# Pupil squared

In bright light, an adult pupil can measure 2 millimetres across; in darkness, it can reach 8 millimetres. The diameter grows fourfold, while the circular opening's area grows sixteenfold.

## Open the pupil

Slide from 2 to 8 millimetres. The model tracks the opening's geometric area. Look at your pupil in a mirror under steady light, and use the calculator as an approximate reference.

## The short answer

The area of a circular opening follows the square of its diameter: `A = π × (d / 2)²`. Moving from 2 to 8 millimetres makes the diameter ratio 4 and the area ratio 4² = 16.

The pupil is a transparent opening in the centre of the iris. The iris sphincter narrows it in light, while the dilator muscle widens it in darkness. The retina and brain adjust sensitivity separately, so a geometric factor of 16 does not automatically produce a scene that looks sixteen times brighter.

## Your measurement

Enter an approximate diameter between 2 and 8 millimetres. The calculator reports its area and ratio to the 2 millimetre reference. In natural conditions, size depends on light, age, medication and alertness. The model is educational, not clinical.

## Sources and limit

- [NCBI Bookshelf, The Pupils](https://www.ncbi.nlm.nih.gov/books/NBK381/) for the 2–4 mm light range and 4–8 mm darkness range.
- [Mathôt, Pupillometry: Psychology, Physiology, and Function](https://pmc.ncbi.nlm.nih.gov/articles/PMC6634360/) for the approximate 2–8 mm range and geometric factor of 16.
- [Regulation of pupil size in natural vision across the human lifespan](https://pubmed.ncbi.nlm.nih.gov/39100191/) for natural-viewing variation and the effect of age.
- [NHS, Vision loss](https://www.nhs.uk/conditions/vision-loss/) for the safety boundary around changes in vision.

A new or persistent difference between pupils, a sudden change in vision or eye pain needs medical advice. This page is not a diagnosis.