Free Triangle Calculator Online
Solve any triangle by entering the sides and angles you know. This free triangle calculator handles SSS, SAS, ASA, AAS, and SSA configurations and returns all missing measurements plus the area and perimeter.
Enter all three sides to solve the triangle.
Triangle Solved
Obtuse Scalene triangle
How the Triangle Calculator Works
Every triangle has six measurements: three sides (a, b, c) and three angles (A, B, C). You only need three of these (with at least one side) to solve the entire triangle. The triangle calculator identifies which configuration you've provided and applies the right formulas automatically.
Law of Cosines
c² = a² + b² - 2ab·cos(C)
Used for SSS (finding angles from three known sides) and SAS (finding the third side when you know two sides and the included angle). This is a generalization of the Pythagorean theorem — when C = 90°, it simplifies to c² = a² + b².
Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
Used for AAS and ASA configurations. Once you know one side-angle pair, you can find any other side or angle. Watch for the ambiguous case (SSA) where two valid triangles may exist.
Supported Input Combinations
Related Math Tools
Why Use This Free Triangle Calculator?
- Handles all 5 input configurations
- Shows area and perimeter
- Step-by-step solutions
- Detects ambiguous SSA cases
- Always free, no sign-up
What People Use a Triangle Calculator For
Construction & DIY
Building a roof? Framing a wall? You need to know rafter lengths and pitch angles. A triangle calculator turns a roof span of 24 feet and a pitch of 35° into an exact rafter length of 14.65 feet. Measure once, calculate once, cut once.
Surveying & Navigation
Triangulation is how surveyors measure distances without walking them. By measuring one baseline and two angles, you can compute all other distances with the Law of Sines. GPS satellites use the same principle in three dimensions.
Homework & Exams
Trigonometry homework goes faster when you can check your answers. Enter your known values, solve by hand, then verify with the triangle calculator. Seeing the step-by-step breakdown helps you understand where you went wrong.
Triangle Calculator Tips
Getting accurate results from any triangle calculator starts with entering the right data. Here are practical tips.
Check the Triangle Inequality
The sum of any two sides must be greater than the third side. If a = 3, b = 4, and c = 10, no triangle exists because 3 + 4 = 7 < 10. The triangle calculator validates this before solving.
Angles Must Sum to 180°
If you enter two angles that already add up to 180° or more, the third angle would be zero or negative — that's not a valid triangle. Keep your angle inputs below 180° combined.
Watch for the Ambiguous Case
SSA (two sides and an angle not between them) can produce two different triangles. For instance, a = 10, b = 6, A = 30° gives two solutions. Always check whether both make sense for your problem.
Frequently Asked Questions
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