Free triangle calculator
Calculate triangle area, perimeter, and angles — enter any combination of sides and angles, updated live, as you type.
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Area via Heron's formula. Triangle inequality: each side must be less than the sum of the other two. Source: Heron of Alexandria.
Results are estimates. Consult a professional.
How the triangle calculator works
A triangle's area, perimeter, and angles are linked by several exact formulas. The basic area formula requires a base and height; Heron's formula computes area from all three sides alone, without needing to know the height. All interior angles always sum to 180°.
Worked example: triangle with sides 5, 7, 8
Given a triangle with sides a = 5, b = 7, c = 8, find the perimeter and area using Heron's formula.
Triangle types and properties
Triangles are classified by their sides (equilateral, isosceles, scalene) and by their angles (acute, right, obtuse). Each type has distinctive properties.
| Type | Sides / Angles | Key property |
|---|---|---|
| Equilateral | All 3 sides equal | All angles = 60° |
| Isosceles | 2 sides equal | Base angles are equal |
| Scalene | All 3 sides different | All 3 angles different |
| Right | One angle = 90° | Pythagorean theorem: a²+b²=c² |
| Acute | All angles < 90° | Longest side² < sum of other two sides² |
| Obtuse | One angle > 90° | Longest side² > sum of other two sides² |
A triangle can belong to both a side-based and an angle-based category (e.g. right isosceles).
Tips for triangle calculations
Keep these principles in mind to avoid common triangle errors.
- Verify the triangle inequality — a valid triangle requires that any two sides sum to more than the third: a+b > c, a+c > b, b+c > a. If violated, no triangle exists.
- Use Heron's formula when height is unknown — if you know all three sides but not the height, Heron's formula gives exact area without needing to calculate height first.
- Remember the angle sum — interior angles always sum to 180°; use this to find a missing angle when two are known.
- Apply the Pythagorean theorem for right triangles — if one angle is exactly 90°, c² = a²+b² where c is the hypotenuse (the longest side, opposite the right angle).
- Scale area correctly — doubling all side lengths multiplies the area by 4, not 2. Area scales with the square of the linear scale factor.
Accuracy and limitations
Results are computed to standard double-precision floating-point accuracy (≈15 significant digits). Heron's formula can lose accuracy for very flat triangles (where one side is nearly equal to the sum of the other two) due to catastrophic cancellation; a numerically stable variant uses sorted sides. This calculator assumes Euclidean (flat) geometry. Spherical triangles — such as those on a globe — follow different rules where the angle sum exceeds 180°.
Key terms
About this calculator
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