Triangle Square Footage Calculator
Enter the base and perpendicular height of any triangle. The calculator returns the area using the
formula (base × height) / 2 — works for every type of triangle.
Tip: If you only have the diameter, divide by 2 to get the radius.
L-shape = two rectangles sharing a corner.
Add one row per rectangle and we'll sum them.
Triangle Area Formula
The classic formula is Area = (base × height) / 2, where height is the perpendicular
distance from the base to the opposite vertex, not the length of the other side.
- Base 10 ft, Height 8 ft → (10 × 8) / 2 = 40 sq ft
- Base 14 ft, Height 9 ft → (14 × 9) / 2 = 63 sq ft
- Base 20 ft, Height 15 ft → (20 × 15) / 2 = 150 sq ft
Finding the Height of a Triangle
For a right triangle, the two legs meeting at the right angle are the base and height. Otherwise, measure the perpendicular distance from the opposite vertex to the base line. For an obtuse triangle, extend that line beyond the side if necessary; the perpendicular can land outside the triangle.
For a triangular gable wall, use its horizontal base and vertical rise to the peak. A sloping edge is not the height. Roof-surface measurements lie in the roof plane; do not substitute a wall's vertical rise or a horizontal plan-view dimension.
Gable Wall: Check the Window Fit Before Deducting Its Area
Suppose a flat, symmetric triangular gable wall has a 20 ft horizontal base and an 8 ft vertical rise, with the peak above the base midpoint. A rectangular window opening is 3 ft wide and 4 ft high, horizontally centered beneath the peak. Its sill is 1 ft above the triangle's baseline, so its top is 1 + 4 = 5 ft above that line. These are opening dimensions for the excluded wall face, not nominal window product dimensions.
| Step | Calculation | Result |
|---|---|---|
| Gross triangular wall area | (20 × 8) / 2 | 80 sq ft |
| Wall width at the window top | 20 × (1 − 5/8) | 7.5 ft |
| Window opening area | 3 × 4 | 12 sq ft |
| Net wall face area | 80 − 12 | 68 sq ft |
By similar triangles, the available width narrows with height. At the opening's top, the centered 3 ft width fits inside 7.5 ft, leaving (7.5 − 3) / 2 = 2.25 ft on each side. The wall is wider below that level, and the sill is above the baseline, so the entire rectangle fits inside the triangle. Only then can we deduct all 12 sq ft; for an opening crossing the boundary, deduct only the portion inside the measured face.
Each slanted gable edge is √(10² + 8²) ≈ 12.806 ft. That is a side length, not the 8 ft perpendicular height used to calculate the wall area.
What 68 sq ft means: net vertical wall face area, not roof area or attic-floor area. These wall dimensions do not determine the separate sloping roof surfaces or the horizontal floor plan. It is also not a siding purchase quantity: layout, cuts, trim, waste, and manufacturer instructions still matter. The fit check is geometry, not structural framing approval. Use dimensions from plans or measurements obtained with safe access; do not climb onto a roof to obtain them.
Obtuse Triangle: Extend the Base Line, Not the Base Length
Consider a flat triangle with coordinates in feet: A = (0, 0), B = (12, 0), and C = (−3, 4). Choose AB as the base. The perpendicular from C meets the extended base line at D = (−3, 0), 3 ft beyond A, outside the triangle.
| Measurement | Length | How to use it |
|---|---|---|
| Original base AB | 12 ft | Keep this as the base. |
| Perpendicular CD | 4 ft | This is the height. |
| Sloping side AC | 5 ft | A side, not the height. |
| Extended distance DB | 15 ft | Only for the enclosing-triangle cross-check. |
If the 5 ft side and 3 ft offset are known, the perpendicular height is √(5² − 3²) = 4 ft. Using the original base, the area is (12 × 4) / 2 = 24 sq ft.
Check the result by subtracting the small exterior right triangle ADC from the enclosing right triangle DBC: (15 × 4) / 2 − (3 × 4) / 2 = 30 − 6 = 24 sq ft.
The base remains 12 ft, not 15 ft. Extending the base line only locates the perpendicular foot. Using either the extended 15 ft distance as the base or the sloping 5 ft side as the height would incorrectly give 30 sq ft.
Common Uses for Triangle Square Footage
- Gable walls — calculate the triangular portion above the rectangular wall, then deduct openings that lie within it.
- Triangular floor sections — use dimensions measured in the floor plane. A triangular attic cross-section does not mean the attic floor is triangular.
- Garden beds — area can estimate sod coverage; mulch volume also needs depth.
- Roofing — measure each triangular section in the sloping roof plane, not from a gable elevation.
Worked Examples: A Gable Versus Its Roof, Its Digits, and Its Unit
The three examples below answer questions the widget cannot answer for you. This calculator has no pitch, roof-plane, opening or unit-of-output input — it takes a base and a perpendicular height and returns one area in the unit you typed. Everything else on this page is arithmetic you do before and after that single step.
