Right Triangle Calculator
Calculate all properties of a right triangle using the Pythagorean theorem. Enter any two sides to find the third side, angles, area, and perimeter. Perfect for geometry homework, construction projects, and engineering calculations.
How to Use This Right Triangle Calculator
- Choose your input mode: enter two sides directly, or use a side with an angle
- For two sides mode: enter any two of the three sides (a, b, or c)
- For side + angle mode: enter one side length and one acute angle
- Click "Calculate Triangle" to see all properties
- View the hypotenuse, both legs, angles, area, and perimeter
The calculator automatically determines which values to compute based on your inputs. If you enter both legs (a and b), it calculates the hypotenuse. If you enter one leg and the hypotenuse, it calculates the missing leg.
What is a Right Triangle?
A right triangle is a triangle containing one 90-degree angle (called a right angle). The side opposite the right angle is called the hypotenuse, and it is always the longest side of the triangle. The other two sides are called legs or catheti. Right triangles are fundamental in trigonometry, construction, navigation, and countless engineering applications.
The ancient Egyptians used right triangles with sides in the ratio 3:4:5 to create perfect right angles for building pyramids. Today, right triangles remain essential in architecture, surveying, physics, and computer graphics for calculating distances and angles.
The Pythagorean Theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides:
a² + b² = c²
Where c is the hypotenuse and a, b are the legs. This theorem allows us to find any missing side when two sides are known:
- Find hypotenuse:
c = sqrt(a² + b²) - Find leg a:
a = sqrt(c² - b²) - Find leg b:
b = sqrt(c² - a²)
Additional formulas used:
- Area:
Area = (a x b) / 2 - Perimeter:
P = a + b + c - Angle A:
A = arctan(a / b)orarcsin(a / c) - Angle B:
B = 90° - A