Equilateral Triangle Calculator — Side, Area, Height & Radii

About the Equilateral Triangle Calculator — Side, Area, Height & Radii

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.

When This Page Helps

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.

How to Use the Inputs

1. Select what you know: side length, area, perimeter, height, circumradius, or inradius.
2. Choose a measurement unit.
3. Enter the known value.
4. Or click a preset to load a common equilateral triangle.
5. View all computed properties: side, area, height, perimeter, circumradius, inradius.
6. All angles are always 60° — no need to compute them.
7. Scroll down for the properties table and reference examples.

Example Calculation

Tips & Best Practices

• An equilateral triangle is the only triangle where all four classic triangle centers (centroid, orthocenter, circumcenter, incenter) coincide.
• The circumradius is always exactly twice the inradius: R = 2r.
• Equilateral triangles tile the plane — 6 meet at every vertex, forming the triangular tiling.
• The area formula √3/4 × a² is one of the most commonly needed geometry formulas in competitions.
• A regular hexagon is made of 6 equilateral triangles — so hexagon area = 6 × equilateral area.

How This Equilateral Triangle Calculator — Side, Area, Height & Radii Works

Where It Helps In Practice

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.

Accuracy And Setup Tips

Frequently Asked Questions

• What is the area formula for an equilateral triangle?

  A = (√3 / 4) × a², where a is the side length. For a = 10, area ≈ 43.30.

• What is the height of an equilateral triangle?

  h = (√3 / 2) × a. For a = 10, height ≈ 8.66.

• Are all angles in an equilateral triangle 60°?

  Yes — by definition, an equilateral triangle has all sides equal and all angles equal to 60°.

• What is the circumradius?

  The circumradius R = a / √3 ≈ 0.577a. It is the radius of the circle passing through all three vertices.

• What is the relationship between circumradius and inradius?

  R = 2r always. The circumradius is exactly twice the inradius in every equilateral triangle.

• How do I find the side from the area?

  a = √(4A / √3). Rearrange the area formula to solve for side length.