with the brackets rather than reprinting the ambiguity
- the minimum blank, from two sources that agree
- one gives “MBS = 2(decentration) + ED + 2” and the other “MSU = FCD − PD + EFFECTIVE DIAMETER (ED)”. Those are the same formula, because the frame PD less the patient PD is exactly TWICE the per-eye decentration. The proof behind this page asserts they agree across a sweep of frame, patient and shape sizes rather than at the one worked example
- the allowance, and the disagreement about it
- the first source builds 2 mm into the formula. The second states the reason verbatim — “always add 2mm to allow for blishes on the edge of the lens” — and reaches 65 mm on its own case. But that same publication’s earlier article works its own example as “67 − 62 + 53 = 58mm blank” with NO allowance, where the allowance would make it 60. Both answers are printed above and the allowance is an input, because reconciling them silently would hide a real 2 mm
- the prism, by Prentice’s rule
- a blank glazed to the frame’s own centres instead of the patient’s is a decentred lens, and Prentice’s rule gives the prism: the decentration in centimetres times the absolute power. At 4.00 D a 2.5 mm error is 1.00Δ. The power must be the power in the MERIDIAN the lens is decentred along, which on a sphero-cylinder at an oblique axis comes from the oblique meridian page and is neither the sphere nor the sphere plus the cylinder
- ANSI Z80.1, as reported and not as read
- the study guide read for this category gives the maximum allowable prismatic imbalance as 0.33Δ vertical and 0.67Δ horizontal. Run backwards, at 4.00 D those are reached at 0.83 mm and 1.68 mm of decentration, which are the two figures above. THE STANDARD ITSELF WAS NOT READ — it is a purchased document — and the tolerance governs the IMBALANCE between the two lenses, which equals the prism in one lens only when the other is correctly centred or plano
Worked example
A 50/17 frame (frame PD 67 mm) on a 62 mm patient PD, effective diameter 53 mm, 2 mm allowance, 4.00 D lens
Decentration. (67 − 62) ÷ 2 = 2.5 mm per lens, nasally. The total across both lenses is 5 mm, which is the frame PD less the patient PD
Minimum blank. 53 + (2 × 2.5) + 2 = 60.0 mm
Or without the allowance, which is how one of the two sources works its own example: 53 + 5 = 58.0 mm. The 2 mm is a real disagreement between two articles in the same publication and both answers are printed above
The other source's worked case, reproduced. A 70 mm frame PD on a 62 mm patient with a 55 mm effective diameter: 8 mm total decentration, 55 + 8 + 2 = 65 mm, which is exactly the figure it reaches
And its monocular case. Half of 70 is 35; less a 31 mm right monocular PD gives 4 mm in for that eye, which is also what it prints. Note that the binocular form gives 4 mm for BOTH eyes here only because 31 is half of 62
The prism if it is ignored. 2.5 mm on a 4.00 D lens is 0.25 cm × 4.00 = 1.00Δ, which is three times the 0.33Δ vertical imbalance tolerance and 1.5 times the 0.67Δ horizontal one as the study guide reports them from ANSI Z80.1 — if the fellow lens is correctly centred, so that this lens's prism is the whole imbalance
Run backwards. At 4.00 D the vertical tolerance is reached at 0.83 mm of decentration and the horizontal at 1.68 mm. Sub-millimetre centration at this power is the tolerance and not a refinement
The temporal case. Reverse the two distances — a 62 mm frame PD on a 68 mm patient — and the decentration is −3.0 mm, temporal, and the blank is 53 + 6 + 2 = 61.0 mm. A formula without the absolute value would say 49 mm and the job would be short by 12 mm of glass
Minimum blank size across frame and patient combinations
| Frame PD | Patient PD | Decentration per eye | ED 48 mm | ED 53 mm | ED 58 mm |
|---|---|---|---|---|---|
| 62 | 62 | 0.0 mm | 50.0 | 55.0 | 60.0 |
| 64 | 62 | 1.0 mm nasal | 52.0 | 57.0 | 62.0 |
| 67 | 62 | 2.5 mm nasal | 55.0 | 60.0 | 65.0 |
| 70 | 62 | 4.0 mm nasal | 58.0 | 63.0 | 68.0 |
| 74 | 62 | 6.0 mm nasal | 62.0 | 67.0 | 72.0 |
| 80 | 52 | 14.0 mm nasal | 78.0 | 83.0 | 88.0 |
| 62 | 68 | 3.0 mm temporal | 56.0 | 61.0 | 66.0 |
Decentration against the reported ANSI Z80.1 imbalance tolerances
| Lens power in the meridian | Prism per mm | Decentration reaching 0.33Δ | Decentration reaching 0.67Δ |
|---|---|---|---|
| 0.50 D | 0.05Δ | 6.60 mm | 13.40 mm |
| 1.00 D | 0.10Δ | 3.30 mm | 6.70 mm |
| 2.00 D | 0.20Δ | 1.65 mm | 3.35 mm |
| 2.75 D | 0.28Δ | 1.20 mm | 2.44 mm |
| 4.00 D | 0.40Δ | 0.83 mm | 1.68 mm |
| 6.00 D | 0.60Δ | 0.55 mm | 1.12 mm |
| 10.00 D | 1.00Δ | 0.33 mm | 0.67 mm |
The frame is wider than the face, so the optical centre has to move and the blank has to be bigger
Frames are manufactured to fit faces, not to centre lenses. A 50/17 frame places its two lens centres 67 mm apart; a patient whose pupils are 62 mm apart therefore needs each optical centre moved 2.5 mm nasally, and the arithmetic is simply the difference halved. The brackets matter: the source read prints the formula without them, and read literally it gives 36 mm rather than 2.5 mm. Its own worked example settles the reading, which is why this page states the convention explicitly instead of reprinting the typography.
Moving the centre means the lens has to be cut from a blank big enough to reach it, and the published formula is the effective diameter plus twice the decentration plus a working allowance. Two independent sources give it — one as “2(decentration) + ED + 2” and the other as “FCD − PD + ED” plus 2 mm — and they are the same formula, because the frame PD less the patient PD is twice the per-eye decentration. The effective diameter is the input most often got wrong, and one of the sources says so in as many words: it is not the widest point and not the longest axis, but twice the longest distance from the boxed centre to the rim.
The allowance is a printed disagreement rather than a constant, and it is on this page as an input because of that. One article in a publication adds 2 mm with the reason attached; an earlier article in the same publication works its own example without it and reaches a blank 2 mm smaller. Neither is a misprint and neither is the standard, so both answers appear in the result list and the reader decides. The same page also keeps the signed decentration visible, because a patient wider than the frame decentres temporally and a formula that forgets the absolute value under-states that blank by four times the decentration.
What makes the centration a tolerance rather than a refinement is the prism. Prentice’s rule turns any centration error into prism — at 4.00 D every millimetre is 0.4Δ — and the study guide read for this category reports ANSI Z80.1 as allowing a prismatic imbalance of 0.33Δ vertically and 0.67Δ horizontally. Run backwards at 4.00 D those are 0.83 mm and 1.68 mm, so a blank glazed to the frame’s centres instead of the patient’s is outside both. ANSI Z80.1 is a purchased standard and was not read, here or in the record that first reported those numbers, so they are given as that guide reports them. One further caution the arithmetic hides: the power Prentice’s rule needs is the power in the meridian you are decentring along, which on a sphero-cylinder at an oblique axis is on the oblique meridian page and is neither the sphere nor the sphere plus the cylinder.
Frequently asked questions
How do I calculate lens decentration?
Subtract the patient’s binocular pupillary distance from the frame PD and halve the result: (67 − 62) ÷ 2 = 2.5 mm nasally per lens. For a prescription lens the monocular form is better — half the frame PD less that eye’s monocular PD — because the binocular form assumes a symmetrical face.
What is the formula for minimum blank size?
The effective diameter plus twice the per-eye decentration plus a working allowance. On a 67 mm frame PD, a 62 mm patient and a 53 mm effective diameter that is 53 + 5 + 2 = 60 mm. One of the two sources read works its own example without the allowance and gets 58 mm, so both are shown.
Is the effective diameter the same as the A measurement?
No. The effective diameter is twice the longest distance from the boxed centre of the lens shape to its edge, and the source read warns explicitly against using the widest point or the longest axis instead. It comes off the tracer or the pattern; estimating it from the shape is the commonest error in this calculation.
How much decentration does ANSI Z80.1 allow?
As the study guide read for this category reports it: a maximum prismatic imbalance of 0.33Δ vertically and 0.67Δ horizontally, which at 4.00 D are reached at 0.83 mm and 1.68 mm of decentration. The standard itself is a purchased document and was not read, so these are given as that guide reports them, and the tolerance governs the imbalance between the two lenses rather than one lens alone.
What if the patient’s PD is wider than the frame PD?
Then the decentration is temporal rather than nasal, the figure above goes negative, and the blank still has to be bigger: 53 mm of effective diameter with 3 mm of temporal decentration needs 61 mm. A formula written without the absolute value subtracts instead of adding and under-states the blank by four times the decentration.
Related calculators
References
- The power of lens decentration. Insight, insightnews.com.au. Accessed 10 October 2026.
- Finding the minimum lens blank size — part 2. Insight, insightnews.com.au. Accessed 10 October 2026.
- Optician’s Friend. Optics Study Guide. opticiansfriend.com. Accessed 10 October 2026. (The page states that its information may contain mistakes and should be independently verified, so every formula taken from it here is corroborated from a second source.)
- Open Exam Prep. Section 15.1: ANSI Z80.1 Prescription Tolerances, National Opticianry Competency Examination study guide. open-exam-prep.com. Accessed 10 October 2026. (ANSI Z80.1 itself is a purchased standard and was not read.)
Not medical advice. For healthcare professionals and education. Reference intervals vary by laboratory and assay — always use your own laboratory's. Never base a dose or a treatment decision on this page alone. Full disclaimer at calcengines.com/disclaimer/