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Looking for Examples of Math in Wodworking

by clin
posted 08-04-2016 02:18 AM

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View bigblockyeti's profile


6201 posts in 2333 days

#1 posted 08-04-2016 02:38 AM

My background is in mechanical engineering of which some of can be carried over to wood working, specifically in calculating loads on members of a structure. Simpler structures like a wall in a house might be a better example than a curvy contemporary piece of furniture where the math can get quite a bit more complicated quickly.

What grade level will she be teaching?

The best example I can remember from early in high school was making scale truss bridges in teams using 1/8” square pine and dyed green wood glue. The objective was to use as little resources and have the maximum weight capacity when tested to failure. It wasn’t so much about the math as the concept of keeping everything triangulated.

Later in high school in mechanical drafting and learning to draw an ellipse knowing only two dimension could be another application relevant if you were to make a elliptical table.

-- "Lack of effort will result in failure with amazing predictability" - Me

View TheFridge's profile


10859 posts in 2098 days

#2 posted 08-04-2016 02:43 AM

pretty much basic math and geometry all the time. Electrician. For offsets and stuff. Percentages of percentages.

-- Shooting down the walls of heartache. Bang bang. I am. The warrior.

View MadMark's profile


979 posts in 2065 days

#3 posted 08-04-2016 02:50 AM

Look at my more general solve on the same thread …


-- Madmark - [email protected]

View JBrow's profile


1368 posts in 1532 days

#4 posted 08-04-2016 03:06 AM


Your daughter is taking on a daunting challenge to convince high school kids that their education has significant value. Some will get it, but it seems in this day and age it is only after several years out of high school that they begin wishing they had taken their education seriously. I recall this very question from my kids; why do I have to learn all this stuff? They seemed impressed with my explanation but their commitment to school remained the same. Nonetheless I applaud her efforts and hope she succeeds.

Here are five pretty basic things derived from math, couched as questions. Most can be used in woodworking but obviously have wider applications.

1. I heard that the base of the pyramids in Egypt is distances evenly divisible by pi. They must not have had a long enough tape measure so could they have used a circle to measure distance? (geometry of a circle)

2. How did geologists come up with a diameter of the earth as 7,917.5 mi? (geometry of a sphere)

3. How do you pour a large concrete pad without the Pythagorean’s theorem and its derived 3, 4, 5 or 6, 8, 10 rules? (geometry of a right triangle)

4. How much carpet is needed to cover my floor? (area)

5. How many board feet of lumber do I need to build a rectangular table top 1-1/2” x 3’ x 6’, allowing for 20% waste? (rectangular volume)

View bbasiaga's profile


1243 posts in 2607 days

#5 posted 08-04-2016 03:09 AM

Common examples:

If I want to make a mitered square, what angle do I cut each piece at? What about a hexagon/heptagon/octagon, etc.

Using sine, cosine, tangent to calculate the angle of a cut from known dimensions, or an unknown dimension from a known dimension and a known angle.

If I want to make an oval/ellipse of a certain dimension, where do I place the foci of my jig to get what I want?

Using geometric principles to figure out angles of pieces that come together.

Caluclating volume of a piece, and using the density of the material to figure out the weight.

This is usually beyond highschool, but you can calculate the load/stress a bolt will be under to determine the diameter and or thread pitch bolt you should use.


-- Part of engineering is to know when to put your calculator down and pick up your tools.

View Mark Shymanski's profile

Mark Shymanski

5623 posts in 4324 days

#6 posted 08-04-2016 03:10 AM

Figuring out gear ratios for clocks.

Creating different cuts of shellac.

