Triangle Calculator
Solve triangle dimensions and properties from given inputs
📐
Triangle Calculator
Enter at least three values including at least one side. The calculator solves remaining sides and angles, and computes area, perimeter, heights, medians, inradius, and circumradius.
🧮 Provide Known Values
📊 Result
Sides
a-
b-
c-
Angles
∠A-
∠B-
∠C-
Perimeter & Area
Perimeter p-
Semiperimeter s-
Area-
Other
Heights (hₐ, h_b, h_c)-
Medians (mₐ, m_b, m_c)-
Inradius r-
Circumradius R-
📚 Triangle facts, theorems, and laws
- It is not possible for a triangle to have more than one vertex with internal angle greater than or equal to 90°, or it would no longer be a triangle.
- The interior angles of a triangle always add up to 180°. An exterior angle equals the sum of the two non-adjacent interior angles.
- The sum of the lengths of any two sides is always greater than the length of the third side.
- Pythagorean theorem (right triangles): a² + b² = c².
- Law of sines: a/sin(A) = b/sin(B) = c/sin(C).
- Law of cosines: a² = b² + c² − 2bc·cos(A) (and cyclic permutations).
Area of a Triangle
- Base-height: area = 1/2 · b · h
- Two sides with included angle: area = 1/2 · a · b · sin(C)
- Heron's formula: area = √(s(s − a)(s − b)(s − c)), where s = (a + b + c)/2
Inradius and Circumradius
- Inradius: r = area / s
- Circumradius: R = a / (2·sin(A)) = b / (2·sin(B)) = c / (2·sin(C))