Math Calculators

Triangle Calculator

Provide any 3 values including at least one side to solve a triangle. Returns missing sides and angles, type, area, perimeter, heights, medians, inradius, circumradius, and vertex coordinates.

When radians are selected as the angle unit, it can take values such as pi/2, pi/4, etc.

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Angle Unit:

About the triangle calculator

A triangle is uniquely determined by any three pieces of information that include at least one side. The classic input combinations are SSS (three sides), SAS (two sides and the included angle), ASA and AAS (a side and two angles), and SSA (two sides and a non-included angle, which can be ambiguous).

This calculator accepts any of the six values — three sides a, b, c and three opposite angles A, B, C — in any combination that totals three values with at least one side. It uses the Law of Cosines, the Law of Sines, and the angle sum (A + B + C = 180°) to recover every missing value.

It then reports a full description of the triangle: its type (equilateral, isosceles, scalene, right, acute, or obtuse), area, perimeter, semiperimeter, the three heights and three medians, the inradius (radius of the inscribed circle) and circumradius (radius of the circumscribed circle), and the coordinates of the vertices, centroid, incenter, and circumcenter.

Angles can be entered in degrees or in radians. In radian mode you can type fractions of π such as pi/2, pi/3, or 2pi/5, and they are evaluated exactly.

How to use

  • Fill in any three of the six fields (sides a, b, c and angles A, B, C), with at least one side.
  • Select degree or radian for angles. In radian mode you can use pi/2, pi/3, etc.
  • Press Calculate to see the full solution, type classification, and a scaled diagram.

Key formulas

Law of Cosines: a² = b² + c² − 2bc·cos(A). Law of Sines: a/sin(A) = b/sin(B) = c/sin(C) = 2R. Area = (1/2)·b·c·sin(A). Heron: Area = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2. Inradius r = Area/s. Heights: h_a = 2·Area/a. Medians: m_a = ½√(2b² + 2c² − a²).

FAQ

Why do I need at least one side?

Three angles alone determine only the shape, not the size, of a triangle — infinitely many similar triangles share the same angles.

What is the ambiguous case (SSA)?

When you know two sides and the angle opposite one of them, there may be zero, one, or two valid triangles depending on the values. This tool returns the principal solution.

How is the circumcenter located?

It is equidistant from all three vertices and lies at the intersection of the perpendicular bisectors of the sides.

What is the incenter?

The incenter is the intersection of the three angle bisectors and is the center of the inscribed circle (radius r = Area/s).