Determining angles for adjacent staves in a multi-sided cylinder (barrel, or mast)

Costing out projects for fun or profit

Calculating volumes of concrete for piers or piles

Calculating power requirements for a circuit

I believe there is a strong correlation between understanding the logic of mathematics and good programming skills (Arduinos and Raspberry Pi platforms are affordable for classroom use)

I am sure there are more but I’ve had a long day on a construction project where I, ironically, used no mathematics at all except at the fast food joint calculating my change at lunchtime. :-)

-- "Checking for square? What madness is this! The cabinet is square because I will it to be so!" Jeremy Greiner LJ Topic#20953 2011 Feb 2

View nightguy's profile


213 posts in 1274 days

#7 posted 08-04-2016 05:00 AM

All the last posters were correct but maybe a bit too deep for them iff they dont have basic math skills already? Simple Fractions and Decimals, she may be taking on a fruitless/dauntless task. I commend her effort!!
So if they do have basic math skills, I have a 3×3’ skid in the warehouse, I can only load it 3’ high, how many cubic feet do I have? How many cubic yards?
I have to pour a concrete slab 3.5” thick by ?X? how many cubic yards of cement do I need?
I have a wall ?x? and I need to cover it in Tyvac wrap, the roll is 12’ x 50’, how many rowels do I need?
Building a wall X length with a 2×4 at each end and one every 16” how many do I need?
I have a Triangle 45 all sides, how many do I need to make a square object? a Rectangular one?
I have a triangle 30
x30x60 same question.
If I have a side of a roof 30’ wide and horizontal to the ridge it is 16’, how many square feet for a 1-4’ pitched roof compared 1-6’ pitched roof?
Mom sends you to the store for a Gallon of Milk, they are out of Gallons and only have Quarts, how many for a Gallon?
Mom needs a cup of Whipping Cream they are out but just have Pints, how much more did you buy?
I could go on for ever, God help your daughters sanity after a few weeks. I commend her effort!!

View nightguy's profile


213 posts in 1274 days

#8 posted 08-04-2016 05:08 AM

Wood working a Board foot, so I have a piece of wood 6” wide by 8’ long x 1 ” thick, how many Board Feet is that? 4.
I have 6”x 8’x 1.5” thick, how many Brd Ft is that? 4 but at a different price range.

View ksSlim's profile


1304 posts in 3502 days

#9 posted 08-04-2016 05:10 AM

Good resource for calculators.

-- Sawdust and shavings are therapeutic

View nightguy's profile


213 posts in 1274 days

#10 posted 08-04-2016 05:55 AM

Good resource for calculators.

- ksSlim

You got to know what to put into them, and know when your fat finger installed a wrong number and the answer does not look right to double check it.

View Tabletop's profile


139 posts in 1359 days

#11 posted 08-04-2016 06:07 AM

Geez! There’s some smart people on here! Makes me feel pretty stupid especially when I sometimes have trouble just reading my tape.

View Tony_S's profile


1070 posts in 3695 days

#12 posted 08-04-2016 10:30 AM

Wood working a Board foot, so I have a piece of wood 6” wide by 8 long x 1 ” thick, how many Board Feet is that? 4.
I have 6”x 8×1.5” thick, how many Brd Ft is that? 4 but at a different price range.

- nightguy

Your first example is correct…second example is 6 board feet, not 4.

In addition to your example of determining the radius of an arc, some other basic geometry used in the stair industry for both straight and curved stairs…
Pi r2 or Pi D
a2 + b2=c2
Pretty basic stuff, but essential for a good stair builder, or rail installer and/or site measure and/or estimator.

-- “Wise men speak because they have something to say; fools because they have to say something.” – Plato

View mahdee's profile


4291 posts in 2379 days

#13 posted 08-04-2016 10:47 AM

I use french curve rulers both in woodworking and trading stocks. They do the math for me.


View Jim Finn's profile

Jim Finn

2782 posts in 3534 days

#14 posted 08-04-2016 10:59 AM

When I worked as a sheet metal worker I often needed to know how long a duct was required to offset an certain amount at 45°, using 45° ells. I multiplied the offset by the square root of 2. (1.41) to get this dimension. When making a round pipe I needed to know the total circumference of the wanted round duct in order to make it. C=pi d Just two examples in working with metal..

