A triangle is the simplest closed shape in geometry, yet it shows up everywhere in the built world: gable ends on houses, triangular shingles on a roof, sails on a boat, bike frames, ramps, and the wedge of a pizza. To buy the right amount of paint, carpet, sod, fabric, or roofing material, you need the area of that triangle — and this calculator gives it to you in seconds.
You can work in two ways. When you know a base and the perpendicular height, the classic rule Area = ½ × base × height is all you need. When you only know the three side lengths, switch to Heron's formula, which computes the area from the sides alone. Type your numbers and the area updates instantly — and, in the three-sides route, you also get the exact perimeter and the semi-perimeter that Heron's formula relies on. In base-height mode the perimeter is estimated assuming an isosceles triangle with the given base and height; switch to three-sides mode for the exact perimeter.
How to Use
- Pick a Calculation Method. Choose "base-height" if you can measure one side (the base) and the straight-up distance from that base to the opposite corner. Choose "three-sides-heron" if you have measured all three edges but cannot easily measure a height.
- Enter the Base (b) — the side you decided to treat as the bottom. It can be any side; the formula does not care which one is horizontal.
- Enter the Height (h) — the perpendicular distance from the base to the opposite vertex. This is the vertical distance a plumber's level would show, not the length of a slanted side.
- If you chose the three-sides route instead, fill in Side a, Side b, and Side c. The two shorter sides together must be longer than the longest side; if they are not, the sides cannot close into a triangle and the area reports 0 rather than a nonsense number.
- Read the result card: Triangle Area is highlighted, followed by the semi-perimeter and the perimeter (both populated only in three-sides / Heron mode), and the values you entered so you can double-check them.
- Repeat with different units. If your measurements were in feet, the area comes out in square feet; in centimeters, it comes out in square centimeters. Keep your unit consistent — never mix feet for one side and meters for another.
The Two Formulas Behind the Calculator
The base-and-height rule comes straight from a rectangle: if you cut a rectangle along its diagonal, each half is a right triangle with exactly half the rectangle's area. That intuition generalizes to every triangle, not just right ones, which is why
A = ½ × b × h
always works as long as h is the perpendicular height to base b. For example, a base of 10 ft and a height of 5 ft give ½ × 10 × 5 = 25 square feet.
When the height is awkward to measure — think of a steep roof or an irregular lot — Heron of Alexandria gave us a way around it nearly two thousand years ago. Call the three sides a, b, c, and define the semi-perimeter s = (a + b + c) / 2. Then
A = √( s × (s − a) × (s − b) × (s − c) )
For a 3-4-5 triangle, s = 6, and the area is √(6 × 3 × 2 × 1) = √36 = 6 square units. The same formula gives the familiar equilateral result too: three sides of 10 ft give s = 15 and an area of about 43.3 square feet, matching A = (√3 / 4) × 10².
Examples
Example 1 — Painting a triangular gable. A homeowner's gable wall is a triangle with a base of 24 ft and a height of 8 ft. The area is ½ × 24 × 8 = 96 square feet. A gallon of exterior paint covers about 350 sq ft, and they want two coats (roughly 192 sq ft of coverage needed). At $45 per gallon, one gallon is plenty, so the paint budget is about $45 — plus a 10% overage for touch-ups brings it to roughly $50.
Example 2 — Sod for a triangular lawn. A landscape crew lays sod on a triangular lot with base 30 ft and height 18 ft. Area = ½ × 30 × 18 = 270 sq ft. Sod sells for about $0.65 per square foot, so the material cost is 270 × $0.65 ≈ $176. A 15% waste allowance for cuts and curves adds about $26, bringing the order to near $200 before delivery.
Example 3 — Fabric for a triangular sail. A sail maker measures three edges as 6 m, 8 m, and 10 m (a scaled-up 3-4-5 right triangle). Using Heron's formula: s = 12, area = √(12 × 6 × 4 × 2) = √576 = 24 m². The waterproof nylon costs $18 per square meter, so the sail fabric alone costs about $432, with seam tape and reinforcing patches adding another 12% — around $52 — for a finished cost near $484.
Example 4 — A large parcel boundary (base-height route). A surveyor walks off a triangular plot: the baseline along the road is 1,000 ft, and the perpendicular distance to the third corner (measured by a sight level) is 1,000 ft. Using base-and-height: ½ × 1,000 × 1,000 = 500,000 square feet, which is roughly 11.5 acres. At a zoning density of 8 units per acre, that supports about 92 units — useful early on, before any engineering dollars are spent. Switch to three-sides mode later once the surveyor has pinned down the exact edge lengths; the perimeter will then update to the real value.
FAQ
What is the formula for the area of a triangle?
The most common formula is A = ½ × base × height, where the height is the perpendicular distance from the base to the opposite vertex. If you only know the three sides, use Heron's formula: s = (a + b + c)/2, then A = √(s(s−a)(s−b)(s−c)). Both give the same answer; pick whichever inputs you have.
How do I find the area of a triangle without the height?
Use Heron's formula. Add the three sides, divide by two to get the semi-perimeter s, subtract each side from s, multiply the three results together, and take the square root. This works for any triangle — acute, obtuse, or right — as long as the sides can actually form a triangle.
Is a right triangle's area just half of a rectangle?
Yes. A right triangle with legs b and h is exactly half of an b-by-h rectangle, so its area is ½ × b × h. This is the easiest special case: the two legs double as the base and the perpendicular height, no extra measurement needed.
How do I calculate area in square feet?
Measure the base and the height in feet, then apply ½ × base × height. If your measurements were in inches, convert them to feet first (divide by 12), or compute in square inches and divide by 144 to get square feet.
What is Heron's formula and when should I use it?
Heron's formula computes area from the three side lengths alone: s = (a+b+c)/2 and A = √(s(s−a)(s−b)(s−c)). Use it when you can pace or measure all three edges but cannot drop a perpendicular height easily — for example, across an uneven field, a roof plane, or a plot of land.
How is the area of an equilateral triangle different?
An equilateral triangle with side s follows A = (√3 / 4) × s², which is just Heron's formula with all three sides equal. A side of 10 ft gives about 43.3 sq ft. It is a convenient shortcut, but Heron's formula on this page will compute it the same way if you enter 10, 10, 10 in three-sides mode.
Does the calculator handle very large or very small triangles?
Yes. The engine uses floating-point arithmetic and comfortably handles sides in the millions (for example, a 1,000,000-by-1,000,000 base-height triangle returns 500,000,000,000 area units) as well as tiny fractional values for craft or physics work. Just keep all measurements in the same unit.
Disclaimer
This triangle area calculator is provided for informational purposes only and does not constitute engineering, surveying, construction, or design advice. Results are based on the measurements you enter and on the standard Euclidean formulas A = ½bh and Heron's formula; they assume planar, two-dimensional geometry and consistent units. Real-world jobs such as roofing, landscaping, or structural design require professional verification, allowance for waste, and local building codes. Always confirm critical measurements with a qualified professional before purchasing materials or beginning construction.