GUIDE 06 / 07
From px/s to °/s — How to Calibrate Your Screen and Convert Units
Learn how to find the real length of 1 px using a bank card's width or your screen diagonal, and how to calculate angular speed and Landolt ring acuity from your viewing distance, with formulas and examples.
A px (pixel) has a different real-world length on every screen. Research records dynamic vision in °/s (change in visual angle per second) because the angle seen from the eye is a unit that's comparable regardless of screen size. This site's calibration panel does the following math for you.
Step 1: Find the real length of 1 px
Card method — Most bank cards, debit cards, and transit cards follow the international standard ISO/IEC 7810 ID-1, which is 85.60 mm wide. Match the box on screen to the card's width, then calculate as follows.
Length of 1 px (mm) = 85.60 ÷ box width (px)
Example: If the box width matches the card at 323 px, then 1 px ≈ 0.265 mm.
Diagonal method — If you know your screen's diagonal in inches, you can calculate using the screen resolution (CSS pixels) reported by your browser.
Length of 1 px (mm) = diagonal (inches) × 25.4 ÷ √(width px² + height px²)
If your browser's zoom level or your OS's display scaling isn't 100%, CSS pixels won't match actual pixels, introducing error. The card method is more accurate.
Step 2: Converting px/s to °/s
If a target moves at v mm/s near the center of the screen, and the distance between your eye and the screen is D mm, the angular speed seen from your eye is approximately v ÷ D radians per second.
Angular speed (°/s) ≈ Speed (px/s) × length of 1 px (mm) ÷ distance (mm) × 57.3
Example: 1,000 px/s, 1 px = 0.25 mm, distance 60 cm (600 mm) → 1,000 × 0.25 ÷ 600 × 57.3 ≈ 23.9 °/s
This formula is most accurate when the target passes near the center of the screen. Near the edges, the eye is farther away and at more of an angle, so the actual angular speed is slightly smaller. That's why °/s values are for approximate comparison only.
Step 3: Converting Landolt ring size to acuity
The Landolt ring is an optotype defined by the international standard ISO 8596, where the ring's diameter is 5 times the gap's width, and the stroke thickness equals the gap's width. If you can identify the gap when it forms an angle of 1 minute of arc (1/60 of a degree) from your eye, that's 1.0 decimal acuity.
Decimal acuity = 1 ÷ angle formed by the gap (minutes)
Example: At a 60 cm distance, 1 minute of arc is about 0.175 mm. On a screen where 1 px = 0.265 mm, a 4 px gap (1.06 mm) is about 6.1 minutes, corresponding to a decimal acuity of about 0.16.
This site's KVA mode calculates this value from the ring's diameter at the moment you press, and shows it as converted acuity. Digit targets are approximated using the convention that a character height of 5 minutes of arc corresponds to 1.0 acuity.
Things to watch when reading converted acuity
- A screen test's converted acuity includes the size increase during your reaction time, screen brightness, and the roughness of pixel edges. It can't be directly compared to a KVA value from an eye clinic's tester.
- At 60 cm, the gap for 1.0 acuity is smaller than 1 px and can't be drawn accurately on screen. A screen test can, in principle, only cover a lower range of acuity.
- Comparisons are most meaningful between values measured under the same calibration and the same distance.