Triangle calculator
A triangle is fully determined by any three values — three sides (SSS), two angles and a side (AAS/ASA), or two sides and an angle (SAS/SSA). Enter three known values and this.
Enter any 3 known values (sides and/or angles). Angles in degrees.
Need at least 3 known values to solve.
Sides (a, b, c)
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Angles (A, B, C)
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Area
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Perimeter
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Formulas
Law of cosines (SSS/SAS):
c² = a² + b² − 2ab cos(C)
Law of sines (AAS/ASA):
a / sin(A) = b / sin(B) = c / sin(C)
Area (Heron’s formula):
s = (a + b + c) / 2
Area = √(s(s−a)(s−b)(s−c))
Example
3-4-5 right triangle (SSS):
- Angles: A ≈ 36.87°, B ≈ 53.13°, C = 90°
- Area = 6, Perimeter = 12
Frequently asked
What combinations can this calculator solve?
SSS (three sides), AAS/ASA (two angles + one side), SAS (two sides + included angle), and SSA (two sides + opposite angle). It cannot solve with fewer than three known values.
What is the law of cosines?
c² = a² + b² − 2ab cos(C). Used when three sides are known (SSS) or two sides and an angle are known (SAS).
What is the law of sines?
a/sin(A) = b/sin(B) = c/sin(C). Used with AAS, ASA, or SSA combinations.
Why does SSA sometimes have no solution?
SSA can be ambiguous: depending on the given values, there may be no triangle, one triangle, or two valid triangles. This calculator returns the first (acute-angle) solution.
How do I share my calculation?
Click "Share with my numbers" to copy a URL with your inputs.