-- No PHD just a DD214 Lubbock Texas

View Nhapplewood's profile


9 posts in 1273 days

#15 posted 08-04-2016 12:51 PM

Ask them to solve problems involving the most efficient way to build a particular item. For example – you have 3 pieces of 1×6x8 lumber and you wish to build a square coffee table. What are the max dimensions the table can be? Then take it a step further and have them try building a mini version of something using balsa wood, or maybe a full size version depending on the school’s facilities.

I’m not great at math but I teach high school. Kids like to solve problems and they like when there are multiple solutions they can share with each other.

Good luck to your daughter.

View BigYin's profile


421 posts in 3028 days

#16 posted 08-04-2016 01:01 PM

relate maths to specific jobs to conect the how and the why

. Carpenter – measure to frame and roof house. make a box. make and fit window etc
. Blacksmith – work out the size of metal bar to cut off to make another object
. Pipefitter – how long to cut to form bends and strait runs.
. Chef – how much food and booze to buy how much to portion and how much to sell for including Food+ utilities+ taxes+ wages+ depreciation+ maintainance+ insurance+ repairs+ Permits+ licences+ Trash+ Bribes+ gifts+ Protection money etc
. Military – if you cant count you cant get in
. Lawn service – pricing cutting, fertiliser, weedkiller, hourly outlays (Truck, gas, tools Wages etc)
. slinging burgers at Mcdanalds – to check you wages so boss cant cheat you

-- ... Never Apologise For Being Right ...

View Dustin's profile


707 posts in 1352 days

#17 posted 08-04-2016 01:59 PM

The golden ratio: the convergence of the quotient of a fibonacci number divided by its previous term as the series approaches infinity. Roughly 1.618 to 1. A frequently used proportion in determining what is aesthetically pleasing, found in art, architecture, furniture, etc.

-- "Ladies, if your husband says he'll get to it, he'll get to it. No need to remind him about it every 6 months."

View Hammerthumb's profile


2996 posts in 2587 days

#18 posted 08-04-2016 02:17 PM

I have 14 stone tabletops to make for a restaurant. Each top is 3ft x 5ft. The stone that is specified for the project comes in 55”x122”x3/4” slabs. The material cost me $12.50 per square ft.

1. How many slabs do I have to order to complete the project?
2. How much will the slabs cost?
3. How much of the material will be un-useable waste?

-- Paul, Duvall, WA

View OggieOglethorpe's profile


1276 posts in 2722 days

#19 posted 08-04-2016 02:36 PM

Take a look…

View GR8HUNTER's profile


6837 posts in 1324 days

#20 posted 08-04-2016 02:40 PM

2 + 3 = 6 ??? ......... LOL
serious now … I went to trade school for 4 years for sheet medal …...... they trained us in math …...... BUT in the real world …... there is always short cuts that are much faster.

-- Tony---- Reinholds,Pa.------ REMEMBER TO ALWAYS HAVE FUN

View 000's profile


2859 posts in 1511 days

#21 posted 08-04-2016 02:52 PM

Here are 2 formulas I came up with. I don’t believe they are perfect formulas, but from my experimenting they come pretty close for me.
1st is a formula for finding the length of 1 side of a hexagon using the width.
Width divided by 1.732051615

2nd is finding a 22 1/2 deg angle using the width.
Width x .4142173 (add answer to width to determine distance to measure to for 22 1/2 angle)

Like I said, they are not perfect formulas. I find them to work very well with measurements up to a couple of feet but haven’t tried them on a bigger scale.

View Ocelot's profile


2383 posts in 3250 days

#22 posted 08-04-2016 03:25 PM

There’s lots of math/arithmetic in just about any construction project or in making almost anything.

If you are going to build anything, you have to figure how much material to buy.

How many boxes of flooring? How many bundles of shingles? How many cubic yards of concrete? How many fence boards? How many board feet of lumber? How many gallons of paint?

I would start with those kind of questions.

Every day on Craig’s List you see people trying to sell the extras after having bought too much for their project.


