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Triangle area calculator
Calculate triangle area, perimeter, altitudes and type from base-height, Heron, two sides and angle or coordinates.
Triangle area calculator
Compute area, perimeter, heights, and classify the triangle using base and height, three sides (Heron), two sides plus included angle, or Cartesian coordinates.
Input data
e.g. 10
Length of the base
e.g. 6.5
Perpendicular to the base
e.g. 7
e.g. 8
e.g. 9
e.g. 5
e.g. 7
0–180
Included angle between a and b
e.g. 0 ; 0
e.g. 8 ; 0
e.g. 3 ; 6
0–10
Applies rounding to every output
Results
Geometric visualization
The triangle is drawn to relative scale with a reference base, height and side.
Calculate to view the triangle.
Sides (a, b, c)
—
Triangle type
—
Height relative to a (hₐ)
—
Perimeter (P)
—
Semiperimeter (s)
—
Area conversions
mm²
—
cm²
—
m²
—
in²
—
ft²
—
Includes every output and unit
Formulas used
- Base and height: A = (b · h) / 2
- Heron: s = (a + b + c) / 2, A = √(s(s − a)(s − b)(s − c))
- Two sides and angle: A = (a · b · sin θ) / 2
- Coordinates: A = |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)| / 2
- Height from a: hₐ = 2A / a
Which formulas does each mode use?
Base–height relies on A = (b · h) / 2; three sides uses Heron’s formula; two sides plus the included angle uses A = (a · b · sin θ) / 2; and the coordinates mode applies the shoelace formula, taking the absolute value to keep the area positive.
Can I enter the angle in degrees or radians?
The calculator expects degrees. If you have radians, convert them by multiplying by 180/π before entering the value so the area stays consistent.
How does the coordinate calculation work?
We apply the coordinate determinant: area is computed from x₁y₂ + x₂y₃ + x₃y₁ − (y₁x₂ + y₂x₃ + y₃x₁) and we take the absolute value/2, so the result is correct whether the points are clockwise or counterclockwise.
Which triangle types does the tool report?
Results include side-based classification (equilateral, isosceles, or scalene) and angle-based classification (acute, right, or obtuse), shown alongside perimeter, semiperimeter, and heights.
How can I save or share the outputs?
The “Copy results” button sends every magnitude and conversion with the chosen unit and decimal precision to your clipboard. Paste it into a report or document without losing formatting.
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Found an error or missing a feature?
Send us the example so we can review this calculator and turn real cases into improvements or automated tests.
