What this calculator does
The eye focuses on near objects by changing the shape of its lens, and the range over which it can do this is the amplitude of accommodation. It declines steadily and predictably from childhood, which is why reading glasses eventually become universal.
The decline is relentless. A 10 year old has an average amplitude of 15.50 dioptres with a near point around 6.5 cm; by 45 that is 5.00 D at 20.0 cm, and by 60 it has fallen to 0.50 D, which puts the near point at 200 cm.
The formula
Hofstetter's three formulas give average, minimum and maximum expected amplitude as straight-line functions of age. The near point in centimetres is 100 divided by the average amplitude.
| Term | Meaning |
|---|---|
| Dioptre (D) | The unit of optical power. Amplitude in dioptres is the reciprocal of the near point in metres. |
| Near point | The closest distance at which the eye can focus clearly. |
| Presbyopia | The age-related loss of accommodation, symptomatic once amplitude falls below about 4 to 5 D. |
The inputs explained
| Field | What to enter |
|---|---|
| Age (years) | Age in years. It is the only input, since accommodation declines almost entirely as a function of age. |
When to use it
Understanding why reading glasses become necessary
The near point moves beyond comfortable reading distance in the mid-forties.
Checking a measured amplitude against expectation
Clinical measurement is compared against the age-expected range.
Explaining presbyopia
The decline is a normal optical change rather than a disease.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does accommodation decline with age?
Expected amplitude at four ages.
| Age | Average amplitude | Approx. near point |
|---|---|---|
| 10 years | 15.50 D | 6.5 cm |
| 30 years | 9.50 D | 10.5 cm |
| 45 years | 5.00 D | 20.0 cm |
| 60 years | 0.50 D | 200.0 cm |
Questions
Why does accommodation decline?
Chiefly because the lens stiffens with age and becomes less able to change shape. The ciliary muscle that drives the change also loses some effectiveness, but the lens is the main factor.
Why do reading glasses become necessary in the forties?
Because that is when the near point moves beyond comfortable reading distance of roughly 35 to 40 cm. The decline has been happening since childhood; the forties is simply when it crosses the threshold that matters.
Can accommodation be preserved with exercises?
The evidence does not support it. The loss is a physical change in the lens rather than a matter of muscle fitness, and no eye exercise has been shown to reverse it.
How is amplitude measured clinically?
Usually by the push-up method, moving a target closer until it blurs, or with minus lenses. Both give somewhat different figures, and push-up tends to overestimate because of depth of focus.
For tooth proportion in orthodontics, see the Bolton ratio calculator. For a general health baseline, see the BMI calculator.