If you’ve ever used, or seen, a scientific calculator, you’ve seen a key to switch angle units between degrees, radians, and grads. Degrees and radians are both pretty common, of course, but why does anyone want to divide a right angle into 100 grads instead of 90 degrees? Who uses that feature, and why?
The Wikipedia article on the gon and the gradian has a few details (although it’s admittedly sparse.)
We have a deposition tool that measures the substrate carousel position in grads. Really annoying. The company is out of business. I don’t know if the two are linked.
[QUOTE=ElvisL1ves]
why does anyone want to divide a right angle into 100 grads instead of 90 degrees?[ /QUOTE]
grads are a decimal unit, and are subdivided into simple 100ths, just like the meter is subdivided into cetimeters…Degrees are not decimal units–they are subdivided into 60 minutes and then another 60 seconds.So every time you want to do a simple calculation (say, adding two angles), you have to do first do TWO extra steps–convert the seconds into decimal minutes, then convert the decimalized minutes into decimal degrees. (most pocket calculators have a simple button that does this, but it still requires you to press an extra button before doing the actual calculation that you want to complete.
try this example–add two angles : 75 degrees, 45 minutes, 20 seconds plus 25 degrees 15 minutes 10 seconds.
or add 75.753 plus 25.251
Which is easier?
Land surveyors (those guys you see on the side of the road with an instrument mounted on a tripod) make hundreds or even thousands of angle measurements during a day’s work.
Grads are great!!!
The only real use or experience I have with angles is mathematically, and in mathematics I always prefer (especially when using calculus or any higher math) radians.
With the advent of wide-spread automated calculation, grads become yet another metric solution in search of a problem.
I was trying to make a joke based on “grads” vs. “undergrads”, but it was getting too contrived to bother with…
Does anyone still measure angles in minutes and seconds, or have they gone the way of the slide rule?
The only time I see minutes and seconds still used is for latitude and longitude.
I don’t know if they use minutes and seconds in the day-to-day work, but I’ve certainly heard my father, a tunnel engineer, refer to angles in those terms.
When I first heard about grads (they were a third angular measure converrsion available on the HP series of calculators) I asked the same question. At the time, I was told that grads were used in the military.
I never understood the need for grads, since they are so close to degrees (90 degrees = 100 grads), and the explanations given to me for them never made sense. (You don’t get much more resolution with grads, the number of degrees is as easy to hear under battlefield conditions as the number of grads, and you can use degrees with decimal fractions instead of degree-minute-seconds if you want ease od calculation). On the other hand, it’s easy to take halves and thirds of 90 degrees, and the values of sines and cosines for 30 degrees and 60 degrees are significant and easy to remember. all grad measure can give you is something significant at 50 grads = 45 degrees.
Nope. Can’t see the advantage.
Astronomers still use arcminutes and arcseconds (carefully distinguished from ordinary minutes and seconds, which measure time) when describing the angular size of an object, the angular distance between two objects, or the declination component of an object’s celestial coordinates.
101 degrees 30 seconds. And I just read it off, unlike that decimal approximation where you have to convert, add, and convert back to get something close to the true answer. 
Of course I was brought up doing DMS, feet and inches, pounds and ounces, and a barrel of ale in London. And I can make change without a cash register too! 
Hey, I used to be able to add shillings and pence in my head, too. (ah,…Half-crowns, florins, thrupenny bits—but I never quite understood guineas)
But do you really want to give up decimal currency and go back to the “old ways”?
Militaries use mils (milli-radians) as their angle measurement, at least for artillery. One interesting point is that a US mil is1/6400 of a circle, while European ones are 1/6000 of a circle.
I was about to say that, Bytegeist. But even astronomers very seldom use degrees, arcminutes, and arcseconds together in the same context. So you might say, for instance, that the Moon has an angular size of half a degree, or if you wanted to be more precise, 31 arcminutes. But one would almost never specify “31 arcminutes and 5 arcseconds”. Such precision is rarely useful in astronomy; the one place where it is useful is in stellar parallax, and there, the angles are all less than an arcsecond anyway, so you’re still not mixing units.
I’ll stick with Canadian dollars and cents, thanks, but I’m sure I could pick up shillings and pence pretty quickly if I had to. Dunno about half-crowns and florins though.
Anyway, the trick with change is NOT to add and subtract, just count. Count enough pennies to reach a round amount, then nickels, dimes, and so on, until you reach the tendered amount. The same idea works with all those other units too.
A fair point. You would seldom see an angle given fully in degrees, arcminutes, and arseconds — not outside of a star catalog anyway. (And who memorizes those?) Still, you have to be familiar with the units, despite their quaint antiquity.
Also, aren’t galaxy surface brightnesses usually given in magnitudes per square arcsecond, or something similar?
Good points, but do land surveyors really use grads?
Saying that grads are decimal-based doesn’t really explain why they’re useful for anything - I don’t think I’ve ever used arcminutes or arcseconds when dealing with degrees. All through high school and now college, I’ve just used decimals: 78.289 degrees + 41.310 degrees = 119.599 degrees
And really, the choice of 100 grads as a right angle isn’t that much better than the choice of 90 degrees. They’re both arbitrary.
If 360 degrees = 100 grads, then I might agree that there’s some merit to that system. But 400 grads to 360 degrees? What’s the point?
Oops, didn’t see this before I posted.
Wouldn’t that mean that neither uses milliradians? A milliradian would be (approximately) 1/6283 of a circle.