Math Tools
Right Triangle Calculator
Solve a right triangle from known sides and calculate the missing side, area, and perimeter.
Right Triangle Calculator
Solve a right triangle from known sides and calculate the missing side, hypotenuse, area, and perimeter.
Enter the two legs of a right triangle to calculate the hypotenuse, area, and perimeter.
Formulas
a² + b² = c²
Area = 1/2 × a × b
Perimeter = a + b + c
Results
Leg a
3
Leg b
4
Hypotenuse
5
Area
6
Perimeter
12
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What this calculator does
This calculator solves a right triangle from either two legs or from the hypotenuse and one leg. It also calculates the area and perimeter.
What is a right triangle calculator?
A right triangle calculator is a tool that helps you solve a right triangle quickly when you know two sides. It can find the missing side using the Pythagorean theorem and also calculate the area and perimeter of the triangle.
This is useful in geometry, school assignments, construction, engineering, trigonometry, surveying, and everyday measurement problems where right triangles appear.
Right triangle formulas
Pythagorean theorem
a² + b² = c²
Right triangle area formula
Area = 1/2 × a × b
Right triangle perimeter formula
Perimeter = a + b + c
Right triangle formula reference table
| Formula | What it finds |
|---|---|
| a² + b² = c² | Pythagorean theorem for a right triangle |
| c = √(a² + b²) | Find the hypotenuse from two legs |
| a = √(c² - b²) | Find a missing leg from the hypotenuse and one leg |
| Area = 1/2 × a × b | Find the area using the two legs |
| Perimeter = a + b + c | Find the total distance around the triangle |
Examples of right triangle calculations from two legs
These sample values show how the missing side, area, and perimeter are calculated.
| Known values | Hypotenuse | Area | Perimeter |
|---|---|---|---|
| leg a = 3, leg b = 4 | 5 | 6 | 12 |
| leg a = 5, leg b = 12 | 13 | 30 | 30 |
| leg a = 8, leg b = 15 | 17 | 60 | 40 |
How to solve a right triangle step by step
If you know both legs of the right triangle, square each leg, add the results, and take the square root to find the hypotenuse. This is the standard use of the Pythagorean theorem.
If you know the hypotenuse and one leg, square both values, subtract the smaller square from the larger square, and take the square root to find the missing leg.
After all three sides are known, calculate the area using one-half multiplied by the two legs, and calculate the perimeter by adding all three sides together.
Common right triangle examples
The most famous right triangle example is the 3-4-5 triangle. Its legs are 3 and 4, and its hypotenuse is 5. Another common example is the 5-12-13 triangle. These are often used in classrooms and practical measurement problems.
Right triangles also appear in ladders leaning against walls, roof slopes, ramps, diagonal measurements, navigation, construction layouts, and many geometry exercises.
When a right triangle calculator is useful
A right triangle calculator is useful when you need to find a missing side quickly without doing the full calculation by hand. It can save time in geometry homework, drafting, engineering sketches, construction work, and any measurement task involving a right angle.
It is also helpful for checking answers, understanding the relationship between the legs and the hypotenuse, and applying area and perimeter formulas correctly.
Right triangle calculator FAQ and common questions
How do you find the hypotenuse of a right triangle?
Use the formula c = √(a² + b²), where a and b are the two legs of the triangle.
How do you find a missing leg of a right triangle?
Use the formula missing leg = √(c² - known leg²), where c is the hypotenuse.
How do you calculate the area of a right triangle?
Multiply the two legs and divide by 2. The formula is Area = 1/2 × a × b.
How do you calculate the perimeter of a right triangle?
Add leg a, leg b, and the hypotenuse together.
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse.
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