Right Triangle Perimeter Calculator

A right triangle has one 90° angle. The two sides forming the right angle are the legs (a and b); the side opposite is the hypotenuse (c).

P = a + b + c

Where c = √(a² + b²) by Pythagoras. So if you measured both legs, the hypotenuse falls out for free, and the perimeter follows.

Where right triangle perimeters show up:

• Stair stringer length. The stringer is the diagonal board that supports the steps. For a staircase rising 8 ft over 12 ft horizontal run, stringer length = √(64 + 144) ≈ 14.42 ft. Perimeter of the right-triangle “side view” = 8 + 12 + 14.42 = 34.42 ft of total framing material.
• Roof rafter. A common rafter spans from eaves to ridge. For a 6:12 pitch roof on a 24 ft wide house, run = 12 ft and rise = 6 ft. Rafter length = √(144 + 36) ≈ 13.42 ft.
• Wheelchair ramp. For ADA-compliant 1:12 slope, a 30 in rise needs a 360 in run. Ramp surface (hypotenuse) ≈ 360.5 in. Perimeter (run + rise + ramp surface) ≈ 750.5 in = 62.5 ft.
• Diagonal bracing. A 4 ft × 6 ft brace on a fence or gate has hypotenuse √(16 + 36) ≈ 7.21 ft.
• Sailboat triangle sails. Most jib and mainsail shapes approximate right triangles. The boom (foot) is the horizontal leg, the mast (luff) is the vertical leg, and the leech is the slanted hypotenuse.

Worked example — stair stringer:

You’re framing stairs from a deck down to a patio. The deck is 36 in above the patio. You want a 7-inch riser, so 36 / 7 ≈ 5.14 — make it 6 risers of 6 in each. Standard tread depth is 10 in. Total horizontal run = 5 × 10 = 50 in (one less tread than the number of risers).

Stringer length = √(36² + 50²) = √(1296 + 2500) = √3796 ≈ 61.6 in. Buy a 6-ft pre-cut stringer or cut your own from a 2×12.

Total framing for one stringer’s “right triangle outline” = 36 + 50 + 61.6 = 147.6 in. Multiply by however many stringers you need (typically 2 or 3 across the stair width).

The 3-4-5 family of integer right triangles:

3-4-5, 5-12-13, 8-15-17, 7-24-25 — these are the most useful integer right triangle triples. Builders use 3-4-5 (or 6-8-10, 9-12-15) for laying out perfectly square corners on a building site: measure 3 ft along one wall, 4 ft along the perpendicular, and the diagonal must be exactly 5 ft. If it’s off, the corner isn’t 90°.