Calculate triangle area, perimeter, angles, altitudes, circumradius, inradius, and classification. Supports base-height, Heron's formula, and SAS methods with unit selection and a complete 15-prop...
The area of a triangle is one of the most fundamental calculations in geometry. Whether you are a student solving homework problems, an engineer designing structural components, or a homeowner measuring an oddly shaped plot of land, knowing how to find a triangle's area is an essential skill.
This calculator supports three different methods so you can work with whatever measurements you have. The simplest approach uses base and height: multiply the base by the height and divide by two. When you know all three side lengths but not the height, Heron's formula computes the area using only the sides. And when you know two sides and the angle between them, the SAS (Side-Angle-Side) formula handles the calculation.
Triangles appear everywhere in the real world — from roof trusses and sail panels to surveying irregular land parcels and creating computer graphics. Understanding area computation unlocks applications across architecture, physics, engineering, art, and everyday problem solving. This tool gives you accurate results in seconds, no matter which measurements you start with.
Computing triangle area by hand is straightforward for simple cases, but Heron's formula involves square roots of products, and the SAS method requires trigonometric functions — both are easy to miscalculate without a tool. This calculator handles all three methods instantly and shows which formula it used, so you can verify the approach. It is especially valuable when comparing results across methods to double-check your measurements.
Method 1 — Base & Height: A = ½ × b × h Method 2 — Heron's Formula (three sides a, b, c): s = (a + b + c) / 2 A = √(s(s − a)(s − b)(s − c)) Method 3 — SAS (two sides a, b and included angle C): A = ½ × a × b × sin(C)
Result: 30
Using the base-and-height method: A = ½ × 10 × 6 = 30 square units. This is the simplest triangle area formula — half of the rectangle formed by the base and height.
Triangles are the simplest polygon and the building block of more complex shapes. Any polygon can be divided into triangles, and any curved surface can be approximated by a mesh of triangles (this is how 3D graphics work). Understanding triangle area is therefore the foundation for computing areas of all shapes.
The base-and-height method is simplest but requires knowing the perpendicular height, which is not always directly measurable. Heron's formula needs only the three sides — ideal for surveying or situations where you can measure edges but not heights. The SAS method is useful in engineering and navigation, where angles are often known from instruments. All three methods produce the same result for the same triangle.
Architects use triangle area calculations to estimate roofing materials for gable ends. Surveyors divide irregular land parcels into triangles and sum their areas. Physicists compute cross-sectional areas of triangular beams for stress analysis. Even artists use triangle geometry to create balanced compositions and perspective drawings.
Multiply the base by the perpendicular height, then divide by 2. The formula is A = ½ × base × height. For example, a triangle with a base of 8 cm and a height of 5 cm has an area of 20 cm².
Heron's formula calculates the area of a triangle when you know all three side lengths. First compute the semi-perimeter s = (a+b+c)/2, then the area is √(s(s-a)(s-b)(s-c)). It works for any triangle, regardless of shape.
You need the included angle between those two sides as well. With two sides a and b and the angle C between them, use A = ½ × a × b × sin(C). Without the angle, two sides alone do not uniquely determine the area.
Area is always in square units of whatever length unit you used. If your sides are in centimeters, the area is in square centimeters (cm²). If in feet, the area is in square feet (ft²). Be consistent with your units.
Rearrange the base-height formula: h = 2A / b. If you know the area is 30 and the base is 10, the height is 2 × 30 / 10 = 6.
Yes, all three methods work for right triangles. For a right triangle, the two legs serve as the base and height, making the ½ × b × h method particularly straightforward.
For an equilateral triangle with side length s, the area is (√3/4) × s². For example, an equilateral triangle with side 6 has area (√3/4) × 36 ≈ 15.59 square units.