Math

Instant, private, and free

Isosceles Right Triangle Calculator.

Calculate the hypotenuse, area, and perimeter from an equal leg.

On-device calculationNo signup

Set your values

Results update as you type.

02 / ANSWER

Equal leg

0.000000units

Hypotenuse

0.000000units

Area

0.000000units²

Perimeter

0.000000units

Results update automatically as you type.

Use Cases

Geometry homework and math practice

Quickly verify your manual calculations for isosceles right triangle problems, ensuring accuracy in assignments or self-study.

Example: Check the hypotenuse of a triangle with leg 7 units.

Design and construction planning

Determine dimensions for right-angle structures like roof trusses, ramps, or decorative elements where equal sides are used.

Example: Find the diagonal length for a square cut in half.

Frequently Asked Questions

What is an isosceles right triangle?: An isosceles right triangle has two equal legs and a right angle (90°) between them. The hypotenuse is opposite the right angle and is longer than each leg. It is also a 45-45-90 triangle.
How do I calculate the hypotenuse from the equal leg?: The hypotenuse is the equal leg multiplied by the square root of 2 (√2). For example, if the equal leg is 5 units, the hypotenuse is 5√2 ≈ 7.07 units.
What are the formulas for area and perimeter?: Area = (leg²)/2. Perimeter = leg + leg + hypotenuse = 2*leg + leg*√2. For leg = 5, area = 12.5 square units, perimeter ≈ 17.07 units.

Tips & Common Mistakes

Tips

Ensure the equal leg value is positive; negative lengths are not valid.
Use the same unit for all measurements; the calculator outputs in the same unit.
Remember that the hypotenuse is always the longest side in a right triangle.
For quick mental estimates, multiply the leg by 1.414 to approximate the hypotenuse.

Common Mistakes to Avoid

Confusing the equal leg with the hypotenuse; the hypotenuse is always √2 times the leg.
Forgetting to square the leg when calculating area; area = (leg²)/2, not leg/2.
Using different units for leg and expecting consistent results; always convert to the same unit first.

Last updated: August 13, 2026

Use Cases

Geometry homework and math practice

Quickly verify your manual calculations for isosceles right triangle problems, ensuring accuracy in assignments or self-study.

Example: Check the hypotenuse of a triangle with leg 7 units.

Design and construction planning

Determine dimensions for right-angle structures like roof trusses, ramps, or decorative elements where equal sides are used.

Example: Find the diagonal length for a square cut in half.

Frequently Asked Questions

What is an isosceles right triangle?

An isosceles right triangle has two equal legs and a right angle (90°) between them. The hypotenuse is opposite the right angle and is longer than each leg. It is also a 45-45-90 triangle.

How do I calculate the hypotenuse from the equal leg?

The hypotenuse is the equal leg multiplied by the square root of 2 (√2). For example, if the equal leg is 5 units, the hypotenuse is 5√2 ≈ 7.07 units.

What are the formulas for area and perimeter?

Area = (leg²)/2. Perimeter = leg + leg + hypotenuse = 2*leg + leg*√2. For leg = 5, area = 12.5 square units, perimeter ≈ 17.07 units.

Tips & Common Mistakes

Tips

Ensure the equal leg value is positive; negative lengths are not valid.
Use the same unit for all measurements; the calculator outputs in the same unit.
Remember that the hypotenuse is always the longest side in a right triangle.
For quick mental estimates, multiply the leg by 1.414 to approximate the hypotenuse.

Common Mistakes to Avoid

Confusing the equal leg with the hypotenuse; the hypotenuse is always √2 times the leg.
Forgetting to square the leg when calculating area; area = (leg²)/2, not leg/2.
Using different units for leg and expecting consistent results; always convert to the same unit first.

Use Cases

Geometry homework and math practice

Quickly verify your manual calculations for isosceles right triangle problems, ensuring accuracy in assignments or self-study.

Example: Check the hypotenuse of a triangle with leg 7 units.

Design and construction planning

Determine dimensions for right-angle structures like roof trusses, ramps, or decorative elements where equal sides are used.

Example: Find the diagonal length for a square cut in half.

Frequently Asked Questions

What is an isosceles right triangle?

An isosceles right triangle has two equal legs and a right angle (90°) between them. The hypotenuse is opposite the right angle and is longer than each leg. It is also a 45-45-90 triangle.

How do I calculate the hypotenuse from the equal leg?

The hypotenuse is the equal leg multiplied by the square root of 2 (√2). For example, if the equal leg is 5 units, the hypotenuse is 5√2 ≈ 7.07 units.

What are the formulas for area and perimeter?

Area = (leg²)/2. Perimeter = leg + leg + hypotenuse = 2*leg + leg*√2. For leg = 5, area = 12.5 square units, perimeter ≈ 17.07 units.

Tips & Common Mistakes

Tips

Ensure the equal leg value is positive; negative lengths are not valid.
Use the same unit for all measurements; the calculator outputs in the same unit.
Remember that the hypotenuse is always the longest side in a right triangle.
For quick mental estimates, multiply the leg by 1.414 to approximate the hypotenuse.

Common Mistakes to Avoid

Confusing the equal leg with the hypotenuse; the hypotenuse is always √2 times the leg.
Forgetting to square the leg when calculating area; area = (leg²)/2, not leg/2.
Using different units for leg and expecting consistent results; always convert to the same unit first.