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Hex and Square: Across Flats vs Across Corners
Guide · Updated October 28, 2026
Hex and square sizes are given across the flats (AF). When you machine a hex or square from round bar, or check whether a hex fits in a collet or a bore, you need the distance across the corners (AC). For a regular hexagon AC = AF ÷ cos 30° = 1.1547 × AF. For a square AC = AF × √2 = 1.4142 × AF.
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Step by step
- Get the across-flats size: From the drawing or by measuring flat to flat with a caliper or mic.
- Pick the factor: Hex: 1.1547. Square: 1.4142. Octagon: 1.0824.
- Calculate across corners: AC = AF × factor.
- Choose stock: Round stock must be at least AC; add allowance if you want sharp corners.
- Verify: Measure all three flat pairs on a hex and both on a square.
Factors
- Hex: AC = AF ÷ cos 30° = 1.1547 × AF
- Square: AC = AF × √2 = 1.4142 × AF
- Octagon: AC = AF ÷ cos 22.5° = 1.0824 × AF
Going the other way, the largest hex you can cut from a round of diameter D is AF = D × cos 30° = 0.866 × D, and the largest square is AF = D ÷ √2 = 0.7071 × D.
Worked example: 3/4 in hex from round
A 0.750 in AF hex has AC = 0.750 × 1.1547 = 0.866 in. Stock of 7/8 in (0.875 in) leaves the corners fully formed with about 0.0045 in per side of cleanup; 1 in stock wastes more but allows a chamfer. If you only have 0.850 in bar, the corners will be slightly rounded, because 0.850 is less than 0.866.
On a mill with a dividing head or 5C hex block, cut the first flat at a depth of (D − AF) ÷ 2 = (0.875 − 0.750) ÷ 2 = 0.0625 in, index 60°, and repeat. Measure across the first pair of flats before cutting the rest.
Worked example: 1 in square in a collet
A 1.000 in square has AC = 1.4142 in, so it will not pass through a 1-3/8 in (1.375 in) round bore, but it fits a 1-1/2 in (1.500 in) bore. For the largest square from 1.000 in round, AF = 1.000 × 0.7071 = 0.707 in.
Use square or hex collets for gripping on the flats instead of round collets on the corners, which mark the corners and grip poorly.
FAQ
What is across flats?
The distance between two parallel flats, the normal way hex and square sizes are specified.
What is the hex across-corners factor?
1.1547, which is 1 ÷ cos 30°.
What is the square factor?
√2 ≈ 1.4142.
How do I check a hex?
Measure all three flat pairs; they should match within the tolerance. Set a comparator with gage blocks built free at gageblockcalc.com.
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