Triangle Calculator

What is the Triangle Calculator?

A triangle calculator figures out unknown sides, angles, area, and perimeter when you give it enough known values to work with. It handles all three main cases: knowing two sides and an angle (SAS), two angles and a side (AAS/ASA), or all three sides (SSS). Architects, surveyors, students in geometry or trigonometry, and anyone building something with angled parts finds it useful. CalciHub's version solves the triangle fully and displays all results in one place.

How Does It Work?

Three main formulas power the calculation:

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

Law of Cosines: c² = a² + b² − 2ab × cos(C)

Area: A = ½ × base × height

or A = ½ × a × b × sin(C)

a, b, c = the three sides

A, B, C = the three angles opposite to their respective sides

All angles in a triangle sum to 180°

How to Use CalciHub's Triangle Calculator

1. Enter the values you know, sides, angles, or a combination.

2. Leave the unknown fields blank.

3. Select degrees or radians for angle input.

4. Click Calculate.

5. The calculator fills in all missing values along with the area and perimeter.

Tip: You need at least three pieces of information to solve a triangle, and at least one of those must be a side length. Three angles alone do not give a unique triangle, there are infinitely many similar triangles with the same angles.

A Quick Example

A triangular plot of land has two sides of 8 meters and 10 meters, with an included angle of 60°.

Known: a = 8, b = 10, angle C = 60°

Using Law of Cosines:

c² = 8² + 10² − 2(8)(10)cos(60°)

= 64 + 100 − 160 × 0.5

= 164 − 80 = 84

c = √84 ≈ 9.17 meters

Area = ½ × 8 × 10 × sin(60°) = ½ × 80 × 0.866 ≈ 34.64 m²

The third side is about 9.17 meters and the plot covers roughly 34.6 square meters.

Frequently Asked Questions