Kerfing is in simple terms the act of cutting a series of kerfs (cuts) in a piece of wood in close proximity, so the wood can be curved. It is important not to make the cuts too deep, resulting in the wood cracking completely through, or not deep enough so instead of bending, it snaps. The wood needs to be cut to the point that the remaining fibers are free to bend. You can only kerf by crosscutting- you cannot kerf with the grain as the likelihood of the work piece splitting is huge. This doesn’t have to be solid stock either – you can kerf whole sheets and bend entire panels. However, it is very dependent on the type of wood, the moisture content, the relative humidity, the width of the blade, etc.

The result is pretty spectacular.

To fix the kerfing, use lots of glue. You can fill it, and if you want to disguise the kerfing, use an appropriate wood filler.It is a great technique, and is worth persevering with until you get one that is successful. If you are getting consistent failures, the chances are you are being too conservative on the depth of cut, and the outside of the curve is resisting the bend and fracturing. Whatever you do, don’t bend the kerf the other way. Not that the wood doesn’t bend that way, but it looks pretty silly, and makes for an incredibly weak curve. Bent in, the spines all end up impacting on each other, and therefore support each other. They also give you something to glue together. A kerfed curve is never going to be a structural member, but where absolute strength is not required and the curve is important for aesthetics, then this technique may be worth considering.

Now onto the meat. The formula I use for determining how to kerf my panel or board is this:

Take the Outside Perimeter of the radius and subtract the Inside Perimeter. This gives the amount of frame to be removed.

Divide this amount by the thickness of the saw blade. This gives the number of saw cuts.

Last, divide the Outside Perimeter of the radius by the number of saw cuts. This gives the distance between saw cuts.

I have put all of this into an excel spreadsheet to make it very easy for you.

Excellent job! I was looking for that kind of formula and you nailed it!
However I can suggest a different approach (that in my case was easier to work with).
I tweaked some parts of your variables and found out that the same outcome for number of cuts will be found if you just put the thickness of your board and the thickness of your saw.
It can be calculated appr. (if you just count PI as 3.14) by (6.28 * board thickness)/saw thickness.
Am I right?

Hi, I’m a few years late, but I was confused with this too, eventually managing to decipher it, so perhaps I can help clarify—it’s just a matter of a wonky overlap of carpenters’ terms-of-art and geometry terminology. And a missing step that might not be so obvious to everyone.

By “perimeter(s) of the outside/inside radius,” OP is referring to the length of a section of a constant curve, which if you imagine extends until both ends meet each other, would be a circle. The perimeter of a circle is of course a circumference, and a finite “slice” of a circumference with two end points is an arc. So what is meant by “perimeter(s) of the outside/inside radius” is actually arc lengths.

Step 0:
Since your kerf bend will be made from a material with a given thickness, the inner and outer radii (and therefore their arc lengths) are codependent. You have to CHOOSE one of the radii; i.e. you decide what you want the radial curvature of either the inner surface or the outer surface of the bend to be: If you determine the outer radius 𝑟ₒ, then the inner radius 𝑟ᵢ is equal to the desired outer radius minus the thickness 𝑡 of the material, or 𝑟ᵢ = 𝑟ₒ – 𝑡 . If you determine the inner radius, then the outer radius is equal to the desired inner radius plus the the thickness of the material, or 𝑟ₒ = 𝑟ᵢ + 𝑡 .
For example, if I want to kerf bend 3/8″ thick plywood such that the inner curve’s radius will be 4″ (just making up numbers here), then the outer curve’s radius will be 4 3/8″ (4.375″).

