Gear
The pi tape
Engineers' pi tapes are graduated so a wrap reads diameter directly; on a non-circular section they read an equivalent diameter, which is a reminder of what any conversion assumes.
Guides on Gear: Every instrument, and what each costs you, Everything you can wrap, and what each reads, Verifying the thing you measure with
A pi tape is an ordinary wrap-around measuring tape with one change: its markings are stretched by a factor of pi before printing, so a full wrap around a circular object reads out the diameter directly rather than the circumference. Machinists use them to check the diameter of a shaft or a pipe without doing arithmetic by hand.
What the stretching actually does
An unmodified tape wrapped around a circle reads the circumference, C, and the relationship to diameter is C = pi times D. A pi tape's scale is printed at 1/pi of the normal spacing, so the same physical wrap length lands on a mark that is already divided by pi - the tool does the division for you, mechanically, before you look at it. This only works because the object is assumed to be a true circle. The tape has no way to know otherwise; it just reports circumference-divided-by-pi and calls it diameter.
Where the assumption breaks
Wrap a pi tape around something that is not a true circle in cross-section - an oval bar, an out-of-round pipe, a shaft that tapers or bulges - and it still reports a number, because dividing by pi is all it ever does. That number is not a diameter in the sense of "a distance straight across", because a non-circular shape does not have one single diameter; it has a different width depending on where you measure across it. What the tape actually gives you is an equivalent diameter: the diameter of the circle that would have produced the same circumference. For an ellipse even the circumference has no simple formula - the NIST Digital Library of Mathematical Functions (§19.9) gives an ellipse's perimeter as a complete elliptic integral - so no single division recovers its widths. It is a real and sometimes useful number, and it is not the same thing as a diameter measured directly with a calliper, which is why the two disagree on anything that is not a true circle. Diameter-reading instruments are not limited to tapes, either - sizing rings and gauges take a related but different approach to the same underlying question of width.
Why this is worth knowing here
This measurement is a circumference read at midshaft with an ordinary tape, not a diameter - Veale et al. (2015) report a pooled erect circumference of 11.66 cm, which a pi tape would print as an equivalent diameter of about 3.71 cm - and the site is not a true circle in cross-section - closer to an ellipse. A pi tape would hand back an equivalent diameter for that site, which would be a real number and the wrong thing to compare to a calliper reading taken across the narrow axis, for the same reason a calliper reading is the wrong thing to compare to a tape's circumference - two instruments answering related but different questions, dressed up as the same answer. The lesson generalises past pi tapes: any conversion between two shapes of number - diameter to circumference, a photo to a length, a score to a size - is doing arithmetic on top of an assumption, and the arithmetic is only as good as the assumption underneath it.
That is also the honest description of what Rate Cock converts a photograph into: not a measurement in centimetres but a rating, a different unit entirely, the same distinction that applies to an AI model's read of an image, to the numeric scores built the same way, and to a human judge's verdict on the same photo - useful outputs, each built on a stated assumption, and worth reading as such rather than mistaking any of them for the tape measure they stand in for.