How to determine the power of a magnifier lens empirically when no values are given? I have several magnifiers/magnifying-glasses of varying quality with either nothing inscribed on them, or  power ratings that I think are wrong.
How can the power of a magnifier be determined when no values are given?
Kyle Downs at quora.com states:

Magnification $M$ of a single lens is $M=\frac{f}{f-d}$

I don't know for sure if my magnifiers are "single-lenses", so that may complicate this. According to edmundoptics.com:

"Most high quality magnifiers use achromats [a positive simple lens cemented to a negative simple lens] to eliminate color fringing at the edge of objects."

Thus I imagine my higher-quality "jeweler's loupes" may in fact have multiple lenses.
As I understand, focal length can be found by moving a shining a light source and moving a lens so that the projected image of the source displays sharpest on the surface. The distance from surface to lens is the focal length.

(Image from wikipedia.org)
To experiment, I measured the focal length of one my loupes to be about 9mm, and the diameter of the lens about 16mm. Using the formula mentioned above, that would give me a magnification power of 9/(9-16) = -1.29x  ...Which I feel cannot be right. It is much stronger and should be more around 20x or 30x. Plus, the image is not inverted, so the magnification should be a positive value, correct?
Clearly I am going about this wrong.
 A: Having made a hash of my original answer which was pointed out by @Pieter, I have rewritten it.
In this experiment I simultaneously look at an object (black lines ruled 10 mm apart) which is 250 mm from the magnifier/eye and at the virtual image of mm square graph paper formed 250 mm from a magnifier/eye.
Fine adjustment was made by reducing the parallax between the black lines and the virtual image of the graph paper.
Although readings are best taken using an eye I have taken a photograph with a hand held iPhone to show what is seen.
When viewed with the eye the black lines and the virtual image were sharp but I could not achieve that with the iPhone (right hand) photograph.

The experimental arrangement is shown in the left hand diagram.
I used a x10 magnifier and by eye it was relatively easy estimate the magnification as being approximately 10.

There is a real difficulty measuring the short focal lengths of such lenses.
A method  which is relatively easy to perform uses a plane mirror and finds the position of a virtual method by using no parallax.
A: The power of a magnifying glass is relative to the near-limit distance of the standard human eye (25 cm). The lens makes it possible to bring the object closer to the eye, so that it subtends a larger angle than at the near limit. The ratio of the (tangent of the) angles is proportional to the ratio of these distances.

So if the focal length of a loupe is 10 mm, its M = 25.