Now you have to find the arc length 𝑠 for both the inner and outer radii. Fortunately, 99.99% of the time anyone does a kerf bend, the desired sweep angle will be 90º, so you can avoid trigonometry with a shortcut: since 90º is one quarter of a circle’s circumference, all you need to do is divide each circumference by 4, and you have both your outer arc length 𝑠ₒ and your inner arc length 𝑠ᵢ :
𝑠ₒ = (1 ∕ 4) × 2𝜋𝑟ₒ ; and 𝑠ᵢ = (1 ∕ 4) × 2𝜋𝑟ᵢ .
Continuing from the previous example, my kerf bend’s outer arc length would be (1 ∕ 4) × 2𝜋4.375″ = 6.869092337 inches,* and its inner arc length will be (1 ∕ 4) × 2𝜋4 = 6.283185307 inches.*

If you want to make a kerf bend with a sweep angle between 0º and 90º or between 90º and 180º, then you need to implement some light trig: divide the desired angle 𝜃 by 360º, then multiply that by the circumference: 𝑠ₒ = (𝜃 ∕ 360) × 2𝜋𝑟ₒ; and 𝑠ᵢ = (𝜃 ∕ 360) × 2𝜋𝑟ᵢ . For example, if I want a gentler curve with an obtuse angle of, say, 135º, then my outer arc length will be (135º ∕ 360º) × 2𝜋4.375″ = 10.30835089 inches,* and my inner arc length will be (135º ∕ 360º) × 2𝜋4″ = 9.424777961 inches.*

You can now proceed to OP’s instructions:

Step 1:
Subtract the inner arc length from the outer arc length. The result is the amount of material 𝑚 to be removed: 𝑚 = 𝑠ₒ – 𝑠ᵢ .
From previous example, 𝑚 = 6.869092337″ – 6.283185307″ = 0.58590703 inches.*

Step 2:
Divide this amount by the thickness of the sawblade (the kerf) 𝑘. This gives the number of cuts 𝑐 to be made: 𝑐 = 𝑚 ∕ 𝑘 .
E.g. 𝑐 = 0.58590703 ” ∕ (1∕ 16″) = 9.37451248 cuts. Note on rounding, since you can’t have non-whole numbers of cuts: Here I might round down to 9, or UP to 10. Round down to the next lowest whole number for deeper cuts and/or wider kerf widths; round UP to the next greatest whole number for shallower cuts and/or thinner kerf width, in either case regardless of whether the first decimal point is less than or greater than 5. For now, let’s call it 9 cuts.

Step 3:
Divide the outer arc length by the number of cuts (non-rounded) for 𝑑, the inter-cut distance (on-center!): 𝑑 = 𝑠ₒ ∕ 𝑐 .
E.g. 𝑑 = 6.869092337″ ∕ 9.37451248 = 0.7327412867. Here I would scribe with a caliper locked to 0.733″, but if you’re not as concerned with precision as I am, a number like this can be rounded up to 0.75″ (3 ∕ 4″), which is easy to see on your ruler.

*If using a scientific or graphing calculator with a dedicated 𝜋 button, you will get long strings of decimal points, but don’t forget to wait until the very end of your calculations to round off. 4 significant figures should be fine, since with wood, anything more precise than thousandths of an inch is basically pointless.

Excellent job! I was looking for that kind of formula and you nailed it!

However I can suggest a different approach (that in my case was easier to work with).

I tweaked some parts of your variables and found out that the same outcome for number of cuts will be found if you just put the thickness of your board and the thickness of your saw.

It can be calculated appr. (if you just count PI as 3.14) by (6.28 * board thickness)/saw thickness.

Am I right?

Please clarify meaning of inner and outer radius and circumference. How do I measure each? Many thanks. Chris

Thank you so much!

What is the outside perimeter of the radius? This doesn’t make sense. Could you draw a picture.

length of the outside radius

Hi, I’m a few years late, but I was confused with this too, eventually managing to decipher it, so perhaps I can help clarify—it’s just a matter of a wonky overlap of carpenters’ terms-of-art and geometry terminology. And a missing step that might not be so obvious to everyone.

By “perimeter(s) of the outside/inside radius,” OP is referring to the length of a section of a constant curve, which if you imagine extends until both ends meet each other, would be a circle. The perimeter of a circle is of course a circumference, and a finite “slice” of a circumference with two end points is an arc. So what is meant by “perimeter(s) of the outside/inside radius” is actually arc lengths.

