45-45-90 Triangle Calculator
Enter a leg or the hypotenuse of a 45-45-90 triangle to find all sides, area, and perimeter.
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Request a ToolHow to Use the 45-45-90 Triangle Calculator
A 45-45-90 triangle (isosceles right triangle) has two equal legs and a hypotenuse in the ratio 1 : 1 : sqrt(2). Enter either a leg or the hypotenuse to calculate everything.
- Select what you know. Choose whether you are entering a leg or the hypotenuse.
- Enter the length. Type the value in the input field.
- View the results. Both legs, the hypotenuse, area, and perimeter are calculated instantly.
About 45-45-90 Triangles
The 45-45-90 triangle is one of two special right triangles. It is an isosceles right triangle: both legs are equal, and the hypotenuse is sqrt(2) times a leg. You get one whenever you cut a square along its diagonal. This triangle appears throughout geometry, trigonometry, and engineering. It is the basis for the values of sin(45 degrees) and cos(45 degrees), both equal to sqrt(2)/2.
Frequently Asked Questions
What is the ratio of sides in a 45-45-90 triangle?
The two legs are equal and the hypotenuse is sqrt(2) times a leg. The ratio is 1 : 1 : sqrt(2).
How do I find the leg from the hypotenuse?
Divide the hypotenuse by sqrt(2). For a hypotenuse of 10, each leg is 10 / sqrt(2), which is approximately 7.0711.
What is the area of a 45-45-90 triangle?
The area is (1/2) * leg * leg, or leg^2 / 2. Since both legs are equal, the area formula simplifies to half the square of one leg.