△ Triangle Calculator
Solve for all sides, angles, area, and perimeter of a triangle from three known measurements (SSS, SAS, or ASA).
Known Values
Result
How Triangle Solving Works
Depending on which three measurements you know, this calculator uses the Law of Cosines, Law of Sines, and Heron's Formula to solve for the remaining sides and angles.
Formulas
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Heron's Formula: Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2
SAS Area: Area = ½ab·sin(C)
Worked Example
The calculator loads in SSS mode with sides a = 3, b = 4, c = 5 — a classic right triangle. Using the Law of Cosines, the angles come out to A ≈ 36.87°, B ≈ 53.13°, and C = 90° (confirming it's a right angle, since 3-4-5 satisfies the Pythagorean theorem). Using Heron's Formula with s = (3+4+5)/2 = 6, the area is √[6(6−3)(6−4)(6−5)] = √36 = 6, and the perimeter is 3 + 4 + 5 = 12.
Frequently Asked Questions
What is the triangle inequality?
For three side lengths to form a valid triangle, the sum of any two sides must be greater than the third side. If this fails, no triangle exists.
Do the three angles of a triangle always add up to 180°?
Yes, in Euclidean geometry the interior angles of any triangle always sum to exactly 180 degrees.
Which mode should I use?
Use SSS if you know all three sides, SAS if you know two sides and the angle between them, or ASA if you know two angles and the side between them.