Equilateral Triangle Calculator

Category: Geometry
- April 13, 2025
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Calculate and visualize properties of equilateral triangles. An equilateral triangle has three equal sides and equal angles of 60°. This calculator helps you find various measurements including area, perimeter, height, and more.

Equilateral Triangle Calculator

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About Equilateral Triangles

An equilateral triangle is a special triangle where all three sides have equal length and all three internal angles are equal to 60°. These properties make equilateral triangles unique and important in geometry.

Key Properties of Equilateral Triangles
  • Equal Sides: All three sides have the same length.
  • Equal Angles: All three angles are equal to 60°.
  • Regular Polygon: An equilateral triangle is a regular polygon with three sides.
  • Symmetry: An equilateral triangle has three lines of symmetry and rotational symmetry of order 3.
  • Special Centers: In an equilateral triangle, the centroid, orthocenter, circumcenter, and incenter all coincide at the same point.
Formulas for Equilateral Triangles

Where a is the side length:

  • Perimeter: P = 3a
  • Area: A = (√3/4) × a²
  • Height: h = (√3/2) × a
  • Inradius (radius of inscribed circle): r = a/(2√3)
  • Circumradius (radius of circumscribed circle): R = a/√3
  • Altitude: h = (√3/2) × a
  • Median: m = (√3/2) × a
Applications of Equilateral Triangles

Equilateral triangles appear in many applications:

  • Architecture and structural design
  • Engineering and construction
  • Art, graphic design, and logos
  • Crystallography and molecular structures
  • Optics and light reflections
  • Network designs and optimization problems

Equilateral Triangle Calculator Guide

The Equilateral Triangle Calculator is a practical tool for solving triangle measurements when all sides and angles are equal. Whether you're a student, a teacher, or just curious about triangle geometry, this calculator helps you calculate triangle dimensions quickly and clearly.

Key Formulas Used:

  • Perimeter (P) = 3 × side
  • Area (A) = (√3 / 4) × side²
  • Height (h) = (√3 / 2) × side
  • Inradius (r) = side / (2√3)
  • Circumradius (R) = side / √3

What Does This Calculator Do?

This triangle solver calculates all the major properties of an equilateral triangle from a single known value. You can start with the side length, area, height, perimeter, inradius, or circumradius. Once you enter a value, the calculator displays:

  • Side length
  • Perimeter
  • Area
  • Height (altitude)
  • Inradius (radius of the inscribed circle)
  • Circumradius (radius of the circumscribed circle)

It also provides an optional step-by-step breakdown and a visual diagram, making this a helpful triangle geometry helper and triangle side and angle tool.

How to Use the Equilateral Triangle Calculator

  1. Choose what you want to calculate from — side length, area, perimeter, height, inradius, or circumradius.
  2. Enter your known value into the input box that appears.
  3. Select how many decimal places you'd like your results to display.
  4. Optionally choose to show radical forms and calculation steps.
  5. Click Calculate to get results instantly.

The calculator will display all related triangle measurements and optionally show a visual representation. You can also reset everything with the Reset button.

Who Can Benefit From This Tool?

This triangle side calculator is helpful in many everyday and academic situations:

  • Students solving triangle geometry problems
  • Teachers creating examples or checking answers
  • Designers working on geometric art or patterns
  • Engineers and architects needing precise triangle calculations

It complements other tools like the right triangle solver, area calculator, and distance calculator, expanding your geometry toolkit.

Frequently Asked Questions

Can I use this to solve non-equilateral triangles?

No, this calculator is only for equilateral triangles. For other types, consider using a triangle geometry solver or right triangle calculator.

What if I only know the area or inradius?

No problem. You can start from any of the six properties. The calculator will work backward to find the side length and then calculate all other properties.

What does “show in radical form” mean?

Some results can be shown using square roots (like √3) instead of decimals. This can help if you're looking for more exact mathematical forms.

Is this a Pythagorean theorem calculator?

Not exactly. This tool is focused on equilateral triangles. For right triangles, use a right triangle formula or hypotenuse finder.

Why Use a Triangle Calculator?

Manual geometry calculations can be time-consuming. This tool simplifies the process and reduces errors, helping you calculate triangle dimensions faster and with more confidence. It's a useful complement to other tools like the:

Use this equilateral triangle calculator to solve triangle measurements, check your work, and explore geometry more easily.