The AC/A Ratio: Why Reading Comfort Depends on a Number Nobody Prints
Two systems that are wired together
Accommodation is the eye's ability to increase its power for near objects. Convergence is both eyes turning inward to aim at the same near point. They are not independent. In a normally sighted person, accommodating by one dioptre produces a predictable amount of convergence, and converging produces a predictable amount of accommodation. This cross-link is called the accommodative convergence to accommodation ratio, written AC/A, and it is the number that explains why two people with identical prescriptions can have completely different tolerance for near work.
The ratio is expressed in prism dioptres of convergence per dioptre of accommodation. Clinicians commonly work with a reference range in the region of four to six prism dioptres per dioptre, and values well outside that range tend to produce symptoms rather than a measurable change in distance vision, which is precisely why the problem goes undetected for years.
The geometric version: your PD in centimetres
There is an elegant fact hiding in the geometry. Suppose you look at a target at distance d metres. The accommodation demand is 1/d dioptres. The convergence demand, in prism dioptres, is the interpupillary distance in centimetres divided by d. Divide one by the other and the distance cancels:
AC/A (calculated) = PD in centimetres
So a person with a 63 mm PD has a calculated AC/A of about 6.3 prism dioptres per dioptre. This is not a coincidence and not a clinical average; it is what the trigonometry requires if the eyes simply point at the target. It also tells you immediately what the ratio is doing: it is the exchange rate between focusing effort and convergence effort, and its baseline is set by the distance between your pupils.
Real eyes deviate from that baseline in both directions, which is where the interesting cases live. The calculated value tells you what should happen; the measured value tells you what does.
How it is actually measured
Two methods dominate, and they can disagree, which is worth knowing before treating any single figure as definitive.
Gradient method. Measure the near heterophoria, then repeat the measurement with a -1.00 D lens placed before both eyes. The minus lens forces the eyes to accommodate an extra dioptre to keep the target clear, and the change in the phoria is read as the AC/A directly. Do it with +1.00 D instead and the sign reverses. This is the more direct of the two, because it manipulates accommodation and observes convergence rather than inferring from a formula.
Heterophoria method. Take the distance phoria, the near phoria, the PD and the distance to the near target, and combine them arithmetically. This one depends on assuming the calculated baseline, which is exactly the assumption the gradient method tests.
Both are clinical measurements. They require a phoria measurement to be meaningful at all, and neither can be done from a phone or an online test, because the whole measurement rests on dissociating the two eyes and then observing what they do when the dissociation is released.
Why a high ratio makes reading exhausting
If AC/A is high, every dioptre of accommodation drags in more convergence than the target needs. At near, the eyes end up turned inward past the object, pointing in front of it. The visual system then has to spend effort diverging back to the target, and the effort is continuous for as long as the near task lasts. The typical complaints are not "I cannot see", they are "my eyes ache after twenty minutes", "the words go slightly double when I am tired", and "I have to look away to reset". Distance vision is usually perfect, which is why nothing is found until someone specifically tests near alignment.
A low ratio runs the opposite error: convergence falls short of the demand, and the eyes may drift outward at near. Same fatigue, different direction, and a different optical remedy.
The practical point is that this is a ratio problem, not a focusing power problem. A near add reduces accommodative demand and therefore reduces convergence by the ratio; a prism changes the starting alignment without changing the ratio; and exercises aim at the ratio itself. Which one is appropriate depends on the measured numbers, not on which symptom sounds most familiar.
What the ratio does not tell you
A ratio is a slope, not a position. Two people can share an AC/A of seven and be comfortable or miserable depending on where their alignment starts, how much reserve they have to pull against a drift, and how long their near tasks last. The ratio describes how fast convergence changes as focusing changes; the phoria describes where it currently sits. Reading one without the other is like knowing the gradient of a road but not the elevation you are standing at.
Three misconceptions
- "AC/A is a fixed anatomical constant like your PD." It is stable for a given person under given conditions, but it moves with fatigue, with target size and detail, with the method used to measure it, and with the state of the tear film on the day. Two sessions a month apart can differ without anything having changed structurally.
- "A reading add is only for presbyopia." A small plus add is also used in young, fully accommodating eyes precisely because it lowers accommodative demand and therefore convergence in a high-ratio case. The add is doing optics, not replacing lost focusing power.
- "If I can read fine, my near alignment must be fine." Near alignment problems are usually compatible with clear single vision for short periods. The failure is endurance, not acuity, and endurance is not something a Snellen chart measures.
When to have it assessed
Persistent near strain with clear distance vision, occasional doubling at near that resolves when you look up, headaches concentrated behind the eyes after sustained screen work, or a strong dislike of reading compared with distance tasks. These point to a binocular vision assessment rather than a new prescription, and the assessment is a measurement session rather than a conversation. If a new pair of glasses did not change the symptom, the prescription was probably never the problem.