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)
—
Angles (A, B, C)
—
Area
—
Perimeter
—
Copied!
Saved to favorites
Your favorites are on the home page under “Your favorites.” They are saved only in this browser on this device, so they will not appear on another device or browser. No account, no server.
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
References
- