Decentration Calculator
This calculator works out how far each lens's optical center must move from the frame's geometric center to line up with the patient's pupil. Enter the patient's PD and the frame's A and DBL measurements. It returns the frame PD, the total decentration and the decentration per eye, with its direction.
Decentration
How far each lens’s optical center sits from the geometric center of the frame to align with the patient’s pupils.
Formula
Frame PD = A + DBL ; total dec = Frame PD − Patient PD ; per-eye dec = total dec / 2.
Decentration formula
Frame PD = A + DBL (also called the geometric center distance). Total decentration = frame PD − patient PD. Decentration per eye = total ÷ 2. When the frame PD is larger than the patient's PD, the usual case, the optical centers move in (nasally). When it is smaller, they move out (temporally).
Worked examples
A 50, DBL 20, PD 63: frame PD = 70 mm, total decentration 7 mm, so 3.5 mm in per eye. The calculator shows 3.5 mm in (nasal).
A 47, DBL 15, PD 66: frame PD = 62 mm and total decentration -4 mm, so 2.0 mm out (temporal) per eye.
Monocular PDs: decenter each eye from half the frame PD. With A 50 and DBL 20, half the frame PD is 35 mm, so monocular PDs of 31 and 32.5 need 4.0 mm in OD and 2.5 mm in OS. The calculator takes a binocular PD, so do this step by hand.
Reading glasses: use the near PD. The same frame with a near PD of 60 needs 5.0 mm in per eye.
When to use it: avoiding induced prism
Use it when you lay out single-vision lenses, check a finished job, or work out a blank size. Suppose the first frame got -5.00 D lenses with no decentration. Each optical center would sit 3.5 mm out from the pupil, and by Prentice's rule each lens would induce 0.35 × 5.00 = 1.75Δ base in: 3.50Δ base in for the pair. At this power ANSI Z80.1-2020 checks placement rather than prism: the distance between the optical centers must be within ±2.5 mm of the ordered PD, and here it is 70 mm against a 63 mm PD, 7 mm off, so the pair fails.
The 0.67Δ limit on net horizontal prism applies only up to ±2.75 D. With -2.00 D lenses in the same frame, each lens would induce 0.70Δ base in, 1.40Δ for the pair, which also fails, this time on the prism limit.
Common mistakes
Subtracting in the wrong order, which swaps in and out. Forgetting to halve the total. Using a binocular PD for one eye when the monocular PDs differ. Using the distance PD for single-vision reading glasses. Decentration also drives minimum blank size: the more you decenter, the larger the blank you need.
Decentration on the ABO exam
Decentration is the first step in several ABO problems: minimum blank size, induced prism from an incorrect PD, and multifocal segment inset. Review Pupillary Distance (PD) and Frame Measurements (Boxing System), then try the free ABO practice test.
Frequently asked questions
What is the decentration formula?
Decentration per eye = (A + DBL − patient PD) ÷ 2. With A 50, DBL 20 and a 63 mm PD: (70 − 63) ÷ 2 = 3.5 mm in per eye.
Which way do I decenter, in or out?
Toward the pupil. If the frame PD is wider than the patient's PD, move the optical centers in (nasally). If it is narrower, move them out (temporally).
Is frame PD the same as the patient's PD?
No. Frame PD, also called the geometric center distance, is A + DBL and describes the frame. The patient's PD is measured between the centers of the pupils. Decentration is the difference between the two, split between the lenses.
What happens if lenses are not decentered?
The wearer looks through a point away from each optical center and gets prism that was not prescribed. Prentice's rule gives the amount for each lens: the lens power in diopters times the displacement in centimeters.
Related tools and study guides
Ready to try the math on exam-style questions?
Take a free ABO practice test: instant scoring and an explanation after every answer. No card required.
Start the free practice test →