Calculate all properties of an equilateral triangle from side length, area, perimeter, or height. Includes area, height, perimeter, circumradius, inradius, and angles (always 60°).
An equilateral triangle is the simplest regular polygon — a triangle where all three sides are equal and all three interior angles are 60°. It is the most symmetric triangle possible and forms the basis of many patterns in nature, architecture, and design.
Despite its simplicity, the equilateral triangle has a rich set of properties. Its height h = (√3/2)·a, its area A = (√3/4)·a², and its perimeter P = 3a. The circumradius (radius of the circumscribed circle) is R = a/√3 = a·√3/3, and the inradius (inscribed circle) is r = a·√3/6 = R/2. The centroid, circumcenter, incenter, and orthocenter all coincide at the same point — a unique property among triangles.
Equilateral triangles tile the plane perfectly (one of only three regular polygons that do). They appear in truss bridges, geodesic domes, triangular road signs, the faces of tetrahedra and icosahedra, musical instrument bracing, and crystal lattice structures. The relationship R = 2r is famous in geometry and connects the circumscribed and inscribed circles elegantly.
This calculator lets you compute all properties from any one measurement — side length, area, perimeter, height, circumradius, or inradius. A unit selector, presets for common equilateral triangles, and a reference table make exploration easy.
The Equilateral Triangle Calculator — Side, Area, Height & Radii is useful when you need fast and consistent geometry results without reworking the same algebra repeatedly. It helps you move from raw measurements to Side Length, Height, Area in one pass, with conversions and derived values shown together.
Use it to validate homework steps, check CAD or fabrication dimensions, estimate material requirements, and sanity-check hand calculations before submitting work.
Side: a Height: h = (√3 / 2) × a Area: A = (√3 / 4) × a² Perimeter: P = 3a Circumradius: R = a / √3 = a√3 / 3 Inradius: r = a√3 / 6 = R / 2 All angles = 60° R = 2r (always)
Result: Height ≈ 8.66, Area ≈ 43.30, Perimeter = 30, R ≈ 5.77, r ≈ 2.89
With side = 10 cm: h = (√3/2)(10) ≈ 8.66 cm. Area = (√3/4)(100) ≈ 43.30 cm². P = 30 cm. R = 10/√3 ≈ 5.77 cm. r = R/2 ≈ 2.89 cm.
This calculator combines the core geometry formula with the input mode selected in the interface, then derives companion values shown in the output cards, comparison bars, and reference tables. Use it to cross-check both direct calculations and reverse-solving scenarios where one measurement is unknown.
Equilateral Triangle Calculator — Side, Area, Height & Radii calculations show up in coursework, drafting, construction layout, packaging, tank sizing, machining, and quality control. Instead of solving each transformation manually, you can test scenarios quickly and verify whether your dimensions remain within tolerance.
Keep units consistent across every input before interpreting area, perimeter, angle, or volume outputs. For best results, measure carefully, round only at the final step, and compare at least one manual calculation with the calculator output when building confidence.
A = (√3 / 4) × a², where a is the side length. For a = 10, area ≈ 43.30.
h = (√3 / 2) × a. For a = 10, height ≈ 8.66.
Yes — by definition, an equilateral triangle has all sides equal and all angles equal to 60°. Use this as a practical reminder before finalizing the result.
The circumradius R = a / √3 ≈ 0.577a. It is the radius of the circle passing through all three vertices.
R = 2r always. The circumradius is exactly twice the inradius in every equilateral triangle.
a = √(4A / √3). Rearrange the area formula to solve for side length.