Right Triangle & Squaring

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Free Android app — works offline, no pop-up ads.
Get it on Google Play
Rise (ft)
Examples: 12', 5' 3 1/2", 3/4", 2.5m
Run (ft)
Examples: 12', 5' 3 1/2", 3/4", 2.5m
Diagonal (ft)
Examples: 12', 5' 3 1/2", 3/4", 2.5m
Enter measurements above 0 to see results.
36.9°5' 0"4' 0"3' 0"
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Example — type your own measurements above.
Estimates only. Check measurements, product labels and local building codes before you buy or build.

How the Right Triangle & Squaring Calculator works

A right triangle has one square corner. Give this calculator two of rise, run and diagonal, or one side and an angle, and it finds the missing side, both angles and the pitch. In pipe work the offset, the run and the travel of an offset make exactly this triangle. The Square check mode gives the diagonal of a rectangle and a 3-4-5 triple for squaring a layout.
The method is the Pythagorean theorem: rise² + run² = diagonal². For a missing leg, subtract: rise = √(diagonal² − run²). The angle between the run and the diagonal is arctan(rise ÷ run), and the pitch is rise ÷ run × 12, shown as X/12.
Example: a 3' rise over a 4' run (36" and 48"). Diagonal = √(36² + 48²) = √(1,296 + 2,304) = √3,600 = 60", or 5'. The angle is arctan(36 ÷ 48) = 36.87°, the other angle is 90° − 36.87° = 53.13°, and the pitch is 36 ÷ 48 × 12 = 9/12.
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 or metric, and a plain number is read as feet. To square a frame or a layout, measure both diagonals: when they match, 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 3' and 4' legs, √(9 + 16) = √25 = 5'. Enter the two legs and leave Diagonal blank.

How is a pipe offset a right triangle?

The offset is one leg, the run (advance) is the other and the travel is the diagonal. A 12" offset over a 12" run has a travel of √(144 + 144) = 16.97" and a 45° angle, the same answer the Pipe Offset Calculator gives for 45s.

How do you square a layout 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 show 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' rectangle measures √(120² + 96²) = √23,616 = 153.675", or 12' 9 11/16", corner to corner. If the two diagonals differ, the frame is out of square.

How do you find an angle 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° − 16.26° = 73.74°.