In this video, Scott Wadsworth of Essential Craftsman shares a clever field trick for finding small angles without any math — no Pythagorean theorem, no trigonometry, no protractor. Using just a tape measure and a pencil, he demonstrates the 58-unit rule, a practical approximation method rooted in the same concept pilots use for navigation. He covers real-world applications like valley flashing angles, building settlement, and driveway slope, and shows where the method is accurate and where it starts to break down. Find more trade tips and craftsmanship content at the Essential Craftsman YouTube channel.

TRANSCRIPT:

Here's a trick to find small angles without math. No Pythagorean theorem, no trigonometry, no protractor, no nothing. Just a tape measure and a pencil. You can find small angles with remarkable accuracy using the 58-unit rule.

Ever heard of it? I hadn't either. It came in a comment from Randy Peterson. He wrote, "Ever heard of the 58-unit rule for finding small angles using only a tape?" Then he told me how to do it. I searched online and finally found a description. My brother was visiting—he's a pilot—and he said, "Oh, that's the 60-unit rule in aviation." It's all the same, and it will amaze your friends and might get you out of a jam.

The disclaimer: it's approximate

First, the disclaimer. This is approximate, and it's fast, but it'll only get you close.

In aviation, as my brother explained it, it's the 60-unit rule. When you fly 60 miles out on a straight line and check where you are relative to your course, if you're one mile left or right, you're one degree off. If you're three miles off at 60 miles out, you're three degrees off course—say, because of a crosswind—and you adjust your heading accordingly. Sixty units. When you're 5,000 or 50,000 feet up, that's close enough.

Real-world use cases

But if you need to measure something on the ground—say you've got a cricket running into a wall, or a weird valley that has to be roofed, like on our spec house project, where the only solution is a piece of bent sheet metal—maybe you get up there with an angle finder and a piece of cardboard and cut a template to capture that long, narrow point where the valleys come together. Or maybe you use this rule instead.

Another use case: maybe there's been some extreme settlement in a building, and you need to describe to an engineer how many degrees it has settled. If you use the 58-unit rule and you have a level—so you can establish a level reference out 20 or 30 feet—you don't need a laser. You can get measurements using just a tape that lets you communicate what you're seeing to someone who isn't standing there looking at it with you.

The math behind it (briefly)

Okay, so here's my chalkboard—it's a piece of Baltic birch with masking tape on it. The near edge of this piece of tape is a 10-degree angle right here. I've added 10 more, so this is 20 degrees, this is 30 degrees, this is 40 degrees, and five more degrees makes this a 45-degree angle.

Let me show you first where the method is accurate. Here's a 10-degree angle according to this drafting protractor, which I think is pretty good—and it is pretty much right. I'll show you in a second how I determined that. But here's a 45-degree angle. And it is not as right, because the discrepancy in the method adds up. My big speed square—which I'm not a fan of—shows it's off by this much, and by the time you come out to the point where we're doing the tape measure work, we're almost 3/8 of an inch off. But at these 10-degree increments, it's off maybe a 16th—and it's really hard to measure a 16th of an inch and worry about it too much in something like this.

I don't know about you, but for me it's been a long time since high school or freshman college math. A little refresher: there are 360 degrees in a circle, but 2π radians—which means 6.28 radians in a circle. If you divide that out, you end up with 57.3 degrees per radian. I'm not going to try to explain exactly why that ties into this, because I probably can't—but the upshot is the 58-unit rule.

How the 58-unit rule works

If you come out from the apex of your angle 58 units—we're going to use 29 inches, which is 58 half-inch increments—and mark that distance, then you measure on a square line over from that point the number of units that equals the angle in degrees.

So in this case, we're doing it on a square line: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. That means the line from that 10-unit point back to the apex of the angle describes a 10-degree angle. Can you see that? Fifty-eight units out, and the number of those same units measured over to intersect the other line tells you the number of degrees. Pretty interesting, right?

Measuring an existing field condition

Now, Randy Peterson pointed out that if you have an existing condition—rather than trying to establish a specific angle—you measure out on both sides of the triangle. In this case we were trying to create a 10-degree angle, but if you're measuring a field condition to find the existing angle, you measure 29 inches (58 half-inch units) on each side of the wedge—and it works well for low angles. Let's say this is a valley flashing: you come out 58 units on this side, 58 units on the other side, and then measure between those two points to find the angle.

And that, my friends, is just a hair over 5—which is 10 divided by 2—so you can call the sheet metal shop with confidence and say the angle at the deflection point on that valley flashing is 10 degrees.

Other applications and limitations

It's approximate—but valley flashings are approximate. The same goes for driveway slope. If you don't have any other way to do it and you can get a level line, measure out 58 units and measure up. That number of units is your degrees of slope. Handy.

Now, just to reinforce the point—if I put a 45-degree angle on here and measured across, it wasn't even close. But stacking smaller increments adds up to close enough for construction. If it's close enough for a pilot, it's probably close enough for a carpenter.

Closing thoughts

Pythagoras has got nothing to do with this in the field. Trigonometry is irrelevant out here. But a tape measure and a pencil—in this case—will get some magic done. And in most cases, it's accurate enough that when you walk away, you'll know: I did some good work there today, and nobody else knew how to do it.

Thanks for watching Essential Craftsman, and keep up the good work.