Step 0:

Since your kerf bend will be made from a material with a given thickness, the inner and outer radii (and therefore their arc lengths) are codependent. You have to CHOOSE one of the radii; i.e. you decide what you want the radial curvature of either the inner surface or the outer surface of the bend to be: If you determine the outer radius 𝑟ₒ, then the inner radius 𝑟ᵢ is equal to the desired outer radius minus the thickness 𝑡 of the material, or 𝑟ᵢ = 𝑟ₒ – 𝑡 . If you determine the inner radius, then the outer radius is equal to the desired inner radius plus the the thickness of the material, or 𝑟ₒ = 𝑟ᵢ + 𝑡 .

For example, if I want to kerf bend 3/8″ thick plywood such that the inner curve’s radius will be 4″ (just making up numbers here), then the outer curve’s radius will be 4 3/8″ (4.375″).

Now you have to find the arc length 𝑠 for both the inner and outer radii. Fortunately, 99.99% of the time anyone does a kerf bend, the desired sweep angle will be 90º, so you can avoid trigonometry with a shortcut: since 90º is one quarter of a circle’s circumference, all you need to do is divide each circumference by 4, and you have both your outer arc length 𝑠ₒ and your inner arc length 𝑠ᵢ :

𝑠ₒ = (1 ∕ 4) × 2𝜋𝑟ₒ ; and 𝑠ᵢ = (1 ∕ 4) × 2𝜋𝑟ᵢ .

Continuing from the previous example, my kerf bend’s outer arc length would be (1 ∕ 4) × 2𝜋4.375″ = 6.869092337 inches,* and its inner arc length will be (1 ∕ 4) × 2𝜋4 = 6.283185307 inches.*

If you want to make a kerf bend with a sweep angle between 0º and 90º or between 90º and 180º, then you need to implement some light trig: divide the desired angle 𝜃 by 360º, then multiply that by the circumference: 𝑠ₒ = (𝜃 ∕ 360) × 2𝜋𝑟ₒ; and 𝑠ᵢ = (𝜃 ∕ 360) × 2𝜋𝑟ᵢ . For example, if I want a gentler curve with an obtuse angle of, say, 135º, then my outer arc length will be (135º ∕ 360º) × 2𝜋4.375″ = 10.30835089 inches,* and my inner arc length will be (135º ∕ 360º) × 2𝜋4″ = 9.424777961 inches.*

You can now proceed to OP’s instructions:

Step 1:

Subtract the inner arc length from the outer arc length. The result is the amount of material 𝑚 to be removed: 𝑚 = 𝑠ₒ – 𝑠ᵢ .

From previous example, 𝑚 = 6.869092337″ – 6.283185307″ = 0.58590703 inches.*

Step 2:

Divide this amount by the thickness of the sawblade (the kerf) 𝑘. This gives the number of cuts 𝑐 to be made: 𝑐 = 𝑚 ∕ 𝑘 .

E.g. 𝑐 = 0.58590703 ” ∕ (1∕ 16″) = 9.37451248 cuts. Note on rounding, since you can’t have non-whole numbers of cuts: Here I might round down to 9, or UP to 10. Round down to the next lowest whole number for deeper cuts and/or wider kerf widths; round UP to the next greatest whole number for shallower cuts and/or thinner kerf width, in either case regardless of whether the first decimal point is less than or greater than 5. For now, let’s call it 9 cuts.

Step 3:

Divide the outer arc length by the number of cuts (non-rounded) for 𝑑, the inter-cut distance (on-center!): 𝑑 = 𝑠ₒ ∕ 𝑐 .

E.g. 𝑑 = 6.869092337″ ∕ 9.37451248 = 0.7327412867. Here I would scribe with a caliper locked to 0.733″, but if you’re not as concerned with precision as I am, a number like this can be rounded up to 0.75″ (3 ∕ 4″), which is easy to see on your ruler.

*If using a scientific or graphing calculator with a dedicated 𝜋 button, you will get long strings of decimal points, but don’t forget to wait until the very end of your calculations to round off. 4 significant figures should be fine, since with wood, anything more precise than thousandths of an inch is basically pointless.

What if you are trying to kerf corners… do you use the same formula?

What units? Imperial?