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45 45 90 Triangle Calculator

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30 60 90 Triangle Calculator

A 45 45 90 triangle showing angles and side lengths proportional to Side A

A 45 45 90 triangle is known as a special right triangle and has the angles 45°, 45°, and 90°, hence its name. You might also notice that this triangle is half of a square because sides a and b are equal to each other.

Right triangles are sometimes called rectangular triangles or orthogonal triangles. A triangle is a right triangle when two sides are perpendicular to each other, forming a right angle.

Because of this triangle's predictable angles, the 45 45 90 triangle calculator computes the properties of a triangle given any one of the following measurements:

  • Side (a)
  • Side (b)
  • Side (c)
  • Area
  • Perimeter

Understanding the Formula

The triangle's properties are derived from the measurement provided.

Given Side A:

b=ab=a
c=a2c=a\sqrt{2}
A=12abA=\frac{1}{2}ab
P=a+b+cP=a+b+c

Given Side B:

a=ba=b
c=a2c=a\sqrt{2}
A=12abA=\frac{1}{2}ab
P=a+b+cP=a+b+c

Given Side C:

a=c22a=\frac{c\sqrt{2}}{2}
b=c22b=\frac{c\sqrt{2}}{2}
A=12abA=\frac{1}{2}ab
P=a+b+cP=a+b+c

Given Area:

a=2Aa=\sqrt{2A}
b=2Ab=\sqrt{2A}
c=2Ac=2\sqrt{A}
P=a+b+cP=a+b+c

Given Perimeter:

a=P2+2a=\frac{P}{2+\sqrt{2}}
b=P2+2b=\frac{P}{2+\sqrt{2}}
c=a2c=a\sqrt{2}
A=12abA=\frac{1}{2}ab

Where the following variables are represented as:

  • a = Side A
  • b = Side B
  • c = Side C
  • A = Area
  • P = Perimeter