Calculate area, height, perimeter, and radii from side length
Result
Area and Height
Step-by-Step Derivation
Equilateral Triangle Formula
A = (√3 / 4)s², h = (√3 / 2)s
An equilateral triangle has three equal sides and three 60 degree angles. Because one side determines the whole shape, the area, height, perimeter, and circle radii all come from the same side length.
⚠The side length must be positive. This calculator assumes all three sides are equal.
How Equilateral Triangle Calculation Works
Dropping an altitude splits the equilateral triangle into two congruent right triangles. That creates the height formula and leads directly to the area formula.
Equal Sides
All three sides have the same length.
Equal Angles
Each interior angle is 60 degrees.
Altitude
The height also bisects the base.
Radii
Inradius and circumradius depend only on side length.
💡 Example: For s=8, area=(√3/4)(64)=27.713 and height=(√3/2)(8)=6.928.
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