Solve any triangle — SSS, SAS, ASA or AAS — with all sides, angles, area and perimeter.
Three sides. They must satisfy the triangle inequality: each side shorter than the sum of the other two.
Area
TriangleHow to use this tool
Pick the mode that matches what you know — SSS, SAS, ASA or AAS. The three input labels change to match, so you always know which value goes where.
Enter the three values. For SSS, check the triangle inequality: each side must be shorter than the sum of the other two, or no triangle exists.
Every side, every angle, area, perimeter, type (acute, right or obtuse; equilateral, isosceles or scalene) and the inradius and circumradius are all shown.
A 30-60-90 triangle (sides 1 : √3 : 2) and a 45-45-90 triangle (legs equal, hypotenuse = leg × √2) are flagged automatically when your triangle matches.
Formula & worked example
Worked example (SSS): sides 3, 4 and 5 give angles 36.87°, 53.13° and 90°, area 6 (Heron: semiperimeter 6, √(6×3×2×1) = 6) and perimeter 12. The same triangle entered as SAS — sides 3 and 4 with a 90° angle between them — returns the identical result, hypotenuse 5. A 30-60-90 example: sides 1, √3 (≈1.732) and 2 give angles 30°, 60° and 90° and area ≈0.866.
Limitations — read this before you rely on it
Three angles alone (AAA) cannot determine a triangle's size — only its shape — so that mode is not offered; add at least one side. Very flat triangles (one side almost equal to the sum of the other two) are extremely sensitive to rounding, so treat the last decimal with caution. All angles are in degrees, and areas assume all sides share the same unit.
Frequently asked questions
A triangle calculator solves a triangle from the values you know: SSS (three sides), SAS (two sides and the angle between them), ASA (two angles and the side between them) or AAS (two angles and a side opposite one of them). This general triangle calculator returns every side, every angle, area and perimeter.
Use SSS when you know all three sides, SAS when you know two sides and the angle between them, ASA when you know two angles and the side between them, and AAS when you know two angles and the side opposite one of them. Any three values that include at least one side will do — three angles alone cannot fix the size.
Yes, provided the sides satisfy the triangle inequality: each side must be shorter than the sum of the other two. Sides 1, 2 and 10 fail (1 + 2 is not greater than 10), so no triangle exists and the calculator says so instead of inventing angles.
A 30-60-90 triangle has angles 30°, 60° and 90°, and its sides are always in the ratio 1 : √3 : 2 (short leg : long leg : hypotenuse). So if the short leg is 5, the long leg is 5√3 ≈ 8.66 and the hypotenuse is 10. This calculator flags a 30-60-90 triangle automatically.
An acute triangle has all angles under 90°, a right triangle has exactly one 90° angle, and an obtuse triangle has one angle over 90°. By sides: equilateral (all equal), isosceles (two equal) and scalene (all different).