Equilateral Triangle Calculator
Calculate the perimeter, area, height, inradius, circumradius, and interior angles from the provided side length. Equilateral Triangle Calculator helps students, educators, engineers, and construction professionals analyze equal-sided triangles.
Highlights
- Calculates perimeter, area, height, inradius, and circumradius.
- Provides the equal interior angle of 60°.
- Requires only one input: the triangle’s side length.
- Supports metric and imperial units, including mm, cm, m, in, ft, and more.
- Delivers fast, accurate results for students, educators, engineers, and construction professionals.
Table of Contents
How Equilateral Triangle Calculator Works?
An equilateral triangle has three equal sides and three equal interior angles. Enter the common side length s, and the calculator uses standard geometric relationships to determine the perimeter, area, height, inradius, circumradius, and each interior angle.
The perimeter is the total length of all three equal sides. The area is calculated from the side length using the equilateral-triangle area formula:
Drawing the altitude divides the triangle into two right triangles. Applying the Pythagorean theorem gives the perpendicular height:
The inradius is the radius of the circle inscribed inside the triangle, while the circumradius is the radius of the circle passing through all three vertices:
Because the angles of every triangle total 180°, and all three angles in an equilateral triangle are equal, each interior angle is 60°.
| Output | Formula |
|---|---|
| Perimeter | |
| Area | |
| Height | |
| Inradius | |
| Circumradius | |
| Each interior angle | 60° |
The calculator accepts a positive side length from 0.000001 through 1,000,000,000 and reports length-based results in the selected supported length unit. Area results use the corresponding squared unit, and the angle is reported in degrees.
Practical Use Cases
Students: Students can enter a side length to check homework calculations for perimeter, area, altitude, inradius, circumradius, and the fixed 60° interior angle of an equilateral triangle.
Teachers and educators: Educators can use the calculator to demonstrate how one known side produces several related geometric measurements and to compare the formulas for height, area, and circle radii.
Engineers: Engineers can estimate geometric properties of equal-sided triangular components, including the enclosed area and the locations represented by the incenter and circumcenter through the inradius and circumradius.
Construction professionals: Construction professionals can determine the perimeter, height, and surface area of triangular layouts or supports when all three sides are designed to be equal.
Designers and fabricators: Designers and fabricators can use the calculated dimensions to plan triangular panels, decorative structures, frames, and other components based on a specified equal side length.
Accuracy and Limitations
The calculator uses exact equilateral-triangle formulas involving , so its mathematical results are accurate within the limits of the input precision and displayed rounding. It requires one positive side length between 0.000001 and 1,000,000,000; zero, negative, blank, or out-of-range values are not valid. The calculations assume a perfect equilateral triangle with three exactly equal sides and do not account for material thickness, measurement error, manufacturing tolerances, distorted geometry, or non-equilateral triangles.
Quick Examples
Example #1: Small Geometry Exercise
Calculate the measurements of a small equilateral triangle for a classroom geometry problem.
Example #2: Garden Layout Triangle
Determine the dimensions of an equilateral triangular garden section using its side length.
Example #3: Large Structural Panel
Analyze the geometric properties of a large equilateral triangular construction panel.
