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Isosceles Right Triangle Hypotenuse Calculator.

Find the equal legs and area from an isosceles right-triangle hypotenuse.

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Set your values

Results update as you type.

Hypotenuse: 10 units

Hypotenuse

0.000000units
Equal leg: 7.071068 units

Equal leg

0.000000units
Area: 25 units²

Area

0.000000units²
Perimeter: 24.142136 units

Perimeter

0.000000units

Results update automatically as you type.

Use Cases

Geometry homework and math practice

Quickly verify solutions for isosceles right triangle problems, ensuring accurate leg lengths and areas.

Example: Check that a hypotenuse of 14.14 units gives legs of 10 units and area of 50 square units.

Construction and design calculations

When working with right isosceles triangles in layouts, determine the dimensions needed for a given diagonal or hypotenuse.

Example: Find the side length of a square tile when the diagonal is 12 inches.

Frequently Asked Questions

How do I find the legs of an isosceles right triangle from the hypotenuse?
In an isosceles right triangle, the legs are equal. The hypotenuse is √2 times the leg length. So, divide the hypotenuse by √2 to get the leg length. For example, if the hypotenuse is 10 units, each leg is 10/√2 ≈ 7.07 units.
What is the area of an isosceles right triangle with a given hypotenuse?
The area is half the product of the legs. Since the legs are equal, area = (leg^2)/2. Using the hypotenuse (h), leg = h/√2, so area = (h^2)/4. For h=10, area = 100/4 = 25 square units.
Can I use this calculator for any unit of measurement?
Yes, the calculator accepts any unit for the hypotenuse (e.g., inches, meters, feet). The leg length will be in the same unit, and the area will be in square units of that unit.

Tips & Common Mistakes

Tips

  • Remember: the hypotenuse is always the longest side, opposite the right angle.
  • Use the same unit for all measurements to get consistent results.
  • For quick mental math, multiply the hypotenuse by 0.7071 to approximate the leg length.
  • Double-check your input: the hypotenuse must be a positive number.

Common Mistakes to Avoid

  • Forgetting to divide by √2 and instead multiplying, which gives a leg longer than the hypotenuse.
  • Using the hypotenuse as the leg length, leading to incorrect area calculations.
  • Entering a negative or zero value for the hypotenuse, which is invalid for a triangle.

Last updated: August 13, 2026