Right Triangle Calculator
Calculate right triangle properties.
Right Triangle Dimensions
Triangle Results
Area
6.00
square units
Perimeter
12.00
Hypotenuse
5.00
Angles:
A: 36.9°
B: 53.1°
C: 90° (Right Angle)
About This Calculator
The Right Triangle Calculator helps you calculate various properties of right triangles including area, perimeter, angles, and side lengths. A right triangle has one 90-degree angle, and the side opposite this angle is called the hypotenuse.
Enter two sides to calculate the third side using the Pythagorean theorem, or enter angles to calculate side lengths. The calculator verifies that the triangle is a right triangle and calculates all missing properties automatically.
Formula & Calculation Method
Right Triangle Formulas:
Pythagorean Theorem:
a² + b² = c² (where c is the hypotenuse)
Area:
A = (1/2) × a × b
Perimeter:
P = a + b + c
Angles:
A + B + C = 180° (C = 90°)
sin(A) = opposite/hypotenuse
cos(A) = adjacent/hypotenuse
tan(A) = opposite/adjacent
In a right triangle, one angle is always 90 degrees. The hypotenuse is the longest side and is opposite the right angle. The area is half the product of the two legs (non-hypotenuse sides).
How to Use This Calculator
- Select Mode: Choose to solve using sides or angles.
- Enter Values: Input two sides (for side mode) or two angles (for angle mode).
- View Results: See calculated area, perimeter, angles, and all side lengths.
- Verify: The calculator verifies the triangle is a right triangle.
Frequently Asked Questions
What is a right triangle?
A right triangle is a triangle with one 90-degree (right) angle. The side opposite the right angle is called the hypotenuse and is the longest side. The other two sides are called legs.
How do I find the hypotenuse?
Use the Pythagorean theorem: if you know the two legs (a and b), the hypotenuse (c) is c = √(a² + b²). The hypotenuse is always the longest side.
How do I find a leg if I know the hypotenuse and one leg?
Rearrange the Pythagorean theorem: if you know c (hypotenuse) and a (one leg), then b = √(c² - a²). Make sure c is greater than a.
What is the area of a right triangle?
The area of a right triangle is (1/2) × leg1 × leg2. This is because the two legs form the base and height of the triangle (they meet at the right angle).
Expert Reviewed
This calculator was reviewed by NumCalculators Editorial Team, Multi-disciplinary Expert Team