Equilateral Triangle Perimeter Calculator

P = 3 × s

Three equal sides. A 10 cm equilateral triangle has a 30 cm perimeter. An equilateral triangle with 1 ft sides has a 3 ft (36 in) perimeter.

Where equilateral triangles show up in real life:

• Warning signs. A US Yield sign is a 36-inch-equal-sided triangle. Perimeter = 108 in = 9 ft of edge trim per sign.
• Geodesic domes. A typical hobby dome uses equilateral triangles with sides around 3 to 4 ft. Each panel has 9 to 12 ft of edge, which is what matters when you are sealing seams.
• Triangle road signs in many countries. Standard 70-cm side = 210 cm = 2.10 m perimeter.
• Truss design. Equilateral triangles are extremely efficient for load-bearing structures because they distribute force equally on all three sides.
• Triangular tent footprints. A 6 ft equilateral base has 18 ft of ground contact.
• Geometric jewelry. Pendant designs in 1-2 inch equilateral shapes.

Worked example: edging a geodesic dome

You’re building a 12 ft diameter geodesic dome from 3 ft equilateral triangle panels. Each panel perimeter = 9 ft. If the dome has 25 triangles, total edge length = 225 ft, but every interior edge is shared between two triangles, so the actual frame length is about half of that, around 112 ft.

Everything else from the same side s:

• Perimeter: P = 3s
• Height: h = s × √3 / 2 ≈ 0.866 × s
• Area: A = (√3 / 4) × s² ≈ 0.4330 × s²
• Inradius (inscribed circle): r = s × √3 / 6 ≈ 0.289 × s
• Circumradius (circumscribed circle): R = s × √3 / 3 ≈ 0.577 × s

Comparison to other triangles:

For a given perimeter, the equilateral triangle has the largest area of any triangle. Fix the perimeter at 30 ft and watch what the shape costs you:

The same 30 ft of fence, and the area falls away to nothing as the shape flattens. Note that you cannot push this indefinitely: 3, 12, 15 has the right perimeter but 3 + 12 = 15, so the two short sides lie flat along the long one and enclose no area at all. Any two sides must add to more than the third or there is no triangle, only a line.

A related but separate fact about 120° angles

Soap films meeting along an edge always settle at 120°, three at a time, because that is the only angle at which three equal surface tensions balance. Honeycomb cells end up hexagonal for the same reason, a hexagon being the shape whose corners are 120°.

That is worth keeping distinct from the triangle above. An equilateral triangle’s interior angles are 60°, not 120°. The 120° is its exterior angle, and it is the hexagon, not the triangle, that tiles the plane with the least wall for a given cell area.

Quick check. The equilateral triangle is the most symmetric triangle possible. All sides equal, all angles equal (60° each). Sum of interior angles is always 180° for any triangle, so 3 × 60° = 180° works out cleanly.