🔺Triangle Calculator
Enter any 3 sides or angles to solve the rest — SSS, SAS, ASA, AAS, and the ambiguous SSA case are all handled automatically, with a scaled diagram and full working.
Free Triangle Calculator
Given any three sides or angles of a triangle, our free triangle calculator solves the rest instantly. Whether you have three sides (SSS), two sides and an included angle (SAS), two angles and a side (ASA or AAS), or the trickier two-sides-and-a-non-included-angle case (SSA), just enter what you know and get every missing side, angle, the area, and the perimeter — with a scaled diagram and full working shown.
The SSA case is famously ambiguous: depending on your numbers, there can be zero, one, or two valid triangles. Most calculators skip this — ours detects it automatically and shows both solutions when they exist, explaining exactly why.
Invalid inputs (sides that can't form a triangle, angles that don't sum correctly) are caught and explained clearly, not left as a broken result. No sign-up, no downloads — just enter your values and solve. See the About page or the FAQ for more.
Types of triangles (by side length)
Triangles are classified by their side lengths into three main types: equilateral, isosceles, and scalene.
- Equilateral triangle — all three sides are equal in length, and all three interior angles are equal, measuring 60° each. Example: a = b = c = 5, A = B = C = 60°.
- Isosceles triangle — exactly two sides are equal in length. The angles opposite the equal sides are also equal to each other. Example: a = b = 5, c = 8 gives A = B ≈ 36.9°.
- Scalene triangle — all three sides have different lengths, and all three interior angles have different measures. Example: a = 4, b = 5, c = 6.
Formula for a missing side given two sides
If you know two sides and the angle between them (SAS), the third side is found with the Law of Cosines:
c² = a² + b² − 2ab·cos(C)
where C is the angle included between sides a and b. If the triangle is a right triangle (C = 90°), this simplifies to the familiar Pythagorean theorem, since cos(90°) = 0:
c² = a² + b²
If instead you know two sides and a non-included angle (SSA), use the Law of Sines to find the missing angle first, then solve for the remaining side — this is the ambiguous case described above.
About the Triangle Calculator
Supported cases
SSS
Three sides known — solved via the Law of Cosines.
SAS
Two sides and the included angle — solved via the Law of Cosines.
ASA / AAS
Two angles and a side — solved via the Law of Sines.
SSA (ambiguous)
Two sides and a non-included angle — can yield 0, 1, or 2 valid triangles, all shown.
Ambiguous case handling
The SSA case is famous for producing zero, one, or two valid triangles depending on the numbers — the "swinging side" can meet the base at two different points. The calculator checks the sine value produced by the Law of Sines: if it exceeds 1, no triangle exists; if it equals 1, exactly one right-angled solution exists; otherwise both candidate angles are checked for validity and both are shown when valid.
Diagram and validation
A scaled SVG diagram is drawn from the solved side lengths and angles. Inputs that violate the triangle inequality (SSS) or produce an angle sum ≥ 180° (ASA/AAS) are rejected with a plain-English explanation rather than a silent wrong answer or NaN.
Types of triangles (by side length)
Triangles are classified by their side lengths into three main types: equilateral, isosceles, and scalene.
Equilateral
All three sides are equal in length, and all three interior angles are equal, measuring 60° each. Example: a = b = c = 5, A = B = C = 60°.
Isosceles
Exactly two sides are equal in length. The angles opposite the equal sides are also equal to each other. Example: a = b = 5, c = 8 gives A = B ≈ 36.9°.
Scalene
All three sides have different lengths, and all three interior angles have different measures. Example: a = 4, b = 5, c = 6.
Formula for a missing side given two sides
If you know two sides and the angle between them (SAS), the third side is found with the Law of Cosines:
c² = a² + b² − 2ab·cos(C)
where C is the angle included between sides a and b. If the triangle is a right triangle (C = 90°), this simplifies to the familiar Pythagorean theorem, since cos(90°) = 0:
c² = a² + b²
If instead you know two sides and a non-included angle (SSA), use the Law of Sines to find the missing angle first, then solve for the remaining side — this is the ambiguous case described above.
Frequently Asked Questions
How does the triangle calculator work?
Enter any 3 known sides/angles, pick the matching case, and it solves for the rest with steps shown.
What cases does it support?
SSS, SAS, ASA, AAS, and SSA (including the ambiguous case).
What is the SSA ambiguous case?
When you know two sides and a non-included angle, there can be 0, 1, or 2 valid triangles — the calculator detects and shows all valid solutions.
Does it show the steps?
Yes, full Law of Sines / Law of Cosines working with your actual numbers.
What if my triangle is invalid?
It's flagged clearly (e.g. sides that violate the triangle inequality), never a silent wrong answer.
Does it calculate area and perimeter?
Yes, both are shown alongside all sides and angles.
Can I use radians instead of degrees?
Yes, toggle between degrees and radians.
Is it free and unlimited?
Completely free, no sign-up or limits.
Is my data stored?
No, everything runs locally in your browser.
Does it work on mobile?
Yes, fully responsive including the diagram.