△ Triangle Calculator
Calculate sides, angles, area, and perimeter of any triangle using SSS, SAS, or right triangle methods.
Triangle Type
Leave one side blank to calculate it, or enter all three to verify.
Area
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Perimeter
0
Side a
0
Side b
0
Side c
0
Angle A
0°
Angle B
0°
Angle C
0°
Type
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Triangle Formulas
Pythagorean Theorem: a² + b² = c² (right triangles)
Law of Cosines: c² = a² + b² − 2ab·cos(C)
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Area (SSS): √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2 (Heron's formula)
Area (SAS): ½·a·b·sin(C)
Law of Cosines: c² = a² + b² − 2ab·cos(C)
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Area (SSS): √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2 (Heron's formula)
Area (SAS): ½·a·b·sin(C)
Triangle Classifications
- By sides: Equilateral (all equal), Isosceles (two equal), Scalene (all different)
- By angles: Acute (all <90°), Right (one =90°), Obtuse (one >90°)
When does a triangle not exist? +
A valid triangle requires: (1) All sides must be positive. (2) Triangle inequality: each side must be less than the sum of the other two. (3) All angles must be positive and sum to 180°. If any condition fails, no triangle is possible with those measurements.