Calculators > Geometry > Plane > Triangle Calculator: Equilateral Triangles

Triangle Calculator for Equilateral Triangles

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a =   m
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Answer:

a =   m
K =   m2
P =   m
s =   m
h =   m
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Equilateral Triangle Shape

Equilateral Triangle Diagram with Angles A, B and C and sides opposite those angles a, b and c respectively and altitude h
A = angle A
a = side a
B = angle B
b = side b
C = angle C
c = side c
K = area
P = perimeter
s = semiperimeter
h = altitude

Equilateral Triangle Calculator

An equilateral triangle is a special case of a triangle where all 3 sides have equal length and all 3 angles are equal to 60 degrees. The altitude shown h is hb or, the altitude of b. For equilateral triangles h = ha = hb = hc.

If you have any 1 known you can find the other 4 unknowns. So, if you know the length of a side = a, or the perimeter = P, or the semiperimeter = s, or the area = K, or the altitude = h, you can calculate the other values. Below are the 5 different choices of calculations you can make with this equilateral triangle calculator. Let us know if you have any other suggestions!

Formulas and Calculations for a equilateral triangle:

  • Perimeter of Equilateral Triangle: P = 3a
  • Semiperimeter of Equilateral Triangle: s = 3a / 2
  • Area of Equilateral Triangle: K = (1/4) * √3 * a2
  • Altitude of Equilateral Triangle h = (1/2) * √3 * a
  • Angles of Equilateral Triangle: A = B = C = 60°
  • Sides of Equilateral Triangle: a = b = c

1. Given the side find the perimeter, semiperimeter, area and altitude

  • a is known; find P, s, K and h
  • P = 3a
  • s = 3a / 2
  • K = (1/4) * √3 * a2
  • h = (1/2) * √3 * a

2. Given the perimeter find the side, semiperimeter, area and altitude

  • P is known; find a, s, K and h
  • a = P/3
  • s = 3a / 2
  • K = (1/4) * √3 * a2
  • h = (1/2) * √3 * a

3. Given the semiperimeter find the side, perimeter, area and altitude

  • s is known; find a, P, K and h
  • a = 2s / 3
  • P = 3a
  • K = (1/4) * √3 * a2
  • h = (1/2) * √3 * a

4. Given the area find the side, perimeter, semiperimeter and altitude

  • K is known; find a, P, s and h
  • a = √ [ (4 / √3) * K ] = 2 * √ [ K / √3 ]
  • P = 3a
  • s = 3a / 2
  • h = (1/2) * √3 * a

5. Given the altitude find the side, perimeter, semiperimeter and area

  • h is known; find a, P, s and K
  • a = (2 / √3) * h
  • P = 3a
  • s = 3a / 2
  • K = (1/4) * √3 * a2

For more information on triangles see:

Weisstein, Eric W. "Equilateral Triangle." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EquilateralTriangle.html

Weisstein, Eric W. "Altitude." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Altitude.html