45-45-90 Triangle Calculator
Solve a 45-45-90 isosceles right triangle from one leg. Computes both legs and the hypotenuse using the special ratio 1:1:sqrt(2). Ideal for geometry, carpentry, and tiling problems.
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How to use this tool
- Enter leg (shorter sides) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your hypotenuse and the full breakdown beneath it.
Formula
hypotenuse = leg * sqrt(2); both legs are equal
How it works
In a 45-45-90 triangle the two legs are equal and the hypotenuse is leg × √2.
Worked example
Leg = 5
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- 5
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- 7
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- 7
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- 5
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Common mistakes to avoid
- Multiplying the hypotenuse by sqrt(2) to find the leg — it is the leg that is multiplied by sqrt(2) to get the hypotenuse, not the other way around.
- Entering the hypotenuse as the input when the tool asks for a leg, producing a hypotenuse that is sqrt(2) times too large.
- Rounding sqrt(2) to 1.4 early in the calculation, which introduces noticeable error in precise carpentry or tiling work.
Key terms
Frequently asked questions
- Why is the hypotenuse exactly leg x sqrt(2)?
- By the Pythagorean theorem, hyp squared = leg squared + leg squared = 2 x leg squared, so hyp = leg x sqrt(2). This is the defining property of all 45-45-90 triangles.
- If I know the hypotenuse, how do I find the leg?
- Divide the hypotenuse by sqrt(2), or equivalently multiply it by sqrt(2)/2 which is approximately 0.7071. Both legs are equal.
- Where do 45-45-90 triangles appear in carpentry?
- Any time you cut a square piece diagonally — such as mitering a picture frame corner or laying diagonal floor tiles — you create a 45-45-90 triangle. The diagonal cut length is the leg times sqrt(2).