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Triangle Area Calculator

Computes the area of any triangle from base and height, from three sides (Heron's formula) or from two sides and their included angle in degrees, and reports which method was used.

When to use

You need the area of a triangle and know either its base and height, all three sides, or two sides and the angle between them.

Do not use when: You need the missing sides or angles as well (use triangle-solver), or the triangle is right-angled and you want all its parts (use right-triangle).

Formula

Method 1: area = base × height / 2. Method 2 (Heron): s = (side_a + side_b + side_c) / 2, area = √(s·(s − side_a)·(s − side_b)·(s − side_c)). Method 3: area = ½ · side_a · side_b · sin(included_angle_deg).

Inputs are checked in that order: base and height first, then three sides, then two sides with the included angle. Three sides must satisfy the triangle inequality.

Inputs

Parameter	Type	Unit	Required	Description
`base`	number	units	no	Length of one side chosen as the base (method 1, with height). Range: > 0
`height`	number	units	no	Perpendicular distance from the base to the opposite vertex (method 1). Range: > 0
`side_a`	number	units	no	First side (methods 2 and 3). Range: > 0
`side_b`	number	units	no	Second side (methods 2 and 3). Range: > 0
`side_c`	number	units	no	Third side (method 2, Heron's formula). Range: > 0
`included_angle_deg`	number	degrees	no	Angle between side_a and side_b in degrees (method 3). Range: > 0

Outputs

Output	Type	Unit	Description
`area`	number	units²	Triangle area in the square of the input unit.
`perimeter`	number	units	Sum of the three sides (only for the three-side and two-sides-plus-angle methods).
`method`	string		Which of the three formulas was applied.

Example

Base 10, height 4: {"base":10,"height":4} → {"area":20,"method":"Base × height / 2"}

Sides 7, 8, 9 (Heron): {"side_a":7,"side_b":8,"side_c":9} → {"area":26.8328,"perimeter":24,"method":"Heron's formula (three sides)"}

Sides 5 and 7 with 60° between them: {"side_a":5,"side_b":7,"included_angle_deg":60} → {"area":15.1554,"perimeter":18.245,"method":"Two sides and included angle (½·a·b·sin C)"}

GET https://tttkmbb.com/api/v1/calculate/triangle-area?base=10&height=4

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/triangle-area (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/triangle-area · Markdown: https://tttkmbb.com/geometry/triangle-area.md · JSON definition: https://tttkmbb.com/geometry/triangle-area.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="triangle-area"
OpenAPI operationId: calculate_triangle_area
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Heron's formula (reference)
Wolfram MathWorld – Triangle Area (reference)

FAQ

Which height do I use?

The perpendicular distance from the chosen base to the opposite vertex, not the length of another side. For an obtuse triangle the foot of the height can lie outside the base.

Is the angle in degrees or radians?

Degrees. Convert radians with degrees = radians × 180 / π before entering them.

Why does Heron's formula return an error?

The three sides must satisfy the triangle inequality (each side shorter than the sum of the other two); otherwise no triangle exists.

Related calculators

Triangle Solver — Get all sides and angles, not just the area.
Right Triangle Calculator — Right triangles from any two sides.
Regular Polygon Calculator — Area of an equilateral triangle as a 3-sided regular polygon.