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Last updated: July 31, 2026

Equilateral Triangle Area Calculator

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Formula

area=(√3/4)s^2; height=(√3/2)s

Where:

  • s=s
Equilateral Triangle AreaA shaded equilateral triangle showing its side length s and height, used to compute its area.heightsFormulaA = (√3/4)s²s = side length
The area of an equilateral triangle depends only on its side length s, using the height derived from the 30-60-90 relationship.

Worked Examples

Side length 6

Common classroom example.

  1. 1A=(√3/4)·6²
  2. 2h=(√3/2)·6
Final Answer: area≈15.588457, height≈5.196152

Side length 10

Larger triangle.

  1. 1Substitute s=10 in both formulas
Final Answer: area≈43.30127, height≈8.660254

Side length 2.5

Decimal side length.

  1. 1Evaluate area and height formulas
Final Answer: area≈2.706329, height≈2.165064

Introduction

Calculate equilateral triangle area and height directly from side length.

Formula and Method

Equilateral Triangle Area Calculator uses: area=(√3/4)s^2; height=(√3/2)s

  • Enter all required inputs

  • Apply the underlying math formula(s)

  • Compute supporting terms where needed

  • Round numeric outputs for stable display

Input Fields

Provide values for: s.

  1. 1

    s: s

Output Fields

The calculator returns: area, height.

  1. 1

    area: Area of the equilateral triangle

  2. 2

    height: Height (altitude) of the triangle

Validation Rules

Input validation is applied before calculation to prevent invalid math states.

  • s must be finite.

  • s must be positive.

  • Uses exact equilateral-triangle formulas.

  • Outputs are rounded to 6 decimals.

How to Use This Calculator

Fill in the inputs, run the calculator, and review primary output first.

  • Enter the required values

  • Click calculate

  • Check the primary output

  • Use example scenarios for verification

Practical Uses

This calculator supports learning, quick checks, and day-to-day technical problem solving.

  • Homework and exam preparation

  • Engineering and science sanity checks

  • Classroom demonstrations

  • Fast recalculation with different inputs

FAQs

What does the Equilateral Triangle Area Calculator compute?

Calculate equilateral triangle area and height directly from side length.

Which inputs are required?

Required inputs: s.

How should I format numbers?

Use finite numeric values; decimals and negative numbers are allowed unless restricted by validation rules.

How are results rounded?

Numeric outputs are rounded to about 6 decimal places for readability.

Why might I see an error?

s must be finite.

Can I use this for learning and verification?

Yes. Use the examples and formula section to verify manual calculations quickly.