How the Right Triangle & Squaring Calculator works
A right triangle has one square (90°) corner. Give this calculator any two of rise, run and diagonal, or one side and the angle, and it finds the missing sides, both angles and the pitch. The Square check mode gives the diagonal of a rectangle, so you can check that a deck, slab or wall layout is square.
The method is the Pythagorean theorem: rise² + run² = diagonal². To find a leg, subtract instead: rise = √(diagonal² − run²). The angle between the run and the diagonal is arctan(rise ÷ run), and the pitch is rise ÷ run × 12, written as X/12.
Example: a run of 12' (144") and a diagonal of 12' 6" (150"). Rise = √(150² − 144²) = √(22,500 − 20,736) = √1,764 = 42", or 3' 6". The angle is arctan(42 ÷ 144) = 16.26°, the other angle is 90° − 16.26° = 73.74°, and the pitch is 42 ÷ 144 × 12 = 3.5/12.
Enter exactly two sides and leave the third blank; the diagonal must be longer than either of the other sides. Lengths can be feet, inches and fractions (12' 6") or metric, and a plain number is read as feet. For layout, measure both diagonals of the rectangle: when they are equal, the corners are square.
Frequently asked questions
How do you find the hypotenuse of a right triangle?
Square both legs, add them and take the square root: √(rise² + run²). With a 3' rise and a 4' run, √(9 + 16) = √25 = 5'. Enter the two legs and leave Diagonal blank; the calculator also shows the angle (36.87°) and the pitch (9/12).
How do you square a deck or foundation with 3-4-5?
From a corner, measure 3' along one side and 4' along the other and mark both. When the corner is square, the marks are exactly 5' apart. Bigger multiples such as 6-8-10 or 9-12-15 catch smaller errors; the Square check mode picks the largest one that fits your layout.
What should the diagonal of a rectangle measure?
√(length² + width²). A 10' × 8' frame should measure √(120² + 96²) = √23,616 = 153.675", or 12' 9 11/16", corner to corner. If the two diagonals differ, rack the frame along the longer diagonal until they match.
How do you find the angle of a right triangle from two sides?
Take the inverse tangent of rise ÷ run. A 42" rise over a 144" run is arctan(0.2917) = 16.26°. The other sharp angle is 90° minus that, 73.74°.
How do I turn a slope angle into a pitch?
Pitch = tan(angle) × 12. 30° gives tan 30° × 12 = 0.577 × 12 = 6.93, about 7/12. In Side + angle mode, enter one side and the angle and the calculator shows the pitch along with the other sides.