1. The gable triangle is not the roof it sits under
Take a symmetric gable with a 20 ft horizontal base and an 8 ft vertical rise, on a building whose ridge runs 30 ft. The wall triangle is (20 × 8) / 2 = 80 sq ft, which is what the calculator displays for that pair (80.00). The roof is a different surface, in a different plane:
| Surface | Calculation | Area |
|---|---|---|
| Gable wall face (vertical) | (20 × 8) / 2 | 80 sq ft |
| Rafter length (sloped edge) | √(10² + 8²) = √164 | 12.81 ft |
| One roof plane (sloped) | 30 × 12.8062 | 384.19 sq ft |
| Both roof planes | 2 × (30 × √164) | 768.37 sq ft |
| Horizontal footprint | 20 × 30 | 600 sq ft |
Two numbers on that list are easy to grab by mistake. The 12.81 ft rafter is a length, not the 8 ft height — using it as the height inflates the gable to (20 × 12.8062) / 2 = 128.06 sq ft, 60% too much. And the 600 sq ft footprint is a plan area, not a roof area. The slope factor converts one into the other: rafter ÷ half-span = 12.8062 ÷ 10 = 1.28062, and 600 × 1.28062 = 768.37 sq ft — exactly the two planes above, which is the check that the factor was built from the right triangle.
The ratio is the practical warning: 768.37 ÷ 80 = 9.605. Ordering roof sheathing from the gable area would be out by a factor of nearly ten, and the gable triangle here is only one of two identical end walls. NCSU's extension engineering text frames the same question for a different purpose — which surface the calculation is about: “Typically, there is the question about what area to consider for the roof.” Its answer is conditional on the building, not universal: for nearly flat roofing, “the roof area can be considered essentially equal to the floor area”, and “The ceiling area then becomes the roof area and is equal to the floor area.” Both statements assume a shallow pitch or a ceiling that replaces the sloped surface — at 8 ft of rise over a 10 ft half-span neither applies, and the sloped plane is 28% larger than the plan.
The three figures answer three different purchases: 80 sq ft of siding on the end wall, 768.37 sq ft of roof covering on the planes, 600 sq ft of floor or ceiling. Enter the base and perpendicular height of the surface you are actually buying.
2. How many of those digits are yours?
Measure a triangle as 12 ft 6 in along the base and 9 ft 8 in up the perpendicular. Enter 12.5 and 9.6667 and the tool displays 60.42 sq ft; the unrounded product is 60.4167 sq ft (725 ÷ 12). Nowhere in that workflow was a length measured to a hundredth of a foot.
A tape read to the nearest half inch on both numbers gives a base between 149.5 in and 150.5 in and a height between 115.5 in and 116.5 in. The area therefore lies between 59.96 sq ft and 60.88 sq ft — a spread of 0.46 sq ft on either side of the exact product. The last digit is doing nothing but recording the arithmetic; the defensible statement about this triangle is “about 60.4 sq ft”. NIST SP 811 puts the rule as follows: “Proper conversion procedure requires rounding this converted numerical value to the number of significant digits that is consistent with the maximum possible rounding error of the unconverted numerical value.” That section was written for unit conversion, and it applies just as directly to a calculator display; the guide also concedes the trade-off in plain terms — “one must often choose between discarding information or providing unwarranted information”.
Two habits follow. First, round the result to the last digit your input precision supports, then apply any cutting allowance to that rounded figure so the allowance and the precision do not fight. Second, keep full precision inside a chain of calculations and round only at the end; the widget does that (it formats the display, not the stored value), and a chain of hand-rounded steps will not reproduce it.
3. Writing the unit so the next reader gets an area
Area notation is where a correct calculation turns into a wrong order. Take the tidy number 144 sq ft (a 12 ft × 12 ft triangle pair, or any 144 sq ft surface) and let three different notational slips run through it:
| Intent | Correct step | Slip | Wrong result |
|---|---|---|---|
| Square yards of the same area | 144 sq ft ÷ 9 = 16 sq yd | ÷ 3 (the linear factor) | 48 sq yd — three times too many |
| Cubic feet of a 4 in depth | 144 sq ft × (4 ÷ 12) ft = 48 cu ft | unit dropped: “144 × 4” | 576 of nothing in particular |
| Square meters of the same area | 144 × 0.09290304 = 13.38 sq m | linear factor (0.3048) | 43.89 sq m — 3.3× too many |
The area factor is the square of the linear one, so a linear conversion used on an area is wrong by exactly that second power: 3² = 9 for yards, and 0.3048² = 0.092 903 04 for meters. NIST's style rules target the ambiguity directly: “values of quantities must be written so that it is completely clear to which unit symbols the numerical values of the quantities belong”, and for spelled-out names it settles the word order — “When the names of units raised to powers are spelled out, modifiers such as "squared" or "cubed" are used and are placed after the unit name”, while “The modifiers "square" or "cubic" may, however, be placed before the unit name in the case of area or volume.”
