Right Triangle Calculator — Find All Properties from Any 2 Sides
Hypotenuse (c)
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Area
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Perimeter
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Angle A (opposite side a)
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Angle B (opposite side b)
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How to Solve a Right Triangle
A right triangle has one 90-degree angle. The side opposite the right angle is the hypotenuse (c), and the other two sides are called legs (a and b). The Pythagorean theorem states that a squared plus b squared equals c squared, which lets you find any missing side when you know the other two.
This calculator also computes the two non-right angles using inverse trigonometric functions. Angle A (opposite side a) equals arctan(a/b), and Angle B (opposite side b) equals arctan(b/a). These two angles always sum to 90 degrees.
The area of a right triangle is simply half the product of the two legs: A = (1/2)(a)(b). The perimeter is the sum of all three sides. Right triangles are fundamental in construction, navigation, and engineering for calculating distances, slopes, and structural loads.
Frequently Asked Questions
What is 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: a squared + b squared = c squared. It only applies to right triangles.
What are Pythagorean triples?
Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem. Common examples include (3,4,5), (5,12,13), (8,15,17), and (7,24,25). Any multiple of a triple is also a triple.
How do you find the hypotenuse?
Square each leg, add the results, and take the square root: c = sqrt(a squared + b squared). For example, if legs are 3 and 4, hypotenuse = sqrt(9+16) = sqrt(25) = 5.