Triangle Calculator

Step 1: Fill any 3 of the 6 fields (sides a, b, c and angles A, B, C). At least one field must be a side — angles alone don't fix the triangle's size.

Step 2: Switch the angle unit to radians if you want to enter values like `pi/2` or `pi/4`. Degrees is the default.

Step 3: Click Calculate. The calculator auto-detects which case applies (SSS, SAS, ASA, AAS, or SSA) and returns area, perimeter, all sides, all angles, and the triangle's type.

A triangle is a three-sided polygon with three angles that always sum to 180 degrees. Triangles are classified by their sides (equilateral, isosceles, scalene) and by their angles (acute, right, obtuse).

Triangles are the simplest polygon and the most rigid — they cannot be deformed without changing side lengths. This makes them essential in structural engineering: bridges, roof trusses, and geodesic domes rely on triangular shapes for stability.

Knowing any three independent measurements (three sides, or two sides and an angle, etc.) fully determines a triangle.

Base-height area: A = ½ × base × height

Heron's formula (three sides):
s = (a + b + c) / 2
A = √[s(s−a)(s−b)(s−c)]

Law of cosines (angle opposite side a):
cos(A) = (b² + c² − a²) / (2bc)

Example: Sides 5, 6, 7
s = 9
Area = √[9 × 4 × 3 × 2] = √216 ≈ 14.697

Example 1: Sides 3, 4, 5 → area 6, perimeter 12, type Scalene Right (classic Pythagorean triple).

Example 2: Sides 6, 6, 6 → area 15.588, perimeter 18, type Equilateral (all angles 60°).

Example 3: Base 10 and height 4 → area 20 (base-height mode).

Triangle inequality: Each side must be less than the sum of the other two.

Heron's formula works for any triangle when you know three sides.

Angles always sum to 180° — useful check.

Equilateral = all angles 60°. Quickest to spot.