Gear
The goniometer
A goniometer is a hinged protractor that reads the angle between two axes; it is the instrument the literature uses for curvature, and a phone protractor app approximates it.
A goniometer is two arms joined at a hinge, with a protractor scale printed around the joint. Line one arm along a base axis, the other along a second axis, and the scale reads the angle between them. It is a common tool in physiotherapy for joint range of motion, and it is also the instrument the published literature uses to report curvature - a base axis and a distal axis, and the angle between them at the point of maximum bend.
How it is used for this reading
One arm sits along the axis of the base of the shaft, the other along the axis past the point of curvature. The hinge sits roughly at the point the bend is greatest, and the scale reads the angle the two axes make with each other. Reported this way, curvature is a single number in degrees, comparable across readings taken the same way - the same logic that makes a bone-pressed length comparable to a published figure: a consistent method turns an anecdote into a figure that means something next to another figure.
A plastic clinical goniometer with a clear scale is the standard tool, and the reading only takes a few seconds once both axes are identified. The two axes are the entire measurement - get them wrong and the angle is wrong regardless of how carefully the scale is read.
The phone app substitute
Several phone apps use the device's accelerometer as a digital protractor: hold the phone flat against one axis, note the angle, hold it against the second, and take the difference. This approximates a goniometer reasonably well for a single angle in one plane, because an accelerometer measures tilt relative to gravity with reasonable precision.
It is an approximation rather than a substitute in one respect: a goniometer's two arms are aligned to each other directly, while a phone measures each axis separately against gravity and the angle is derived by subtraction, which adds the error of two readings instead of one. For a rough figure that is a fine trade against not owning a goniometer. For anything you intend to track against a threshold, a physical goniometer removes that extra step.
Sources of error in the reading itself
The hinge needs to sit at the point of maximum curvature, and finding that point by eye carries some judgement - a hinge placed a centimetre off the true point of maximum bend will read a slightly different angle even with both arms correctly aligned to their axes. Repeating the placement a few times and taking the largest angle found, or the median of several attempts, catches most of this without adding much time to the reading.
A second source is how firmly the arms are held against the surface: too light a contact lets the arm drift off the true axis, while pressing hard enough to compress soft tissue can shift the apparent axis by a small amount in the other direction. Consistent, moderate contact - enough that the arm does not wobble, no more - keeps this error small and roughly the same from one reading to the next, which matters more for a figure you intend to compare across sessions than the absolute number does on its own.
What a reading tells you, and what it costs
An angle recorded this way is a description of the shape of one axis relative to another, on the day it was taken, under whatever state the reading was taken in. It says nothing beyond that - not a diagnosis, not a trend, not a comparison to anyone else's figure unless they used the same method and axes you did. Curvature also interacts with length: a pronounced bend shortens the straight-line distance the literature reports as length, which is measured base to tip in a straight line rather than along the curve.
Instruments that do not do this job
A goniometer reads an angle between two lines. It is not the tool a rating service uses to turn a photograph into a score - Rate Cock is producing a judgement from an image, a different kind of output from a degree measurement with a defined zero. Nor is it what an AI model attempting to infer shape from a picture is doing, since a photograph carries no scale or axis reference a goniometer's hinge provides directly. A human observer's impression of shape - the kind a Rate Penis reviewer might offer - is an opinion rather than a degree figure, and the two should not be quoted as though they were the same measurement. A numeric score on a photo-rating tool like Penis Rater sits in the same category - a rating, not an angle - even where both use a number on a scale.
Buy or borrow a clinical goniometer if you want the reading done properly; the phone version is a reasonable stand-in when you do not have one on hand.