Equilateral Triangle
Calculate all properties of an equilateral triangle from one side length: area, height, perimeter, circumradius, and inradius. Free online geometry tool with formulas A = sqrt3/4 x s^2 and h = sqrt3/2 x s.
About This Calculator
The Equilateral Triangle Calculator computes area, height, perimeter, circumradius, and inradius from just one side length. Since all sides are equal (s) and all angles are 60 deg, every property can be derived using sqrt3-based formulas.
Key formulas: Area A = sqrt3/4 x s^2. Height h = sqrt3/2 x s. Perimeter P = 3s. Circumradius R = s/sqrt3. Inradius r = ssqrt3/6. Note that R = 2r for equilateral triangles -- a unique relationship.
Equilateral triangles are fundamental in geometry, trigonometry, tiling patterns, architecture (truss bridges, geodesic domes), and engineering (structural stability calculations). They are studied in math curricula worldwide.
Frequently Asked Questions
What is an equilateral triangle?
An equilateral triangle is a triangle with all three sides equal in length and all three angles equal to 60 deg. It is the most symmetric triangle, with the highest area-to-perimeter ratio of any triangle.
What is the formula for equilateral triangle area?
The area of an equilateral triangle with side s is A = (sqrt3/4) x s^2. For example, a triangle with side 10 has area ≈ 43.30 square units.
How do you find the height of an equilateral triangle?
The height of an equilateral triangle with side s is h = (sqrt3/2) x s. For side 10, the height is approximately 8.66 units.
What is the difference between circumradius and inradius?
The circumradius R is the radius of the circumscribed circle (R = s/sqrt3), while the inradius r is the radius of the inscribed circle (r = ssqrt3/6). The circumradius is always twice the inradius for equilateral triangles.
Is this calculator free?
Yes, all calculators on Calculy are completely free to use.