HackSpace magazine

Maker mathematics

By Gareth Branwyn. Posted

The ultimate maker maths – when considering making something over buying it, you want to be realistic in terms of calculating the cost and the time it will take you. If a widget you’re thinking about buying costs $1500, and you calculate that the realistic cost of making it yourself is $1300, is it worth doing? How you calculate this depends a lot on you, how you value your time, if you think the learning you’ll do in the process is worth it, etc. In some situations, even if it costs more to do it yourself, it still might be worth it for you. And then there’s the ultimate X factor: the sheer joy of making, and ultimately using, an object or tool that you made yourself. That calculation is often the hardest to make.

Estimating project time Carefully, figure out how long a project is realistically going to take and then double it. Especially if it’s a job for someone else, you will look like a miracle-worker when you deliver it ahead of schedule. It’s also great for your own sense of accomplishment to finish projects ahead of time. 

Estimating project costs Come up with a realistic figure for how much the supplies and materials for a project will cost and then triple it. Besides probably needing more than you think, there are also all of the incidental costs that you don’t or cannot foresee.

Adding a hassle tax If you’re working on a project or with a client that you fear might be more difficult than usual, add a hassle tax to your job estimate. This is the extra time, hassle, and heartache this situation is likely to cost you. The amount of tax may vary. When this author ran a graphic design business many years ago, the hassle tax was 20%. If the client baulked at the price, so be it. If they were willing to pay it, the extra hassle was paid for.

Calculating safety factor When working with anything that will come under a live load – something that will come under stress – take the stated load rating of the materials you are working with and multiply by five (or more). Static loads are obviously less prone to stress failure than live loads, but you should always err on the side of caution. In some engineering schools, students are taught to calculate load safety and then told to add a zero to the result.

Calculating hourly rates based on probability From Miguel Valenzuela (inventor of the PancakeBot) comes this gem: one of the biggest challenges we have as freelancers is calculating how much our hourly rate should be. Using probability helps in calculating what you should charge based on the probability of work. Here’s an example:

Shelly wants to make $100,000 per year, and has the ability to work 2000 hours per year. If she works 100% of that time, then she will need to charge $50 per hour. The problem is that Shelly doesn’t actually work 100% of the time. She has calculated that the probability of her working is actually 62%. So, the minimum hourly rate she must charge is $100,000 divided by 2,000 x 0.62 = $80.60 per hour.

Now remember, Shelly can work more or less than 62% of the time, so her probability of work is merely a planning and forecasting tool; it is not set in stone.

Estimating the square roots of small numbers When figuring out the square root of a small number, it’s helpful to know that the square root of 1/1000 = ~.031.

Converting decimals to fractions To convert from decimal to fraction, multiply the amount to the right of the decimal point by the desired denominator to get the numerator. For example, 0.5 ×16 = 8, so 0.5 is 8/16.

Converting model scales and real-world scales to model sizes If you work with model scales, such as those used in model railroading or scale modelling, you sometimes need to convert between the designated scale sizes (e.g. HO-scale or 1:87) and real-world measurements. To do this, there are a number of scale conversion calculators online. Here is one: hsmag.cc/2cONIK.

1-2-3 blocks can make it easy to mark out common sizes

Enter mathematical equations rather than calculating numbers to enter into modelling software Most modelling programs will allow you to enter equations into their parameter fields so that you don’t have to actually calculate the number first.

Handling very large or small numbers in your head Multiplying or dividing large or small numbers is easier if you shift the decimal places on both numbers until you have numbers you can deal with. If the two numbers are on the same side of the equation, shift one to the right and the other to the left, like so:

X = .002 * 10,000

X = .02 * 1,000

X = .2 * 100

X = 2 * 10

X = 20

If they’re on opposite sides of the equation, shift them both in the same direction by multiplying or dividing both by 10:

100X = .5

10X = .05

X = .005  

THANKS to Bryce Lynch, Michael Colombo, Ross Hershberger, Dave Porter, Becky Stern, Jen Foxbot, Miguel Valenzuela