The Equilateral Triangle Calculator is the ultimate tool for the most symmetrical shape in geometry. Because all three sides and all three angles (60°) are identical, knowing just one property—Side, Height, or Perimeter—allows you to instantly calculate every other dimension, including the Area.
Features
Single-Input Solving: Enter just ONE value (Side, Height, or Perimeter) to find everything else.
Symmetry Visualization: Draws the perfect 60-60-60 triangle to scale.
Comprehensive Output: Instantly computes Area, Height, Side Length, and Perimeter in one go.
Step-by-Step Logic: Shows exactly which formula was used to derive the answers.
How to Use This Calculator
Choose Input: Select which dimension you measured (e.g., Side Length).
Enter Value: Type in the number.
Calculate: Click the button to populate the results.
Review Steps: See the math displayed below for educational verification.
Formulas
The calculator uses the following mathematical principles:
Area: $$ A = \frac{\sqrt{3}}{4} a^2 $$
Height: $$ h = \frac{\sqrt{3}}{2} a $$
Perimeter: $$ P = 3a $$
Angle: Always $$ 60^\circ $$
Practical Applications
Architecture: Designing strong, aesthetic triangular structures (trusses).
Graphic Design: Creating logos and tessellations.
Traffic Signs: Most warning signs are equilateral triangles.
Tips for Success
Efficiency: This is the most efficient triangle for enclosing area relative to perimeter.
Height vs Side: Height is always approx. 86.6% of the side length.
Inradius/Circumradius: The centroid is exactly the same center for both inscribed and circumscribed circles.
Frequently Asked Questions (FAQ)
Can I calculate from Area?
Yes, just rearrange the formula: Side = sqrt(4 * Area / sqrt(3)).
Are all angles equal?
Yes, an equilateral triangle is also equiangular (all 60 degrees).
Final Words
Simplify symmetry. The Equilateral Triangle Calculator takes the repetitive work out of geometry, letting you focus on the perfect proportions of your design.