View Ocelot's profile


2383 posts in 3250 days

#23 posted 08-04-2016 03:28 PM

Also, they need to have some sense of how to estimate things using simple math.

How many decimal places do need for a particular calculation?

When is 17 good enough as 1/6th of 100?

Being able to quickly estimate without a calculator gives you a way to check to see if your calculations are reasonable. This is a practical skill.


View Woodknack's profile


13029 posts in 2992 days

#24 posted 08-04-2016 04:24 PM

The flaw here is that woodworking isn’t a real world problem for high schoolers, anymore than roofing, warehousing, chemistry, stocking or any other thing adults do. If you want the kids to relate then the example needs to be from their world. But kids rarely need math so it’s difficult to come up with real world examples that relate to them. I wonder if it wouldn’t be more effective to give them the problem then teach them how to solve it vs teaching them how to solve it and then looking for a problem. Subtle difference but might work.

-- Rick M,

View clin's profile


1076 posts in 1608 days

#25 posted 08-04-2016 04:38 PM

Thanks for all the input. This thread topic seems to be hotter than a “which table saw should I buy thread.”

I know it can be tough to get kids attention when they don’t need to use math in their world. The rent, cable, cell phone, car etc bills all get paid with all that easy money mom and dad make, doing whatever boring thing it is they do when they’re at work. It is easy for them to not relate. Of course not relating to other peoples lives is something a lot of us adults do too.

It will be up to my daughter and the other education professionals to come up with how to connect with the students. But I thought I’d pick the forums brains and put together some examples for her to draw on if she thinks it will be useful.

Good or bad, she’s starting in a very non-traditional school. Her own experience is in traditional classrooms, so she trying to understand how to teach math in this unusual school.

-- Clin

View MrRon's profile


5813 posts in 3855 days

#26 posted 08-04-2016 04:52 PM

An everyday math skill needed would be the conversion of metric to English and back. Another is the conversion of centigrade to fahrenheit and back. The ability to calculate unit weight of an item in a supermarket and compare it to a similar item to determine best price. I would also try to instill in them; to be able to do math in their head instead of relying on a calculator for the answer. It may not work for more complex problems, but by rounding up or down dollars and cents to even dollars simplify working out the answer without a calculator. It will be a close approximation, but close enough for everyday quick math. When I went to school, we had to memorize multiplication and division tables. I don’t know if it is still being done today, but over the years, I have found it a most valuable skill in my everyday needs for a math answer. It gives you the ability to manipulate numbers based on logic. Using logic is far more valuable than remembering formulas.

View lew's profile


12939 posts in 4367 days

#27 posted 08-04-2016 05:45 PM


Rafters and stairs

-- Lew- Time traveler. Purveyor of the Universe's finest custom rolling pins.

View oldnovice's profile


7517 posts in 3980 days

#28 posted 08-04-2016 06:07 PM

I know that many supermarkets now provide this information but I used to quiz my kids on what is a better buy, 12 oz. for $0.56 or 1 pound for for $0.72? They never forgot that everyday math.

Or how many kg are need in this recipe that is in fraction ounces? One of mothers favorites!

My son works in a big box store and he is dismayed when one of the associates can’t even do 10% calculations in there heads.

And that is only the tip of the “stupidberg” they don’t even know that Iowa is a state in the Midwest or that Texas is in the south ….. granted that to most of these kids there is only California …. I could go on but there is way too much to write about.

-- "I never met a board I didn't like!"

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102 posts in 1383 days

#29 posted 08-04-2016 06:20 PM

I don’t know for sure, but I always understood that French Curves were based on mathematics

you might investigate and let us know

View ChuckV's profile


3264 posts in 4139 days

#30 posted 08-04-2016 06:58 PM

Our sons are 12 and 14. I have noticed that they learn stuff when they need it to do something else that they really want to do. For instance, a year ago the older boy went through a frenzy of writing his own computer games. He needed lots of math including geometry, trigonometry and probability. With just a little help, it was amazing to see how quickly he learned these topics so that he could get past the next step in his project.

