Triangle Square Footage Calculator
Calculate the area of a triangle using base × height (the standard formula) or three side lengths (Heron's formula). Useful for gables, attic spaces, and triangular gardens.
Triangle Area Calculator
Two formulas, two situations
Standard formula: area = (base × height) ÷ 2. The height MUST be measured perpendicular (90°) from the base to the opposite point. For a triangle with a 12-ft base and 8-ft perpendicular height: (12 × 8) ÷ 2 = 48 sq ft.
Heron's formula (when you only know the three sides): s = (a + b + c) ÷ 2. Then area = √(s(s-a)(s-b)(s-c)). The multi-shape calculator handles this automatically when you select "Triangle (3 sides)".
Real-world triangles
Roof gables are triangles. For a 30-ft-wide gable end with a roof peak 8.75 ft above the wall plate: (30 × 8.75) ÷ 2 = 131 sq ft of gable.
Attic floor cross-sections are triangles. The walkable floor in an unfinished attic with 8-ft trusses is a triangle - useful for estimating insulation or floor area for "knee-wall" build-outs.
Three formulas for three situations
Base-and-height (most common): (base × height) ÷ 2. Use when you have a clear base and can measure the perpendicular height to the opposite vertex.
Heron's formula (three sides known): s = (a + b + c) ÷ 2, then area = √(s(s-a)(s-b)(s-c)). Use when you can measure all three sides but can't easily get perpendicular height — common for irregular lots and gable ends.
Right triangle shortcut: (leg 1 × leg 2) ÷ 2. The two legs of a right triangle are automatically perpendicular, so they serve as base and height.
Worked Heron example: triangular yard with sides 30, 40, 50 ft. s = 60. Area = √(60 × 30 × 20 × 10) = √360,000 = 600 sq ft. (This is a 3-4-5 right triangle, so 30 × 40 ÷ 2 = 600 confirms it.)
Where triangle area shows up
Gable ends for siding or paint: a 30-ft-wide gable with 6 ft peak height = (30 × 6) ÷ 2 = 90 sq ft per gable. Most houses have 2 gables = 180 sq ft total of triangular wall area.
Vaulted ceilings: the triangular portion above the standard wall height. A 14-ft wide wall vaulting from 8 to 14 ft adds (14 × 6) ÷ 2 = 42 sq ft of paint or wallpaper area.
Triangular yard sections: where a driveway angles, where a lot corner is cut off. Break the lot into rectangles plus triangles, calculate each, sum.
Roof valleys and hips: the triangular flashing areas around valleys contribute to roofing material calculations.
Custom shower seats, niches with angled corners, and decorative wall features.
The perpendicular-height mistake
The most common triangle calculation error is using the slope length (the side) instead of perpendicular height. Perpendicular height is the straight vertical (or straight perpendicular) distance from the base to the opposite vertex — not the distance along the angled side.
Worked illustration: a roof gable has a 30-ft horizontal base and slants up at 30 degrees. The slope length (along the rafter) is 17.3 ft. But perpendicular height is only 8.7 ft. Using slope length instead of height would give (30 × 17.3) ÷ 2 = 259 sq ft. Using actual perpendicular height: (30 × 8.7) ÷ 2 = 131 sq ft — half the wrong answer.
When measuring real gables: measure the wall width along the eave line (base), and measure the vertical distance from the eave line to the peak (height). Don't measure along the slanting rafter.
Pro tips
Height is perpendicular, not slanted
For a triangle leaning to the right, the "height" isn't the right slanted edge - it's the straight-up distance from the base to the top point.
Use Heron's when you can't measure height
Triangular property corners are easier to measure as three side lengths than to find a perpendicular height. Use Heron's formula on the multi-shape calculator.
Right triangles are easiest
A right triangle has one 90° angle - the two legs adjoining that angle ARE the base and height. Just multiply legs and divide by 2.
Equilateral shortcut
For an equilateral triangle (all sides equal): area = (side² × √3) ÷ 4. A 10-ft equilateral triangle has area = (100 × 1.732) ÷ 4 = 43.3 sq ft.