45-45-90 Triangle Calculator
An isosceles right triangle. Sides are in the ratio 1 : 1 : √2.
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Enter a side length and click calculate.
About 45-45-90 triangles
A 45-45-90 triangle is an isosceles right triangle: both legs are equal in length, and the hypotenuse is √2 times either leg. This shape arises naturally when you cut a square along its diagonal.
Frequently Asked Questions
What is a 45-45-90 triangle?▾
An isosceles right triangle with two 45° angles and one 90° angle. Both legs are equal in length.
What is the side ratio?▾
1 : 1 : √2. The hypotenuse is √2 times the length of either leg.
Where do these triangles appear?▾
Anywhere there's a square: cut a square along its diagonal and you get two 45-45-90 triangles. Common in design, architecture, and geometry proofs.
What are the trig values?▾
sin 45° = cos 45° = √2/2 ≈ 0.7071, and tan 45° = 1.