-- “Big man, pig man, ha ha, charade you are.” ― R. Waters

View Richard's profile


1932 posts in 3302 days

#31 posted 08-04-2016 07:45 PM

Oh Man they lost me right after 2 + 2 = 4 , But like ChuckV said they will learn what it takes to do what they want to do. I learned geometry better than any other form of Math because it was needed for what I wanted to do.
I haven’t used Algebra yet and don’t expect to any time soon.

View CM_2016's profile


13 posts in 1328 days

#32 posted 08-04-2016 08:42 PM

Angle/length at which supports should be set at to hold a shelf.

That’s about all I got.

-- Greatness is a lot of small things done well everyday- Ray Lewis

View jwmalone's profile


769 posts in 1314 days

#33 posted 08-04-2016 09:09 PM

I had an old math school book printed in 1895. It started with the definition of a number and ended how to measure for wall paper. ahhh the good ole days.

-- "Boy you could get more work done it you quit flapping your pie hole" Grandpa

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4258 posts in 2589 days

#34 posted 08-04-2016 10:07 PM

How about this one. Building a dog house. What are my measurements. How many sheets of 4X8 plywood do I need, how many 2X4’s, how much insulation, how and can I heat it for fido safely, how many shingles. A simple problem solving format that can be the basis for building an actual house.

-- We all make mistakes, the trick is to fix it in a way that says "I meant to do that".

View Woodknack's profile


13029 posts in 2992 days

#35 posted 08-04-2016 10:42 PM

Our sons are 12 and 14. I have noticed that they learn stuff when they need it to do something else that they really want to do.
- ChuckV

Excellent example and what I meant by “give them a problem and show them how to solve it”. Math is a means to an end, not the end itself. So if you want them to learn math, do something that requires that math. School would be much more effective if it wasn’t sitting around a classroom listening to a teacher drone. My daughter’s HS has taken some steps in that direction. Homework is somewhat rare and many of their classes are designed around real world occupations—digital media, forensics, drama, lots of other things. They still have to teach traditional classes due to state laws and required tests but they offer so much more too.

-- Rick M,

View AandCstyle's profile


3266 posts in 2869 days

#36 posted 08-04-2016 10:52 PM

I agree that ChuckV had the best suggestion. The topics need to be relevant to today’s kids. How many hits do I need to get on Google to make a $1 million if I make $0.005 per hit? How many times does my app need to be downloaded before I can sell the idea for $1 billion? How many miles do I need to drive for Uber to pay for college? Etc.

-- Art

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Arlin Eastman

4275 posts in 3173 days

#37 posted 08-04-2016 11:04 PM

Biggest thing I ran into in the real world is most people do not know how to read a tape measure or I should say knowing their fractions. Then you have dismals, and even simple addition without using their phone.

Or the biggest thing is doing their Check books and making sure it is straight!!!

-- It is always the right time, to do the right thing.

View Richard's profile


1932 posts in 3302 days

#38 posted 08-05-2016 02:18 PM

I had an old math school book printed in 1895. It started with the definition of a number and ended how to measure for wall paper. ahhh the good ole days.

- jwmalone

I am hoping that wasn’t your Elementary School class book. :)

View Dan P's profile

Dan P

738 posts in 2504 days

#39 posted 08-05-2016 05:00 PM

Here is one they could do digitally. Have em put baseboard moldings in rooms with a lot of corners. First have them do it with only tape measure and guessing, one strip at a time. Then have them do it with measurements and calculations cutting all boards before application.

Then pretend the house is 20 or 30 years old and do the same thing again.

-- Daniel P

View Ocelot's profile


2383 posts in 3250 days

#40 posted 08-05-2016 08:18 PM

I agree with Rick M.

Any lesson disconnected from life that they know will be hard for them to learn because there is no natural motivation.

If they care about baseball, talk about batting averages, ERA’s and that sort of thing.

