45-45-90 Triangle Calculator
Find hypotenuse from a leg in an isosceles right triangle
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45-45-90 Triangle Formula
leg : leg : hypotenuse = x : x : x√2
A 45-45-90 triangle is an isosceles right triangle. The two legs are equal, and the hypotenuse is the leg multiplied by √2.
⚠ Enter one leg length. The value must be positive and the other leg is the same length.
How 45-45-90 Triangles Work
This triangle appears when a square is cut along its diagonal. Equal acute angles create equal legs and a fixed hypotenuse ratio.
Equal Legs
Both legs have length x.
Hypotenuse
Hypotenuse is x√2.
Square Diagonal
The same formula gives a square diagonal.
Exact Values
Supports sin45 and cos45.
💡 Example: If each leg is 7, the hypotenuse is 7√2≈9.899495.
Applications of 45-45-90 Triangles
Square Diagonals Special Right Triangles Exact Trig Values Construction
Frequently Asked Questions
What is a 45-45-90 triangle calculator?▼
It calculates the hypotenuse of an isosceles right triangle from one leg.
What is the 45-45-90 side ratio?▼
The ratio is x : x : x√2.
How do I use this calculator?▼
Enter one leg length and click Calculate.
Are the two legs equal?▼
Yes. A 45-45-90 triangle has two equal legs.
Where are 45-45-90 triangles used?▼
They are used in squares, diagonals, exact trig values, geometry, and construction.
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