45-45-90 Triangle Calculator (1 : 1 : √2)

Solve a 45-45-90 right triangle from any one side — legs and hypotenuse in the exact 1 : 1 : √2 ratio.

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Formula

In a 45°-45°-90° triangle the two legs are equal and the hypotenuse is leg × √2 (≈1.41421). Hypotenuse ÷ √2 gives the leg. The angles are always 45°, 45° and 90°.

Examples

InputResult
leg = 10hypotenuse = 14.1421 · area = 50
hypotenuse = 10legs = 7.0711 · area = 25
leg = 5hypotenuse = 7.0711 · perimeter = 17.0711

Frequently Asked Questions

What is the 45-45-90 triangle ratio?

The sides are always in the ratio 1 : 1 : √2 — two equal legs and a hypotenuse that is √2 (about 1.414) times a leg. It is half of a square cut along the diagonal.

How do I find the hypotenuse of a 45-45-90 triangle?

Multiply the leg by √2. A leg of 7 gives a hypotenuse of 7√2 ≈ 9.899. To go the other way, divide the hypotenuse by √2.

Where does 45-45-90 show up in real life?

Cutting square tiles or fabric on the diagonal, bracing a square frame, roof hips at 45°, and any diagonal measurement of a square — the diagonal of a 12-inch square tile is 12√2 ≈ 16.97 inches.

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