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Regular Hexagon Calculator

Geometry

Side, across-flats, area · nut wrench sizes

Quick Answer

Regular Hexagon Calculator: Side, across-flats, area · nut wrench sizes. Regular Hexagon Calculator uses standard geometry formulas to compute accurate results instantly.

Known quantity

mm
Area S
259.81 mm²
Regular hexagon · 6 equal sides
Side a10 mm
Perimeter P = 6a60 mm
Area S = (3√3/2)a²259.81 mm²
Circumradius R = a10 mm
Inradius r = (√3/2)a8.66 mm
Across flats f = √3a17.32 mm
Long diagonal 2a20 mm
Short diagonal √3a17.32 mm

Calculation steps

  1. 1边长 a = 10
  2. 2周长 P = 6a = 60
  3. 3面积 S = (3√3/2)a² ≈ 2.5981 × 10² = 259.81
  4. 4外接圆半径 R = a = 10；内切圆半径 r = (√3/2)a = 8.66
  5. 5对边距 f = √3a = 17.32；长对角线 = 2a = 20；短对角线 = √3a = 17.32

Common nut across-flats (GB / DIN 934)

SpecAcross flats (mm)WrenchEquivalent side a (mm)
M35.55.53.18
M4774.04
M5884.62
M610105.77
M813137.51
M1017179.81
M12191910.97
M16242413.86
M20303017.32
  • Honeycomb optimal: among all equal-perimeter tilings the regular hexagon encloses the most area — that is why bees, and hex floor tiles, save material.
  • Nut "across flats" is the wrench opening (M10 → 17 mm). The equivalent hexagon side is f ÷ √3 ≈ 9.81 mm.
  • Circumradius equals the side (R = a): a hexagon is exactly 6 equilateral triangles, so vertices all sit on one circle.
  • General regular n-gon: S = ½·n·R²·sin(2π/n). For n = 8: S = 2(1+√2)a² ≈ 4.828a² (stop-sign octagon).
  • For layout, area scales with a²: doubling the side quadruples material — watch this when sizing hex tiles or honeycomb panels.

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How to Use

  1. Enter known values: fill sides, radius or angles in the Regular Hexagon Calculator.
  2. Auto-solve the rest: all unknowns are solved instantly — no manual derivation.
  3. See formula and steps: the result panel shows the formula used and the substitution.
  4. Try another case: change any known value to solve again.

Key Points

  • Regular Hexagon Calculator is a free online geometry tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Side, across-flats, area · nut wrench sizes.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Regular Hexagon Calculator formula

Regular Hexagon Calculator uses standard geometry formulas to compute accurate results instantly.

FAQ

How do I use the Regular Hexagon Calculator?
Open the page and fill in the input fields — results update automatically. Side, across-flats, area · nut wrench sizes.
Are the results accurate?
Yes. Standard formulas and conversion factors are used and verified.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. Everything runs locally in your browser.

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Source & Updates

Based on standard Euclidean geometry formulas. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Regular Hexagon Calculator[EB/OL]. https://www.yijiansuan.com/en/c/geometry/hexagon

Results provided by this tool are for reference only and do not constitute professional advice.