Right triangle calculator
Enter any two values — rise, run, diagonal, or angle — and solve for everything else.
Drop calc results into projects and quotes, invoice through your own Stripe, get paid. Built by a contractor.
Try TradeMaster Pro →How It Works
The right triangle is the foundation of construction math. Every rafter, stair stringer, and slope calculation comes down to the relationship between rise (vertical), run (horizontal), and diagonal (hypotenuse).
Enter any two known values and the calculator solves for everything else using the Pythagorean theorem and basic trigonometry. Results include pitch (rise per 12 inches of run) and grade (rise as a percentage of run) — the two most common ways contractors express slope.
The right triangle is the foundation of nearly every construction calculation: stair stringers, rafter lengths, brace cuts, square layouts, slope calculations, and more. Knowing any two values (rise, run, diagonal, pitch, or angle) lets you solve for everything else using the Pythagorean theorem (a² + b² = c²) and basic trigonometry.
Common Uses
- Finding rafter length from roof pitch and span
- Calculating stair stringer diagonal from rise and run
- Converting between pitch, angle, and grade for slopes
- Squaring foundations using 3-4-5 triangles
FAQ
How do I find the diagonal of a rectangle?
The diagonal of a rectangle is the hypotenuse of a right triangle formed by the rectangle's width and length. Use the formula: diagonal = √(width² + length²). For a 12-foot by 16-foot room, the diagonal is √(144 + 256) = √400 = 20 feet. Squaring up a deck or foundation? If your diagonals are equal, your corners are square.
What is the 3-4-5 rule?
The 3-4-5 rule is a quick way to check or create a perfect 90° corner without a square. If one leg measures 3 units, the other leg measures 4 units, and the diagonal between them measures exactly 5 units, the corner is square. It works at any scale: 3-4-5 inches, 3-4-5 feet, or 6-8-10 feet for larger layouts. It's based on the Pythagorean theorem (3² + 4² = 5²) and is the fastest field method for squaring foundations, decks, and walls.
How do I find the angle from rise and run?
The angle is the arctangent of rise divided by run: angle = arctan(rise/run). For a stair with 7" rise and 11" run, the angle is arctan(7/11) = 32.5°. This calculator does the math instantly — just enter any two values and it solves for everything else.