Triangle Area Calculator finds area from the inputs you choose and shows a scaled diagram. It implements three standard, well-known rules: base–height, Heron’s three-sides formula, and the two-sides-plus-included-angle rule.

Triangle Area Calculator
Total Area
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a b c h
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How to use

  1. Select a method: Base + Height, Three Sides (Heron), or Two Sides + Included Angle.
  2. Enter values. Default unit is centimeters; you may switch to mm, m, in, or ft. Inputs and the result use the same unit system.
  3. Press Calculate Area. The tool validates inputs and highlights the relevant sides or angle in the diagram.

Formulas

Base + Height

Area: A = 1/2 × b × h

Use when the perpendicular height to the chosen base is known.

Three Sides (Heron)

Semi-perimeter: s = (a + b + c) / 2

Area: A = √[ s × (s − a) × (s − b) × (s − c) ]

Works for any non-degenerate triangle when all three sides are known.

Two Sides + Included Angle (SAS)

Area: A = 1/2 × a × b × sin C

Here C is the interior angle between sides a and b.

See Encyclopædia Britannica for the classical statement of Heron’s formula

Triangle Area Calculator Online

Units

Choose cm, mm, m, in, or ft. The result is reported in the squared unit: cm2, mm2, m2, in2, or ft2. Switching units rescales both inputs and output consistently.

Input rules and validation

  • All lengths must be positive real numbers.
  • Three-sides method: triangle inequality must hold (each side is less than the sum of the other two).
  • SAS method: included angle strictly between 0° and 180°.
  • Zero area indicates collinear points or a 0°/180° angle.

Worked examples

Base + Height

b = 21 cm, h = 21 cm → A = 1/2 × 21 × 21 = 220.5 cm²

Three Sides (Heron)

a = 7 cm, b = 8 cm, c = 9 cm → s = 12 → A = √(12 × 5 × 4 × 3) = √720 ≈ 26.833 cm²

Two Sides + Included Angle

a = 12 cm, b = 15 cm, C = 40° → A = 1/2 × 12 × 15 × sin 40° ≈ 57.8 cm²

Choosing the best method

  • Base + Height: right triangles or when a perpendicular altitude is known or can be measured.
  • Heron: only side lengths are available (no angles or heights needed).
  • SAS: two sides and their included angle are known from a drawing, survey, or CAD file.

Accuracy and rounding

  • Calculations use double-precision floating point.
  • Output is formatted to up to four decimal places for readability.
  • Change units if the magnitude is inconvenient (e.g., switch from m² to cm² for small parts).

Geometry facts

  • With a fixed base, area scales linearly with its perpendicular height.
  • With fixed sides a and b, area is maximal at C = 90° because sin C is then 1.
  • Among triangles with the same perimeter, the equilateral triangle has the largest area.
  • Any triangle’s area equals half the product of two sides times the sine of the included angle; the base–height rule is a special case where sin C = h/b.

Troubleshooting

  • Triangle inequality not satisfied: adjust the sides so each is less than the sum of the other two.
  • Angle out of range: use the interior included angle between the two entered sides.
  • Area looks too small: check units; mixing cm with m reduces area by a factor of 10,000.

FAQ

  • Can any side be the base? Yes. Pick a side and use its perpendicular height.
  • Does this work for obtuse triangles? Yes. All three methods support obtuse cases with valid inputs.
  • Can I enter decimal angles? Yes. Degrees may be integer or decimal.

What is your triangle? Are you missing any online tools you need? Let us know in the comments!

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