If they use a smartphone, do some work with how many megabytes of data they would use doing various activities.

If they want to have a job to make money, talk about tax rates and how long they have to work to buy whatever it is they want.

View oldnovice's profile


7517 posts in 3980 days

#41 posted 08-06-2016 12:14 AM

I did a lot of abacus learning when I was younger, a long long time ago, which I have totally forgotten!

But there are a lot of videos that show how kids that learn to use an abacus will later to use a “mental” abacus and solve complex problems with their mind.

-- "I never met a board I didn't like!"

View JoeinGa's profile


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#42 posted 08-06-2016 01:09 AM

Show ‘em how to balance a checkbook!

Oh , and …

-- Perform A Random Act Of Kindness Today ... Pay It Forward

View MrRon's profile


5813 posts in 3855 days

#43 posted 08-07-2016 09:06 PM

Old math text books used to be full of practical examples like: “if apples cost 3 for a dollar, how many apples will I get for $5.00”? This may sound like a simple example, but believe it or not, there are many kids who can’t figure it out and there might be some college kids also.

There are some who can’t equate analog time to digital time. I know because my son was one of them. I think he has finally figure it out.

View MadMark's profile


979 posts in 2065 days

#44 posted 08-07-2016 09:17 PM

Lack of understanding of analog time also implies difficulty with ratios & proportions.


-- Madmark - [email protected]

View devann's profile


2250 posts in 3304 days

#45 posted 08-08-2016 01:27 AM

Here is a source of mathematical examples you may find interesting.

-- Darrell, making more sawdust than I know what to do with

View mike02130's profile


170 posts in 1284 days

#46 posted 08-08-2016 02:08 AM

If I have a ten foot banister, how many balusters and at what spacing is needed? That can also be asked, if you have a ten foot wall and want to hang six equally sized pictures, what would the spacing be?

-- Google first, search forums second, ask questions later.

View oldnovice's profile


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#47 posted 08-08-2016 03:52 AM

I guess I was wrong!

-- "I never met a board I didn't like!"

View StLouisWoodworker's profile


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#48 posted 01-22-2017 05:54 PM

I wrote woodworking notes on the following topics that involve applying mathematics. 1. Cutting Compound Miters on a Table Saw 2. Cutting Hexagons on a Table Saw 3. Making Polygonal Shaped Objects on a Table Saw 4. Compound-Angle Joinery 5. Cow-Catcher Design 6. Wire Gauge Conversion to Diameter 7. Spirals In Woodworking 8. Calculus Meets String Inlay
These can be accessed on my website by clicking on woodworking notes

-- Don Snyder (38.6N, 90.3W)

View Kelly's profile


2641 posts in 3556 days

#49 posted 01-22-2017 06:24 PM

Years ago, one of my young sons was complaining about math. I went along with him and said, yeah, there probably won’t be a lot of time’s you’ll have to use more than simple math. Then I launched off into a conversation about building a gocart. In the end, we figured out we could get everything we needed cheap, including a Briggs and Stratten lawn mower motor.

Of course, a project like that would require lot of measuring. Then, if all went well, we had to figure out how fast we could push it, off an under powered motor. That meant learning a bit about ratios and applying them to primary and secondary pulleys.

View bonesbr549's profile


1588 posts in 3679 days

#50 posted 01-22-2017 08:50 PM

I’ve got a real simple one:

You are building a deck on your house. This is going to be a large deck. Lets say for argument 30’x20’ feet.

Since its critical to make that Square, how can you do it and you don’t have a store bought square that would not work well at those distances anyway.

Simple use pythagorean theorem to solve the problem

You simply use your tape measure and go to one corner of your joist box and measure from corner to 3’ make a mark and on the other side measure 4’ and make a mark

Now measure from firs tmark to second mark and if its 5’ you are square and can make your deck properly.

We called it the 3 4 5 method. you can go in multiples and it will work across long distances i.e.. 6 8 10 etc. on and on and on.

-- Sooner or later Liberals run out of other people's money.

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