⬡ Hexagon Lab

Regular Hexagon Calculator

Calculate every regular hexagon measurement, coordinate, material quantity, cost, prism property, tolerance range, scaled dimension, and printable layout from one value.

Calculator inputs

Select the measurement you already know.
Decimals, fractions, and mixed numbers are accepted.

Calculated results

Input—
Side—
Area—
Perimeter—

Interactive diagram

Regular hexagon measurement diagram A labeled regular hexagon showing its side, radii, apothem, diagonals, and principal widths.

Advanced tools

Degrees counterclockwise.
VertexXYAngleDistance from center

Generated code

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Percentage added for cuts and breakage.
Uses the selected output length unit.
Use below 100% for partial effective coverage.
Optional kilograms per cubic meter.
PropertyHexagon AHexagon BDifferenceChange
PropertyMinimumNominalMaximum
Format: measurement,value,unit. Area values use square units.
side perimeter area apothem inradius circumradius short_diagonal long_diagonal across_flats across_corners
RowInputSidePerimeterAreaStatus

Formula used and calculation steps

Formula selected

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Step-by-step solution

    Related circle analysis

    Regular hexagon formulas

    These formulas use side length s, apothem a, perimeter P, and area A.

    Perimeter
    P = 6s
    Area
    A = (3√3 / 2)s²
    Apothem
    a = (√3 / 2)s
    Circumradius
    R = s
    Short diagonal
    d₁ = √3s
    Long diagonal
    d₂ = 2s
    Across flats
    AF = √3s
    Across corners
    AC = 2s
    Side from area
    s = √(2A / (3√3))
    Side from perimeter
    s = P / 6
    Side from apothem
    s = 2a / √3
    Interior-angle sum
    (6 − 2) × 180° = 720°

    Example data table

    SidePerimeterAreaApothemShort diagonalLong diagonal
    2 cm12 cm10.3923 cm²1.7321 cm3.4641 cm4 cm
    5 cm30 cm64.9519 cm²4.3301 cm8.6603 cm10 cm
    10 cm60 cm259.8076 cm²8.6603 cm17.3205 cm20 cm
    1 ft6 ft2.5981 ft²0.8660 ft1.7321 ft2 ft

    Calculation history

    Recent calculations are stored only in this browser.

    How to use this calculator

    1. Select the hexagon measurement you already know.
    2. Enter its positive value. Fractions are accepted.
    3. Choose input and output measurement units.
    4. Select decimal, significant-figure, or scientific formatting.
    5. Press Calculate or edit a field for instant updates.
    6. Review dimensions, formulas, steps, and the live diagram.
    7. Open advanced tabs for coordinates, materials, prisms, and more.
    8. Copy, print, share, or export your completed calculation.

    Understanding regular hexagons

    What is a regular hexagon?

    A regular hexagon has six equal sides. Every interior angle equals 120 degrees. Its vertices lie on one circle. Its sides touch another inner circle. These symmetries make many calculations especially simple.

    Joining the center to every vertex creates six equilateral triangles. Each triangle has the hexagon’s side length. This explains why the circumradius equals the side length.

    Apothem and circumradius

    The apothem runs from the center perpendicular to a side. It is also the inradius. The circumradius runs from the center to a vertex. Their values are different.

    The apothem equals √3 divided by two times the side. The circumradius simply equals the side.

    Diagonals and widths

    A regular hexagon has short and long diagonals. A short diagonal skips one vertex. It equals √3 times the side. A long diagonal connects opposite vertices. It equals twice the side.

    Across flats matches the short diagonal. Across corners matches the long diagonal.

    Area and perimeter

    The perimeter is six times the side. Area may be found using six equilateral triangles. It may also use one-half times perimeter times apothem.

    Both methods produce the same result. Area units must always be squared.

    Real-world applications

    Hexagons appear in tiles, fasteners, honeycombs, maps, architecture, packaging, and mechanical parts. They cover planes efficiently without gaps. They also offer many neighboring connections.

    Regular versus irregular hexagons

    An irregular hexagon may have unequal sides or angles. The formulas here require a regular hexagon. Conflicting measurements may indicate an irregular shape or incorrect data.

    Accuracy

    Keep extra decimal places during intermediate calculations. Round only the final answer. This reduces accumulated error and keeps related values consistent.

    Frequently asked questions

    Can I calculate from the area?

    Yes. Select Area, enter the square-unit value, and choose its base unit. The calculator derives the side before calculating every other measurement.

    Are the apothem and inradius identical?

    Yes. In a regular polygon, the apothem is the radius of the inscribed circle. Both reach a side at a right angle.

    Why does the circumradius equal the side?

    The center divides a regular hexagon into six equilateral triangles. Each triangle has equal radii and side lengths.

    What is the distance across flats?

    Across flats is the perpendicular distance between two opposite sides. It equals twice the apothem or √3 times the side.

    What is the distance across corners?

    Across corners connects opposite vertices through the center. It equals the long diagonal and twice the side length.

    Can I enter fractions?

    Yes. Enter simple fractions like 3/4 or mixed numbers like 2 1/2. The calculator converts them into decimal values.

    Does grout width change tile coverage?

    Yes. The estimator approximates an expanded repeating cell when grout width is entered. Real layouts may differ near boundaries.

    Can this calculate an irregular hexagon?

    No. These formulas assume six equal sides and equal angles. Irregular hexagons require coordinates, triangulation, or additional side and angle data.