Quantifying sharp


For centuries, men have sharpened tools, knives, swords and razors.  With the proliferation  of disposable utility blades and cartridge razors, what was once a commonplace skill has become a lost art, practiced mostly by knife enthusiasts, hand tool woodworkers and men who shave with straight razors.   Whether sharpening by hand with hones and abrasives can produce a finer edge than industrial scale, mechanized sharpening seems likely, but it is something we will investigate.  Undoubtedly, the modern preference for mechanized and disposable sharpening is the choice of convenience rather than  a confirmation of quality.

In principle, there are two general approaches to quantifying “sharp” or the keenness of a blade’s edge.  The simplest and most common is through comparison and evaluation of use.   Comparing the force to cut, the smoothness of the chiseled wood, the thinness of the sliced vegetable, or the closeness of the shave provides a relative quantification of sharp.   Such comparisons are more than sufficient to allow a practitioner to develop and evaluate a honing  procedure.   To a Scientist, this phenomenological approach begs the questions of why? and how? and provides little insight into how  the process can be improved.

My approach will be to use electron microscopy to physically observe the geometry and polish of the edge and to quantify the edge width and bevel angle.  The goal is to provide an understanding of what is happening at the blade’s edge. The centuries old design of a straight razor provides the ideal system for scientific study of sharpening.  Honing on a flat surface with the bevel and spine contacting the hone fixes the angle of the apex.  The steel used in a straight razor is hardened and tempered to optimize the achievable keenness.  In our experiments, the use of a straight razor will allow us to fix the honing angle at the value determined by the spine thickness and blade width.

The expression razor sharp undoubtedly refers to the fact that the keenness required of a  functional straight razor is very near the limits of what the physical properties of steel permits.  In other words, as sharp as it gets.  I will show that the apex of the blade must be thinned to about 100nm (one tenth of a micron) to comfortably shave facial whiskers.  At the same time, the limit of what can be achieved with honing and stropping of a steel blade is on the order of 50nm.  The intriguing aspect of a straight razor edge is the fact that it can be evaluated in a especially sensitive way, slicing hard whiskers from some of the softest and most sensitive skin.  This provides an added layer of complexity, identifying the properties of a blade that affect the selectivity of cutting whiskers over cutting skin.  Correlation of the microscopic edge characteristics to the shaving performance is also a topic to be investigated.

SEM Imaging

The scanning electron microscope allows imaging of a honed blade’s edge (or apex) at sufficiently high magnification and contrast to assess the polish of the bevel, the uniformity of the edge and to make relative comparisons of sharpness.

Below, two SEM images taken edge-on of honed blades.  Both images were recorded at the same magnification, providing clear evidence that one blade is keener than the other.


10kx edge view of a razor after Gokumyo 20k hone


10kx edge view of a razor after Chosera 1k hone

Although relative comparison of keenness is possible from the edge-view images, quantification of the keenness is challenging without the perspective provided by cross-sectioning of the blade.  A focused ion beam (FIB) is used to cut a cross-section perpendicular to the edge.  From the SEM image, the geometry of this cross-section can readily be measured to determine the edge width and bevel angle.


SEM image of a FIB-milled cross-section with edge geometry measurements

In the above image, the bevel angle near the apex is 19 degrees and the edge width at 3 microns from the apex is 1.65 microns.

In summary, SEM imaging and FIB cross-sectioning allows measurement apex geometry; the edge width, the bevel angle near the apex, and the thickness at a distance from the apex.  With these measurements, it will be possible to quantify the results of various hones, stones, strops and the techniques of their use.

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  22 comments for “Quantifying sharp

  1. Steven
    November 16, 2014 at 4:22 pm

    I followed the link to this page [Using our definitions of “keen” and “sharp”] from https://scienceofsharp.wordpress.com/2014/04/13/the-bevel-set/

    However, I’m not entirely clear on definitions of keen and sharp on this page.

    Is it as follows: (i) sharpness is defined through comparison and evaluation of use while (ii) keeness is evaluated by making empirical observations, such as you have done with the SEM technique?

    Nice site, by the way
    Best wishes

    Liked by 1 person

    • November 17, 2014 at 12:54 am


      With correctly obtained SEM images, it is possible to
      measure the geometry of the edge. This can be quantified with two measurements; the edge width, or more precisely the radius of curvature of the apex and the angle of the bevel at the edge. The bevel is typically convex in the last few microns of the edge, and so measuring the angle between these two curved surface is difficult. Instead, I measure the thickness of the bevel at a distance of 3 microns from the apex. This distance is arbitrary; however, it is the relevant scale for a razor edge. For a straight, triangular bevel the angle and the width at 3 microns are related by simple trigonometry.

