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The rate of taper is 1:20 on diameter, in other words 0.600" on diameter per foot, .050" on diameter per inch. Tapers range from a Number 2 to a Number 20. The diameter of the big end in inches is always the taper size divided by 8, the small end is always the taper size divided by 10 and the length is the taper size divided by 2.
Example (inch, coarse): For size 7 ⁄ 16 (this is the diameter of the intended screw in fraction form)-14 (this is the number of threads per inch; 14 is considered coarse), 0.437 in × 0.85 = 0.371 in. Therefore, a size 7 ⁄ 16 screw (7 ⁄ 16 ≈ 0.437) with 14 threads per inch (coarse) needs a tap drill with a diameter of about 0.371 inches.
The taper is the change in the size of the diameter as you travel down the axis of the taper. So, take 1/2 the change size (1.75") and divide that by 12", arctan of the result is 1/2 the included angle. So 16.5942899... is correct. —Preceding unsigned comment added by SamELLI (talk • contribs) 17:45, 29 April 2008 (UTC) D'oh!
The most popular size is 8 mm which came in several variations but all 8 mm collets are interchangeable. Lorch, a German Lathe maker, started with 6 mm collets and the first Boleys used a 6.5 mm collet. 6 mm collets will fit into a 6.5 mm lathe but it is a poor practice. Another popular size is the 10 mm collet used by Clement and Levin.
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Both the tool and socket have a slight taper. The contemporary square drive screw has all but replaced the Robertson screw proper and is commonly referred to as a Robertson because it has practically identical drive dimensions and the same colour identification system, but the contemporary square drive socket has parallel sides rather than tapered.
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In the modern standard metric version, it is simply a size number, where listed diameter size is the major outer diameter of the external thread. For a taper thread, it is the diameter at the "gauge length" (plus/minus one thread pitch) from the small end of the thread.