To calculate a triangle's area in square feet, multiply the base in feet by the perpendicular height in feet and divide by two — A = (b × h) ÷ 2. The result is written ft² because the formula multiplies two independent lengths: a length in feet times another length in feet equals an area in square feet. That single sentence captures the entire task. The base can be any one of the three sides; the height must be measured at exactly 90° to the base line, reaching the opposite vertex. Both inputs must be positive and share the same unit (feet in this case). The shape of the triangle does not matter: right, acute, obtuse, isosceles, scalene, and equilateral triangles all use the same A = bh/2 expression when a valid base-altitude pair is known. The math runs entirely in your browser on the Triangle Area Calculator, so you can enter feet on both inputs, choose feet as the shared unit, click Calculate area, and copy the ft² answer with the substituted formula visible above it.
What "Square Feet" Means for a Triangle
Square feet is a unit of area, not length. When you say a triangle has 54 square feet, you mean the surface enclosed by the three sides would cover exactly fifty-four 1-foot by 1-foot squares laid flat next to each other. The notation ft² exists because area is the product of two perpendicular lengths. Any area calculation in feet will yield square feet as long as both length inputs were already in feet. This is also why area is the only measurement the calculator outputs that carries a "squared" unit — perimeter would still come out in plain feet because it adds lengths, never multiplies them.
The Formula: A = (b × h) ÷ 2
The governing equation for triangle area is A = bh/2. According to OpenStax Prealgebra 2e, the formula comes from a rectangle: drawing a diagonal through any rectangle splits it into two congruent triangles, and because the rectangle's area is base × height, each triangle inherits exactly half of that. Wolfram MathWorld independently lists the equivalent base-altitude relationship. Because every planar triangle can be paired with a rectangle of equal base and equal perpendicular height, the formula applies to right, acute, obtuse, equilateral, isosceles, and scalene triangles without modification. Readers who want to see the rectangle side of that derivation can follow How to Calculate Rectangle Area in Square Feet Step by Step for the underlying b × h piece.
How to Calculate Triangle Area in Square Feet
- Pick any side of the triangle as the base and measure its length in feet with a tape measure or laser rangefinder.
- Measure the perpendicular distance from that base line to the opposite vertex — also in feet. A framing square or a level held against the base is the simplest way to confirm the 90° angle.
- Multiply base × height, divide by two, and label the result ft². Or open the Triangle Area Calculator, type both values, choose feet as the shared unit, and click Calculate area to get the answer with the substituted formula shown above it and a one-click copy control.
The calculator multiplies base by height first, then divides by two — exactly the order the formula is written. It rounds only the displayed answer to twelve significant digits and labels the unit ft², mm², cm², m², or in² depending on the unit you picked. Nothing is uploaded, no account is needed, and only finite positive values larger than zero are accepted.
How Height Behaves in Different Triangle Types
A common source of error is using a slanted side as the "height." For an isosceles or scalene triangle, the two long slanted sides look tempting, but neither of them is automatically perpendicular to the base. The valid height is the shortest perpendicular distance from the line containing the chosen base to the opposite vertex.
- Right triangle: one of the legs is already perpendicular to the other, so it acts as the height if the other leg is chosen as the base.
- Acute triangle: the altitude drops inside the triangle and lands on the visible base segment.
- Obtuse triangle: the perpendicular altitude may meet an extension of the base outside the visible side. The formula A = bh/2 still applies because the base-altitude pair is what matters, not where the foot of the altitude lands.
- Equilateral triangle: when only the side length s is known, the perpendicular height is s√3/2 and the area becomes √3s²/4. The Triangle Area Calculator does not infer that special case automatically — it asks for the actual perpendicular height so the same input shape handles every triangle type, including non-equilateral ones.
When You Don't Have Base and Height
If your measurements don't include a clean base-altitude pair, the simple A = bh/2 path is not directly available. The table below shows which inputs work with the Triangle Area Calculator and which require a different approach.
| What you know | Formula to use | Works on this calculator? |
|---|---|---|
| Base (ft) + perpendicular height (ft) | A = bh/2 | Yes — enter both in feet |
| Three side lengths | Heron's formula: s = (a+b+c)/2, A = √(s(s−a)(s−b)(s−c)) | No — derive altitude first or use a three-sides tool |
| Two sides + included angle | A = ½ · a · b · sin C | No — the calculator expects base and perpendicular height |
| One side of an equilateral triangle | A = √3 s²/4 | Compute height s√3/2 first, then enter base and that height |
Unit Consistency and Conversion
The two inputs must share a unit. A base of 11 centimeters and a height of 8 centimeters produces 44 square centimeters; a base of 11 centimeters and a height of 8 inches does not produce a clean number, because the multiplication mixes length systems. The Triangle Area Calculator labels the answer in the unit you selected but does not silently convert the entered magnitudes — you must convert before submitting. If you already have an area expressed in some other unit and want it in ft², the Area Converter handles that final step.
Zero base or zero height describes a degenerate shape with no enclosed triangular area, so the page rejects those values rather than presenting them as an ordinary triangle. Scientific notation in the browser input is accepted, and the formatter chooses readable ordinary or exponential notation according to the resulting magnitude.
Worked Example in Feet
A triangular section of a patio has base 12 ft and perpendicular height 9 ft. Walk through the formula step by step:
A = (base × height) ÷ 2 A = (12 × 9) ÷ 2 A = 108 ÷ 2 A = 54 ft²
You can verify the result by drawing a 12 ft × 9 ft rectangle around the triangle. The rectangle covers 108 ft², and the triangle fills exactly half of it, leaving 54 ft². The Triangle Area Calculator shows the same substitution on screen and rounds only the displayed answer, so the underlying 54 is preserved when both inputs are whole numbers.
Practical Uses for Triangle Square Footage
Triangle area in ft² shows up in landscaping sketches, flooring layouts for odd-shaped rooms, fabric cutting for triangular panels, and rough material estimates for triangular signs, sail canvas, or shed roofs. Real projects almost always need extra room for seams, overlap, cutting loss, thickness, uneven boundaries, and measurement uncertainty. Treat the calculator result as a planning baseline, add an allowance for the relevant waste factor, and round according to the precision of your least-precise input — for tape-measure work, two significant digits is usually enough. For surveying, structural design, or regulated construction, rely on verified field measurements and the applicable professional method rather than a two-number ideal estimate.
Related reading: How to Convert Area to Radius: Formula & Unit Prep.