In practice that means 144 sq ft, 144 ft² and 144 square feet are all unambiguous, and ft^2, ft2 or a bare 144 are not — the exponent has to survive the copy-paste, the phone screen and the printout. If the number feeds a depth or a thickness, write the second unit in full (“48 cu ft at 4 in deep”) so nobody reads a volume as an area.
Frequently Asked Questions
How do I calculate the square footage of a triangle?
Multiply the base by the perpendicular height and divide by 2. A 14 ft × 9 ft triangle is (14 × 9) / 2 = 63 sq ft.
What if I don't know the perpendicular height?
For a right triangle, choose one leg as the base and the other as the height. For other triangles, measure perpendicular to the chosen base line from the opposite vertex, extending the line as needed. The perpendicular can land outside the triangle, as in the obtuse example; it need not point vertically down the page. If you know only the three side lengths, use Heron's formula separately. This calculator requires a base and perpendicular height, not three side inputs.
Does this formula work for scalene and isosceles triangles?
Yes. As long as you use the perpendicular height (not the slant length), (base × height) / 2 works for every triangle.
Is a gable wall triangle the same area as the roof above it?
No. A gable with a 20 ft base and 8 ft rise is 80 sq ft of vertical wall face, while the two sloped roof planes over a 30 ft ridge total 768.37 sq ft — 9.605 times more. The gable is one elevation; the roof is a sloped surface measured in its own plane.
How do I get the rafter length and the slope factor?
Treat half the span and the rise as the legs of a right triangle: √(10² + 8²) = 12.81 ft is the rafter length. Divide it by the 10 ft half-span to get the slope factor 1.28062, then multiply the horizontal plan area by it: 600 sq ft × 1.28062 = 768.37 sq ft for both planes together.
Can I use the sloping edge of a gable as the height?
No — that is the most common triangle mistake. The height is the perpendicular distance from the base line to the opposite vertex. In the 20 ft × 8 ft gable the sloping edge is 12.81 ft, but the figure that belongs in (base × height) / 2 is 8 ft.
How many digits should I trust in the calculator's result?
Fewer than the display shows. A triangle taped as 12 ft 6 in by 9 ft 8 in displays 60.42 sq ft, but half an inch of uncertainty on each measurement already spans 59.96 to 60.88 sq ft. Round the result to the digits your tape measure actually justifies.
Should I write 144 sq ft, 144 ft², or 144 square feet?
All three mean the same area; the risk is a notation your reader parses as a length or a volume. Keep the unit attached to its number: 144 sq ft ÷ 9 = 16 sq yd, while 144 × 4 in is a volume of 48 cu ft, not an area.
Does this calculator deduct windows or doors?
No. The tool takes a base and a perpendicular height and returns one area; it has no window, door or opening inputs, and no roof-pitch inputs. Deduct openings by hand, and only after checking the opening fits inside the triangle — see the gable window check above.
Sources and How to Check This Page
- “Refrigeration Load”, Introduction to Postharvest Engineering for Fresh Fruits and Vegetables, NC State Extension — the quoted passage on deciding which surface a roof area refers to, including the flat-pitch case where the roof area equals the floor area. Fetched 2026-10-11; archived as
data/content-audit/evidence/raw11/s-edu-ncstate-refload.txt. It is a heat-load text, so this page uses its area reasoning only, not its refrigeration figures. - NIST Special Publication 811-2008, Guide for the Use of the International System of Units — Sec. 7.7 (make clear which unit symbol belongs to which number), Sec. 9.6 (where "square" and "cubed" go), Sec. 7.9 with Sec. B.7 (significant digits and rounding after a conversion). Every NIST quotation on this page is verbatim from that PDF; archived as
s-nist-sp811-2008.txt. - “U.S. Survey Foot”, NIST — the reason this site's metric conversions use the international foot (0.3048 m exactly), which is what makes the factors above 9 and 0.09290304 rather than survey-based ones. Archived as
s-gov-nist-surveyfoot.txt. - Every figure in the three worked examples is recomputed by
data/content-audit/evidence/raw11/number-recompute-2026-10-11.mjs, which loads the samejs/calc-core.jsthe widget runs on. To check one by hand: √164 = 12.806248…, 12.806248 × 30 = 384.1875, and 600 × 1.2806248 = 768.37; or type 20 and 8 into the calculator above and compare its display with the first table row.
Geometry References
The perpendicular-height rule this calculator depends on is the standard triangle altitude. Wikipedia's "Altitude (triangle)" puts the obtuse case in one caption: “The altitude from A (dashed line segment) intersects the extended base at D (a point outside the triangle).” That is the same extended-base line worked in the obtuse example above — the height is still measured at right angles to the base line, even when it lands outside the figure. Fetched 2026-10-11 and archived as data/content-audit/evidence/raw11/s-src-wikipedia-altitude.txt. It is a tertiary encyclopedia, good for the definition but not an engineering or construction specification; the numerical examples and window-fit check above are our own calculations.