Triangle Calculator

What Is a Triangle?

A triangle is the simplest polygon: three straight sides and three angles. Triangles are classified by their sides — equilateral (all three sides equal), isosceles (two sides equal), scalene (no sides equal) — and by their angles — acute (all angles under 90°), right (one 90° angle), obtuse (one angle over 90°). A triangle calculator solves the rest of a triangle's measurements — missing sides, angles, area, and perimeter — from the few values you know.

One fact governs everything about triangles: the three interior angles always add up to exactly 180°. Know two angles, and the third is simply 180° minus their sum.

How Triangle Math Works

Area formulas

The most common area formula uses base and height:

Area = ½ × base × height

The height must be perpendicular to the base. If you know all three sides instead, Heron's formula works without any height: first compute the semi-perimeter s = (a + b + c) / 2, then Area = √(s(s−a)(s−b)(s−c)).

The Pythagorean theorem

In a right triangle, the side opposite the right angle is the hypotenuse (the longest side). The theorem states:

a² + b² = c²

where c is the hypotenuse. This lets you find any side from the other two: for legs 3 and 4, c = √(9 + 16) = √25 = 5.

Solving a triangle

"Solving" a triangle means finding all unknown sides and angles. You need at least three pieces of information, including at least one side — the standard cases are SSS (three sides), SAS (two sides and the included angle), ASA/AAS (two angles and a side), and SSA (ambiguous — it can yield zero, one, or two solutions). The calculator applies the law of sines (a/sin A = b/sin B = c/sin C) and the law of cosines (c² = a² + b² − 2ab·cos C) behind the scenes.

How to Use This Calculator

1. Enter the sides and/or angles you know (at least three values, including one side).
2. The calculator fills in every missing side and angle automatically.
3. Read off the area and perimeter from the results panel.

Worked Example

Solve the famous 3–4–5 right triangle (legs 3 and 4, right angle between them):

1. Hypotenuse: c = √(3² + 4²) = √(9 + 16) = √25 = 5.
2. Area: ½ × 3 × 4 = 6 square units.
3. Perimeter: 3 + 4 + 5 = 12 units.
4. Angles: one is 90°; the others are arcsin(3/5) ≈ 36.87° and arcsin(4/5) ≈ 53.13°. Check: 90 + 36.87 + 53.13 = 180°. ✓

Tips

• The height in the area formula must be perpendicular to the chosen base — using a slanted side as "height" is the most common error.
• Any two sides of a triangle must add up to more than the third side (the triangle inequality). If your inputs violate this, no triangle exists.
• Keep angle units consistent: this calculator works in degrees, so convert radians first if needed (degrees = radians × 180/π).
• For the SSA case, be aware there can be two valid triangles — check both solutions before using the result.