How to measure a radius?

Looking at the UU Marketplace, (hoping UAS doesn't kick in, but looking anyway, LOL), I saw someone asking for a specific radius on a ukulele. Aside from asking the company/builder, how would you know? How would you measure that?

Radius of what, specifically?

John Colter

Looks like they're looking for a radiused fretboard...

Oh, yes, sorry. Radius of a fretboard. I guess I shouldn't expect anyone to read my mind.

Draw a 12" circle- take 1-3/8 of that circle and that is a 12" radius. Do the same with a 20" circle.....

Cheers

https://www.mathopenref.com/arcradius.html

Because you cannot lay a straight edge under the curved fret, you have to lay it across the top. Position it so the distance to the fret is the same on both ends (picture a balanced see-saw...) and measure it. That will be the height, (h) in the equation.

Or, ask the "company/builder."

Thanks! I'll try to dust off any math skills I might have, and give it a try.

Wiggy said:

https://www.mathopenref.com/arcradius.html

Because you cannot lay a straight edge under the curved fret, you have to lay it across the top. Position it so the distance to the fret is the same on both ends (picture a balanced see-saw...) and measure it. That will be the height, (h) in the equation.

Or, ask the "company/builder."

Click to expand...

What would I measure for the width?

I get what a radius is, the difference between something like a 12 inch radius and a 20 inch radius, but not how I could tell what I have, unless I buy the gauges. I thought the site you linked to would work, but don't know what to measure.

You can make your own gauges out of cardboard. They won't last as long as the StewMac ones, but they'll work fine as a one off.

The low tech way: take a piece of cardboard, a pin, and a string the radius you want to test. Draw the arc, cut it out, and see if it fits cleanly to your fretboard. If not, repeat another size up or down.
It's a bit easier if you have a drawing compass handy.

If you have the toys, a laser cutter or 3D printer'd work too. (

Edit: no surprise - there's a model up on thingiverse: Customizable Fretboard Radius Gauge by SerialNano - Thingiverse

--Rob

Joyful Uke said:

What would I measure for the width?

Click to expand...

It would be the length of the fret, end to end, "as the crow flies."

A caliper would be handy for this, but you should be able to eyeball it with a 1/64" or .5mm machinist scale.

Wiggy said:

It would be the length of the fret, end to end, "as the crow flies."

A caliper would be handy for this, but you should be able to eyeball it with a 1/64" or .5mm machinist scale.

Click to expand...

I misunderstood your previous post to say that was the height. So, if that's the width, what would be the height?

Now that I got started trying to figure this out, I seem determined to figure it out. But obviously, I've got myself confused.

Arcy said:

You can make your own gauges out of cardboard. They won't last as long as the StewMac ones, but they'll work fine as a one off.

The low tech way: take a piece of cardboard, a pin, and a string the radius you want to test. Draw the arc, cut it out, and see if it fits cleanly to your fretboard. If not, repeat another size up or down.
It's a bit easier if you have a drawing compass handy.

If you have the toys, a laser cutter or 3D printer'd work too. (

Edit: no surprise - there's a model up on thingiverse: Customizable Fretboard Radius Gauge by SerialNano - Thingiverse

--Rob

Click to expand...

Back in the old days I would use a beam compass. A pin end and a pencil or cutting blade end joined by a metal beam. Cut an arc of whatever radius on cardstock or thin cardboard.

They also made one that used a ruler or yard stick for the beam for really big radii.

Xacto made a beam circle cutter with specialty blades.

Okay, here's what I see:
standard fretboard radii, which includes:

7-1/4 inch
9-1/2 inch
10 inch
12 inch
14 inch
15 inch
16 inch
20 inch
how do I know which is the flattest and which is the tallest?
I'm bad at geometry.

Nickie said:

Okay, here's what I see:
standard fretboard radii, which includes:

7-1/4 inch
9-1/2 inch
10 inch
12 inch
14 inch
15 inch
16 inch
20 inch
how do I know which is the flattest and which is the tallest?
I'm bad at geometry.

Click to expand...

The bigger the radius, the flatter the fretboard.

A quick comparison of four different radii in a 1.5" wide (neck width) box.

Kenn2018 said:

They also made one that used a ruler or yard stick for the beam for really big radii.

Click to expand...

I always enjoy this video of routing a 15' radius dish:

I bet if you googled "fretboard radius template printable" you'd get a number of results! Then you could print and cut them out and you wouldn't have to worry about drawing them accurately if you're not used to doing things like that.

Ukes are typically in the 10 - 16" range IME, if they are radiused. Smaller numbers are really for matching traditional designs, i.e. vintage stratocasters had 7 1/4" radius, so people building repros of those use that number. A radius bigger than 16" starts to have very little effect - you sometimes see a 20" radius on instruments with wide fretboards (like a 6 string bass guitar) but I've never really seen anything bigger than that. The radii measured in FEET (like the 15' radius in that cool video) are used for dishing backs and tops on acoustic instruments, not for fretboards. A 15 foot radius wouldn't even show up on a fretboard. It's also worth noting that fretboards are radiused in one dimension, across their width, while backs and tops are usually dished in two dimensions, so they follow the shape of a sphere instead of a cylinder (although some builders do use a one-dimensional cylinder profile instead of a dish).

If you're checking an unknown instrument, especially one with a longer neck than a uke - say, a guitar or bass, measure in a few spots. Guitars and basses are sometimes compound, with a narrower radius at the nut end that flares out to a wider radius at the heel end of the neck. This compound shape helps match the actual shape the string paths take, which is basically following the profile of a cone, rather than a cylinder, thanks to the different widths at the nut and bridge. This difference is unimportant on an instrument with a short scale like a uke, but it becomes much more important on something with a very long scale and high sensitivity to trueness of the fretboard, like a fretless electric bass guitar.

Thanks clear and Kenn!

Personally I don't like how radius fretboards have crept into classical guitars and ukuleles.
They seriously don't need them.
heck, I even think they are detrimental to playability - at least for me.

Classical guitar and ukulele play better for me on a fully flat fretboard.
Radius messes with the action and straight saddles that come traditionally on classical guitars and ukuleles.
Radius fretboard means the saddle is also radiused.

Great for steel string guitars. Not particularly advantageous for nylon string and fingerpicking technique.