Triangle Calculator

Every side, angle and the area — from three sides or two and an angle.

Area
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Sides a, b, c
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Angles A, B, C
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Perimeter
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Type
Drawn to scale
How this works
Pythagoras c² = a² + b² (right triangles only) Law of cosines c² = a² + b² − 2ab·cos(C) (any triangle) Heron's area s = (a+b+c)/2, A = √(s(s−a)(s−b)(s−c)) Area from SAS A = ½·a·b·sin(C)
GivenUse
Three sidesLaw of cosines for angles, Heron for area
Two sides and the angle betweenLaw of cosines for the third side
Two legs of a right trianglePythagoras
Any two of a right trianglePythagoras, rearranged
  • Three sides only form a triangle if each pair adds to more than the third — the triangle inequality.
  • The angles always total 180°.
  • 3-4-5 is the smallest whole-number right triangle, which is why builders use it to square a corner.
How do I find the hypotenuse?

Square both shorter sides, add them, take the square root. For legs of 3 and 4: √(9 + 16) = 5.

How do I find the area without the height?

With all three sides use Heron's formula. With two sides and the angle between them, the area is ½·a·b·sin(C).

Why does it say my sides cannot form a triangle?

Because two of them together are shorter than the third — sides of 1, 2 and 10 can never meet. Each pair must add to more than the remaining side.

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