      For convenience, I have suggested the definition of “keen” to refer to the apex width and “sharp” to refer to the final bevel angle. I suggest that this is consistent with the dictionary definitions of the two words.

      The relationship between measured geometry and observed cutting efficiency is something to be studied further. At minimum, this will depend on the material being cut. Edge retention must also be considered. For a razor cutting hair, keenness will primarily determine the ability of the razor to “catch” the hair and penetrate the hard keratin sheath, while sharpness will primarily determine the force required to complete the cut of the hair.


      Liked by 1 person

  2. Rod Gentry
    January 17, 2015 at 1:35 am

    Another area of considerable use of sharp edges is in hunting where thousands, probably millions depend on the keen edge for bowhunting. I would be surprised if the number bowhunting did not exceed straight razor users, though there is probably some overlap. I fall into the Woodworking, leather, hunting, knives, and shaving category.

    Another interesting area is Chabad, the kosher butchering discipline that uses knives that are designed to painlessly kill the animals so slaughtered. Like many of these things it is under study by interested amateurs.


  3. September 2, 2016 at 7:55 am

    With regards to bowhunting, stone age materials like chirt (and other flint), and obsidian, can hold sharper edges than steel. Because if you make a steel edge too sharp, the atoms quickly move around until the edge becomes less sharp. I presume the main advantage of metal weapons lied in durability – it was less likely to chip and shatter against armour and other weapons.

    It must be easier to produce a consistent shape steel arrowhead – which might affect aerodynamics. Perhaps for bowhunting, consistency matters more than sharpness?

    I’m not sure how well flint works for shaving. But on-line videos show that while obsidian blades have application to surgery, they are much too sharp for practical shaving.


    • September 2, 2016 at 10:52 am

      There are many unsubstantiated claims about obsidian blades. Steel blades can be made too sharp to cut anything but air without being damaged, so it makes no sense to me to say anything can be sharper than steel.

      There are many reasons why I define the terms “sharp” and “keen” the way I do. Obsidian (or any cleaved crystal) can have atomic “keeness” but that does not translate to being atomically “sharp” if the apex angle is more than 30 degrees.

      …and atoms don’t move around and make the edge less sharp.

      Liked by 1 person

  4. September 13, 2016 at 10:26 am

    I hate the fact that some of what I obtain from Internet-published literature isn’t always consistent or right. I try, but I get some things wrong. Sigh.

    AFAICT from internet-published literature, Obsidian is a glass (mostly SiO2), not crystalline. Presumably it can be shaped to any desired apex angle, including by grinding stones, but, as with steel, if the angle is too thin, the edge would not be durable enough for a given purpose.

    As a practical matter, steel arrowheads are much more common now. I doubt that sharpness is the only factor. Perhaps they are more durable, more consistent, easier to replace, and/or cheaper to produce?

    Perhaps iron can be shaped to more or less atomic dimensions too. But, some Internet-published literature indicates that to create the hardness (i.e., stiffness) of steel, you need to intermix iron crystal grains with those of other materials (e.g., metal-carbides), which limits attainable width and effective sharpness. (In your images, some foil edges are quite thin – but some sources claim that some foil edges on hardened steel are not themselves hardened steel.)


    • September 14, 2016 at 1:45 pm

      We all know how easy it is to make sharp edges by breaking glass. It may be argued that it is “easier” to make a razor sharp blade from obsidian than steel, but this does not mean that steel can’t be sharper.

      Carbides are typically no smaller than 1 micron, and razor blades have an apex width of less than 1/10 of one micron – carbides are of no consequence at this level of blade keenness.

      Liked by 1 person

      • January 5, 2017 at 11:54 am

        Can you elaborate on the consequence / lack of consequence of carbides? The usual mental model is to think of steel as analogous to concrete … cement and pebbles. We think of the pebbles as adding abrasion resistance, but also as a limiter of strength (“edge stability”) when bevel angles get very acute … because in a thin profile we see too much pebble and not enough glue.

        You seem to be casting doubt on this model.



