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Triangle Calculator

Calculate triangle area from base & height, three sides (Heron's formula), or two sides and an included angle. Detects right triangles automatically.

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Triangle Calculator

Calculation Method

Base

Height

Triangle Area Formulas

Three different formulas cover every triangle scenario in construction. Choose the method that matches the measurements you have available in the field.

Method 1 — Base & Height:
Area = (Base × Height) ÷ 2

Method 2 — Three Sides (Heron's Formula):
s = (a + b + c) ÷ 2
Area = √[s × (s−a) × (s−b) × (s−c)]

Method 3 — Two Sides & Included Angle (SAS):
Area = 0.5 × a × b × sin(C)

Pythagorean Theorem (Right Triangles):
c² = a² + b² → c = √(a² + b²)

Common Right Triangles in Construction

Side A	Side B	Hypotenuse C	Area	Use Case
3	4	5	6	Layout square corners
5	12	13	30	Stair rise/run
6	8	10	24	Larger layout checks
8	15	17	60	Rafter calculations
9	12	15	54	Foundation layout
12	16	20	96	Large foundation diagonals

Roof Pitch and Triangle Geometry

Roof Pitch	Rise (per 12" run)	Slope Angle	Rafter Multiplier
3/12	3 inches	14.0°	1.031
4/12	4 inches	18.4°	1.054
5/12	5 inches	22.6°	1.083
6/12	6 inches	26.6°	1.118
8/12	8 inches	33.7°	1.202
12/12	12 inches	45.0°	1.414

Tips for Triangle Calculations in Construction

Use the 3-4-5 method on any job site to verify square corners quickly and without a calculator.
For gable end walls, calculate the triangle area separately from the rectangular wall below it, then add them together for total siding area.
When measuring an irregular triangular plot of land, Heron's formula is the most practical — just pace or tape the three sides.
The rafter multiplier in the roof pitch table above converts horizontal run to actual rafter length — multiply your roof span by the multiplier.
For hip roof sections, break the hip area into right triangles and calculate each one separately.

? Frequently Asked Questions

How do I calculate the area of a triangle?

The most common method is Area = (Base × Height) ÷ 2, where height is the perpendicular distance from the base to the opposite vertex. If you know all three sides, use Heron's formula: s = (a+b+c)/2, then Area = √[s(s-a)(s-b)(s-c)]. If you know two sides and the included angle, use Area = 0.5 × a × b × sin(C).

What is Heron's formula?

Heron's formula calculates the area of any triangle from its three side lengths without needing the height. First compute the semi-perimeter s = (a + b + c) ÷ 2. Then Area = √[s × (s−a) × (s−b) × (s−c)]. This is especially useful in construction when you can measure three sides of an irregular triangular area but cannot easily measure the perpendicular height.

How do I know if a triangle is a right triangle?

A triangle is a right triangle if the square of its longest side (hypotenuse) equals the sum of the squares of the other two sides: a² + b² = c². This is the Pythagorean theorem. For example, a 3-4-5 triangle is a right triangle because 3² + 4² = 9 + 16 = 25 = 5². Our calculator automatically detects right triangles when you enter three side lengths.

How is triangle area used in construction?

Triangle calculations appear throughout construction: calculating the area of a gable end wall for siding, determining roofing material for hip and gable sections, laying out 90-degree corners using the 3-4-5 method, calculating the area of triangular landscaping beds, and computing the volume of triangular prism-shaped fill areas.

What is the 3-4-5 rule in construction?

The 3-4-5 rule is a field method for laying out perfectly square (90°) corners using the Pythagorean theorem. Measure 3 feet along one side, 4 feet along the perpendicular side, and the diagonal between those endpoints should measure exactly 5 feet. You can scale it up: 6-8-10, 9-12-15, or any multiple of 3-4-5 works for larger layouts.

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💡 Pro Tips

✅ Use 3-4-5 rule to verify 90° corners on site
✅ Heron's formula works when you can only measure sides
✅ For gables, add triangle area to the rectangular wall below
✅ The SAS method is best when you know the included angle