The 45mm Series 7 Apple Watch has a screen of 396 x 484 pixels. That's really quite a bit off from square (turns out it's 9:11, BTW).
Let's
really do the math...
Apple's technical specifications for the 45mm Series 7 reports:
396 by 484 pixels
1143 sq mm display area
and Wikipedia reports the
diagonally measured screen size of the 45mm Series 7 to be
48.29mm
Computing the width, height, and area of the screen from this, we get:
# angle = math.atan2(height_px, width_px)
angle = math.atan2(484, 396)
angle = 0.8850668158886104
# width_mm = diag_mm * math.cos(angle)
width_mm = 48.29 * math.cos(0.8850668158886104)
width_mm = 30.579052891523215
# height_mm = diag_mm * math.sin(angle)
height_mm = 48.29 * math.sin(0.8850668158886104)
height_mm = 37.37439797852837
# area_in_mm = width_mm * height_mm
area_in_mm = 30.579052891523215 * 37.37439797852837
area_in_mm = 1142.8736925742573
(Ridiculous number of decimal places because I'm just letting Python do all the math)
That 1142.87... result seems to match Apple's officially reported 1143 sq mm, so assuming we're working with properly square pixels, that nails down the screen size pretty accurately. 48.29mm is 1.9011811 inches, and the article discusses a 1.901 inch screen on the 45mm Series 7 - close enough.
The rumored screen is a 1.99 inch screen, which would be 50.546mm. Assuming the same aspect ratio as the existing screen (and, once again, square pixels), we can re-run the math above with a 50.546mm screen and we get:
width_mm = 50.546 * math.cos(0.8850668158886104)
width_mm = 32.0076373463436
height_mm = 50.546 * math.sin(0.8850668158886104)
height_mm = 39.12044564553106
area_in_mm = 32.0076373463436 * 39.12044564553106
area_in_mm = 1252.153037049505
Series 7 screen is 1142.87 sq mm and proposed Series 8 (1.99") screen is 1252.15 sq mm. Doing the math:
((1252.153037049505 / 1142.8736925742573) - 1) * 100
= 9.561804177074219
So, it's an increase in area of approximately
9.56%, which is much closer to 10% that
@lucas stated, and quite a bit off from either the
5% the article stated or the
15.14% you calculated.
By the way, running the numbers through the screen size script I normally use, I get this for the current screen:
48.29mm at 396w x 484h ==> 30.57905mmW x 37.3744mmH (9.0:11.0*44, 0.82:1) x 328.93105dpi
And this for the new screen:
50.546mm at 414w x 506h ==> 32.00764mmW x 39.12045mmH (9.0:11.0*46, 0.82:1) x 328.53409dpi
Exact same aspect ratio, and pretty close on the DPI. The minor difference in DPI I expect comes down to the actual screen size being something slightly different than 1.99 inches given in the article. Assuming they're not changing the pixel size... let's see...
# screen_size -v -m 50.485 414 506
50.485mm at 414w x 506h ==> 31.96901mmW x 39.07323mmH (9.0:11.0*46, 0.82:1) x 328.93105dpi
That hits the same exact DPI as the S7 screen, using a screen measurement of 50.485mm. That's 1.98759843 inches. So, I'd guess the 1.99 inch number quoted in the article should be closer to 1.9876 inches (or just go with 50.485mm, because that's probably how it's written in the specs at the factory).
Sounds like the real number is in the vicinity of 1.9876, and one source rounded that up to 1.99, and then another source rounded
that up to 2 inches.
By the way, if the screen was 50.485mm (1.98759843 inches) diagonal (to have the same DPI), the ratio to the S7 screen would be 1.092975, or about
9.3% larger.