Looking for Examples of Math in Wodworking

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Forum topic by clin posted 08-04-2016 02:18 AM 1336 views 0 times favorited 47 replies Add to Favorites Watch
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485 posts in 413 days

08-04-2016 02:18 AM

I just answered a question about figuring out an arc and this got me thinking about how math is used in woodworking. My daughter is going to start teaching high school math in a few weeks, in a charter school that is using project oriented teaching. My daughter is trying to pull together as much real-world examples as she can. In part to help combat the too commonly held belief that you never use math anyway, so why learn it.

Anyway, I’d appreciate any examples you can provide where you use math in the real world. Doesn’t need to be restricted to woodworking, though that is in keeping with LJ.

I don’t need lengthy details or diagrams, though if you have some specific formulas that would be great. But I do want them to be real examples. I can think up all sorts of things where I might use it. But as an engineer I use it where most people wouldn’t bother.

Thanks in advance for any ideas and examples.

-- Clin

47 replies so far

View bigblockyeti's profile


3569 posts in 1138 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.

View TheFridge's profile


5672 posts in 903 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


965 posts in 870 days

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

Look at my more general solve on the same thread …


-- Madmark -

View JBrow's profile


741 posts in 337 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


730 posts in 1412 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

5300 posts in 3130 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 80 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 80 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


1203 posts in 2307 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 80 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


61 posts in 165 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


597 posts in 2500 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.

-- It is the mark of an educated mind to be able to entertain a thought without accepting it. Aristotle

View mahdee's profile


3454 posts in 1185 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

2390 posts in 2339 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..

-- "You may have your PHD but I have my GED and my DD 214"

View Nhapplewood's profile


9 posts in 79 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.

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