Pythagorean Theorem Calculator
Find the hypotenuse or a missing side of a right triangle with a² + b² = c² — plus the angles, area and perimeter.
About this tool
Enter two sides of a right triangle and get the third with the Pythagorean theorem, a² + b² = c². Choose whether you know both legs (to find the hypotenuse) or one leg and the hypotenuse (to find the other leg). The calculator shows the working step by step, both acute angles, the area and the perimeter — useful for homework, roof rafters, ramps, ladders and checking that a corner is square.
Frequently asked questions
In a right triangle, the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the two other sides, the legs: a² + b² = c². With legs 3 and 4: 3² + 4² = 9 + 16 = 25, so the hypotenuse is √25 = 5.
Rearrange the formula: b = √(c² − a²). If the hypotenuse is 13 and one leg is 5, the other leg is √(169 − 25) = √144 = 12. The hypotenuse must always be longer than each leg, otherwise there is no right triangle.
To check that a corner is square, measure 3 units along one side and 4 units along the other. If the diagonal between the two marks is exactly 5 units, the corner is 90°. Multiples work too — 60, 80 and 100 cm or 6, 8 and 10 feet — and larger triangles give a more accurate check.
With trigonometry: the angle A opposite side a is arctan(a ÷ b), and the third angle is 90° − A because the angles of a triangle add up to 180°. For the 3-4-5 triangle the angles are 36.87°, 53.13° and 90°.
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