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Regular Octahedron Surface Area Calculator

Enter the edge length. The calculator returns SA = 2√3·a², the total area of the eight equilateral triangles.

A regular octahedron is a Platonic solid with 8 equilateral triangle faces — like two square pyramids stuck base-to-base. Its surface area is 2√3·a².

Mix and match length units per input (mm, cm, m, km, in, ft, yd, mi) and pick the area unit you want for the result (mm², cm², m², km², in², ft², yd², mi², acres or hectares). The calculator shows the formula being used and a clear breakdown so you can sanity-check the maths and not just trust the number.

Looking for other shapes? See our Surface Area Calculator hub for the full list of 3D shapes we cover.

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What this calculator does

Computes the surface area of a regular octahedron from its dimensions, using the formula SA = 2√3·a². Supports all common length units on input and any area unit on output, with a worked breakdown.

Who it is for

Students, teachers, DIYers, builders, fabricators, packaging designers and anyone who needs the surface area of a regular octahedron quickly and accurately.

How to use it

Enter Edge length (a). Choose your preferred unit for each input — you can mix units freely (e.g. some in inches and others in feet). Pick the area unit for the answer (m², ft², in², cm², acres, hectares and more). The result, the formula and the breakdown appear instantly.

How the calculation works

SA = 2√3·a². An octahedron with edge 1 m: SA = 2√3 ≈ 3.464 m².

Worked example

An octahedron with edge 1 m: SA = 2√3 ≈ 3.464 m².

Assumptions and limitations

  • Closed solid: all faces (ends, base, sides) are included.
  • Length unit conversions use exact factors (1 in = 0.0254 m, 1 ft = 0.3048 m, 1 yd = 0.9144 m, 1 mi = 1609.344 m).
  • Area outputs convert from m² using exact factors squared.

Frequently asked questions

How does an octahedron compare to a cube?

An octahedron is the 'dual' of a cube — each face of one corresponds to a vertex of the other. Their volumes and surface areas relate by simple proportions.

What units can I use in this regular octahedron calculator?

You can enter dimensions in millimetres (mm), centimetres (cm), metres (m), kilometres (km), inches (in), feet (ft), yards (yd) or miles (mi) — and you can mix units freely between fields. The result can be shown in any area unit: mm², cm², m², km², in², ft², yd², mi², acres or hectares.

How accurate is this regular octahedron surface area calculator?

Calculations use the exact closed-form formula (SA = 2√3·a²) with full double-precision arithmetic, so the answer is as accurate as your inputs. Length conversions use exact SI/Imperial factors (1 in = 0.0254 m, 1 ft = 0.3048 m).

Is this regular octahedron surface area calculator free to use?

Yes — every calculator on Korvaix is completely free, with no sign-up, no ads in the result, and no usage limit. You can run as many calculations as you need.

What is the difference between surface area and volume?

Surface area is the total area of the outside of a 3D shape, measured in square units (m², ft²). Volume is how much space the shape takes up inside, measured in cubic units (m³, ft³). Surface area is what you need for paint, packaging, heat loss and surface coatings; volume is what you need for capacity, weight and material fill.

Where else can I find surface area calculators on Korvaix?

Visit our Surface Area Calculator hub for the full list of 17 common 3D shapes. Each shape has its own dedicated page with the formula, worked example and unit-by-unit breakdown.

Related calculators

  • Annulus Area Calculator — Enter the outer and inner radii. The calculator returns A = π·(R² − r²).
  • Area Calculator — Pick a 2D shape — circle, square, rectangle, triangle, trapezium, parallelogram, ellipse, regular polygon, rhombus, sector, annulus or kite
  • Capsule Surface Area Calculator — Enter the radius and the straight middle length. The calculator returns 4πr² for the two rounded ends plus 2πrh for the cylindrical side.
  • Circle Area Calculator — Enter the radius. The calculator returns A = πr², the area of the flat disc.
  • Circular Sector Area Calculator — Enter the radius and the angle in degrees. The calculator returns the sector's area: A = ½·r²·θ (with θ converted to radians).
  • Cone Surface Area Calculator — Enter the base radius and height. The calculator splits the answer into the base (πr²) and the lateral surface (πr·s), where s = √(r²+h²) is

Related guides

Sources and references

Standard geometric surface area formula. SI and Imperial unit conversions per the International System of Units (SI) and NIST.

Last updated

Last reviewed: 2026-04-21.