        • January 5, 2017 at 4:38 pm

          The concrete analogy fails because the carbides are very well bonded to the iron matrix. The carbides don’t just “pop out” when the edge is thinned around them.

          This role of carbides in edge retention and performance is fairly complex and I will explain it in detail at some point in the future.


  5. Stefano
    February 1, 2017 at 5:43 am

    I can’t wait to hear your explanation of this complex topic.
    While i am keen to think that huge carbide clusters might actually “pop out” or fracture, thanks to your pictures i now see the edge more like made of plastic, the carbides being harder plastic than the matrix suorrounding them, rather being diamond-like features embedded in chalk.


  6. Bryan
    February 14, 2017 at 5:04 pm

    Could you please clarify how you determine apex and apex width? For an ideal triangular wedge, the apex is a well-defined line, and the apex width is zero. For a real edge at the resolutions you are considering, the apex is an irregular region. So I assume you do some curve or surface contour fitting to define apex and apex width.


    • February 14, 2017 at 6:17 pm

      Typically the apex (at a particular point) can be approximated by a semi-circle and I define the edge width as the diameter of that circle. In general, I am giving a ball-park number that is typical of the apex produced by the particular method, measured at various points along the length of the blade.


      • Bryan
        February 14, 2017 at 10:23 pm

        Thanks. Do you simply visually superimpose and size a semi-circle on the image, or do you click on an array of points on the image and do a curve fit? Also, from your displays, it looks like the 3 micron distance that you use for the bottom edge width is measured from the base of the apex, not from the top tip. Is this correct? (I realize the difference is small in most instances, but I just want to clarify your conventions.)


        • February 16, 2017 at 10:52 am

          For a cross-section, it’s straight forward to use the circle measurement tool. Having made these sorts of measurements tens of thousands of times, I have become quite proficient at estimating dimensions of objects in the microscope.

          The 3 micron distance is always measured from the apex. We could also characterize the near-apex by the included-angle but this is difficult to measure when there is a convex geometry. To fully characterize the apex region, we should measure the width at several distances from the apex; however, I have found that the 3-micron distance is the most relevant to cutting performance.


  7. Miller
    July 3, 2017 at 12:23 pm

    I am curious what equipment is being used to set the bevels when not using a straight razor, or if it is freehand.


    • August 14, 2017 at 11:57 am

      The knives I’ve shown here are all sharpened freehand, although I often use a jig for thinning a new knife.


  8. kaesees
    August 6, 2020 at 2:32 pm

    Have you seen the research just published by UMadison on razor blades cutting hair? It appears they used the same low-energy SEM imaging you’ve been working with here for years.


    • August 7, 2020 at 11:34 am

      Thanks, no I hadn’t seen it, appears to have been published just today. It appears they weren’t aware of the importance of prepping your beard before shaving.


  9. February 12, 2021 at 11:48 pm

    You mention some metrics for “razor sharpness” e.g. 0.1 micron (100nm) at the apex and 1.65 microns as the width behind the end. I notice that your site mainly focuses on this and exploring the limits of the what the material and tools can achieve . Do you have some recommended values for other regular applications where toughness/edge retention is also important? e.g. axes, pruning shears, skinning knives, kitchen knives, surgical scalpels etc? What is the minimum equipment required? I note that Juranitch in his book, “The Razor Edge Book of Sharpening” suggests that a 600 grit stone is generally adequate for this purpose (along with regular use of a smooth steel hone).


    • February 14, 2021 at 10:45 am

      It’s actually very complicated, as there are a variety of ways in which material is separated or “cut.” Many types of separation don’t require a keen edge, shearing and splitting for example. I hope to expand on this at some point in the future.

      As to the honing steel, I think it is important to think of sharpening and honing as completely separate tasks. Sharpening is about thinning the bevel, and can be done with any grit. Honing is about shaping the apex and the last few microns of the edge which can be done with a honing rod. So, yes there is no need for anything other than a medium-fine grit like 600 and a honing rod to maintain most knives. This is obviously not the correct approach for razors or scalpels though.


  10. Dress Filliam
    February 23, 2021 at 3:30 am

    Those edge pictures seem like done somehow from above – otherwise it would be just a triangle of cross section seen. When measuring angles, do you take into consideration that angle value raises because of this oblique view?


    • February 23, 2021 at 5:59 am

      The view is tilted 36 degrees from normal to the cross-section, and yes all images with measurements are tilt-corrected to compensate for foreshortening.


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