Triangle Calculator
SSS - Three Sides
SAS - Two Sides, Included Angle
ASA - Two Angles, Included Side
AAS - Two Angles, Non-Included Side
Live Triangle
How to Use This Calculator
Select the input mode that matches what you know about your triangle: SSS if you have all three sides, SAS if you have two sides and the angle between them, ASA or AAS if you have two angles and a side. Enter your values and press Calculate. The tool finds all missing sides, angles, area, and perimeter.
Triangle Basics
A triangle has three sides (a, b, c) and three angles (A, B, C). The angle A is opposite side a, angle B is opposite side b, and angle C is opposite side c. This labelling is used by convention in every triangle formula.
One fact is always true for every triangle: the three angles add up to exactly 180 degrees. If you know two angles, the third is always 180 minus the sum of the other two. This is a quick way to check your inputs.
The Input Modes Explained
| Mode | Stands For | What You Provide |
|---|---|---|
| SSS | Side-Side-Side | All three side lengths |
| SAS | Side-Angle-Side | Two sides and the angle between them |
| ASA | Angle-Side-Angle | Two angles and the side between them |
| AAS | Angle-Angle-Side | Two angles and a side not between them |
Key Formulas Used
Law of Sines: a / sin(A) = b / sin(B) = c / sin(C). Use this when you have two angles and a side.
Law of Cosines: c^2 = a^2 + b^2 - 2ab x cos(C). Use this when you have three sides or two sides and the included angle.
Area: Area = 0.5 x a x b x sin(C). This works for any triangle, not just right triangles.
Types of Triangles
- Equilateral: All three sides equal. All angles are exactly 60 degrees.
- Isosceles: Two sides equal. The two base angles are equal.
- Scalene: All sides different. All angles different.
- Right: One angle is exactly 90 degrees. The Pythagorean theorem applies.
- Obtuse: One angle is greater than 90 degrees.
Common Mistakes to Avoid
- Entering angles that do not add up to 180. The calculator will catch this, but double-check your values first.
- Using degrees when the formula expects radians, or vice versa. This tool uses degrees, which matches most school problems.
- Violating the triangle inequality: any side must be shorter than the sum of the other two sides.
- Confusing the included angle with a non-included angle when choosing SAS or AAS mode.