Triangle Calculator
Calculate all sides, angles, heights, inradius, circumradius and area of any triangle.
Enter at least 3 values including at least one side — the rest is calculated instantly.
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cm
cm
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cm
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Area
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Perimeter
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Height ha
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Height hb
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Height hc
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Inradius r
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Circumradius R
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Types of Triangles
Classified by sides
Equilateral
3 equal sides · all angles 60°
Isosceles
2 equal sides · 2 equal base angles
Scalene
All 3 sides different · all 3 angles different
Classified by angles
Acute
All 3 angles are less than 90°
Right
One angle equals exactly 90°
Obtuse
One angle is greater than 90°
Frequently Asked Questions
Several methods exist. With two sides and their included angle: Area = ½ × a × b × sin(C). With three sides (Heron's formula): Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2 is the semi-perimeter. For a right triangle, Area = ½ × base × height, since the two legs are perpendicular. This calculator uses the half-product formula automatically once the triangle is fully solved.
The law of cosines generalises the Pythagorean theorem to any triangle: a² = b² + c² − 2bc·cos(A). It lets you find a missing side when two sides and the included angle are known (SAS), or any angle when all three sides are known (SSS). When A = 90°, cos(A) = 0 and it reduces to a² = b² + c².
The law of sines states: a/sin(A) = b/sin(B) = c/sin(C). The ratio of each side to the sine of its opposite angle is constant across the triangle. It is used when two angles and one side are known (AAS or ASA). The ambiguous case (SSA — two sides and a non-included angle) may yield zero, one, or two valid triangles.
The triangle inequality states that the sum of any two sides must be strictly greater than the third side: a + b > c, a + c > b, b + c > a. If this condition fails, the three lengths cannot form a closed triangle. Equivalently, each side must be strictly between the absolute difference and the sum of the other two.
You need at least three independent values including at least one side. Valid combinations: SSS (three sides), SAS (two sides + included angle), ASA (two angles + the side between them), AAS (two angles + any one side). Three angles alone (AAA) only determine the shape, not the size. The ambiguous SSA case may have 0, 1, or 2 solutions.