Solve any triangle using SSS, SAS, ASA, AAS, and SSA methods. Calculate sides, angles, area, perimeter, heights, medians, and more
A triangle is a three-sided polygon with three vertices and three angles. The sum of all interior angles in a triangle always equals 180° (or π radians). Triangles can be classified by their sides (equilateral, isosceles, scalene) or by their angles (acute, right, obtuse). Our triangle calculator can solve any triangle when you provide at least three measurements: three sides (SSS), two sides and the included angle (SAS), two angles and one side (ASA or AAS), or two sides and a non-included angle (SSA - ambiguous case).
In our triangle calculator, we use standard notation where sides and angles are related as follows:
The sum of angles A + B + C is always 180° (or π radians).
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Every triangle has three medians, which intersect at a single point called the centroid.
The centroid divides each median in the ratio 2:1, with the longer segment near the vertex.
The inradius (r) is the radius of the inscribed circle (incircle), which is the largest circle that will fit inside the triangle.
The center of the incircle is called the incenter, where the angle bisectors meet.
The circumradius (R) is the radius of the circumscribed circle (circumcircle), which passes through all three vertices of the triangle.
The center of the circumcircle is called the circumcenter, where the perpendicular bisectors of the sides meet.
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides and angles. This law is particularly useful for solving triangles when you know two angles and one side (ASA or AAS) or two sides and a non-included angle (SSA).
The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is useful for solving triangles when you know three sides (SSS) or two sides and the included angle (SAS). This law is a generalization of the Pythagorean theorem.
Heron's formula allows you to calculate the area of a triangle when you know all three sides. First calculate the semiperimeter s = (a + b + c)/2, then use the formula below. This is one of the most elegant formulas in geometry.
These examples show how our triangle calculator can handle:
You can adapt any real-life situation involving triangles to one of these patterns and let the calculator do the work for you.