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. At the ADA 1:12 maximum slope, a 30 in rise needs a 360 in run, which is also the longest single run ADA allows before a landing. Ramp surface (hypotenuse) = √(360² + 30²) = 361.25 in. Perimeter = 360 + 30 + 361.25 = 751.25 in, or 62.6 ft. Notice how little the slope adds: the ramp surface is only 1.25 in longer than the flat run beneath it.
• Diagonal bracing. A 4 ft × 6 ft brace on a fence or gate has hypotenuse √(16 + 36) ≈ 7.21 ft.
• Sailboat mainsails. A Bermuda main is close to a right triangle at the tack, where the boom meets the mast. The foot runs along the boom, the luff up the mast, and the leech is the slanted trailing edge.

Worked example: a stair stringer

You’re framing stairs from a deck down to a patio. The deck is 36 in above the patio. Aim for a 7-inch riser and 36 / 7 = 5.14, which is not a whole number, so take 6 risers of exactly 6 in. Standard tread depth is 10 in, and there is always one fewer tread than riser because the deck itself is the top one, so the horizontal run is 5 × 10 = 50 in.

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 and 7-24-25 are the integer triples worth memorising. Builders use 3-4-5 to lay out square corners: measure 3 units along one wall, 4 along the perpendicular, and the diagonal has to come out at exactly 5.

Scale it up as far as the site allows. A 3 mm error over a 3 ft triangle becomes 30 mm over 30 ft, so use 6-8-10 or 9-12-15 on a foundation and 30-40-50 if you have the room. The bigger the triangle, the finer the angle you can actually resolve with a tape.