Triangle Calculator
Solve area, perimeter and angles from three valid sides, or find area from a base and perpendicular height.
Triangle area
Positive side lengths with strict triangle inequality for three-side mode. Angles use degrees. Base and height alone do not determine perimeter or angles. Floating-point resolution limits extremely near-degenerate triangles.
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How this calculator works
Three side lengths determine an ideal triangle only if every pair sums to more than the third. The tool applies a stable rearrangement of Heron’s formula for area and uses the corresponding cosine/area relationship to find angles opposite A, B and C. Base-and-height mode needs the perpendicular height, not a sloping side. It gives area only because many different triangles share the same base and height.
Formula
Perimeter = a+b+c; s = (a+b+c)/2; area = √(s(s−a)(s−b)(s−c)). Angle A follows cos(A) = (b²+c²−a²)/(2bc). Base-height area = base × perpendicular height/2.
Assumptions & limitations
Positive side lengths with strict triangle inequality for three-side mode. Angles use degrees. Base and height alone do not determine perimeter or angles. Floating-point resolution limits extremely near-degenerate triangles.
Worked example
Sides 3, 4 and 5 give perimeter 12 and area 6 square units. Opposite angles are approximately 36.869898°, 53.130102° and 90°. A separate base of 6 and perpendicular height 4 gives area 12 without determining the remaining sides.
Our approach to calculations ↗Common questions
Why are sides 1, 2 and 3 rejected?
They form a straight degenerate segment, not a triangle with positive area. The sum of any two sides must be greater than the third.
Can base and height determine the perimeter?
No. The location of the top vertex can change side lengths while keeping the same base and perpendicular height.
Which side matches angle A?
Angle A is opposite Side A. The same naming convention applies to B and C.