From the archives: A question submitted by a reader about the exact size of a minute of angle at 100 yards. The answer came from the one and only Gen. Julian Hatcher. As published in the June 1954 issue of American Rifleman.
I would like to know the exact size of a minute of angle at 100 yards. It is usually called an inch, but according to my calculations it is nearer 13⁄64", being exactly 1.0472".—Emmett G. Hopkins, Bellevue, Iowa.
Answer by General Hatcher: You are correct. The minute of angle is not exactly an inch at 100 yards.
This is explained in The Book of The Garand as follows:
“There are 360 degrees in a circle and 60 minutes of arc in each degree, so that there are 21,600 minutes of angle in a complete circle. The circumference of a circle also equals 2 Pi or 2 x 3.1416 x the radius. Hence for any range, R, a minute equals 6.2832 R divided by 21,600 or 6.2832 ⁄ 21,600 R which, when divided out, is .000291 R.Thus if R is 100 yards or 3,600", one minute at that distance will be 3,600 x .000291, or 1.0476". Likewise at 1,000 yards a minute will cover 10 times that space or 10.476". Because the distance covered at 100 yards is so close to being exactly an inch, the fraction is disregarded in range work, and we commonly hear it said that a minute of change on the rear sight will move the point of impact one inch on the target for every 100 yards of range. That is certainly near enough for all practical purposes, especially as the ‘minute’ change in any target rear sight is usually not quite exactly a minute but varies somewhat with variations in sight radius and sight mounting.”
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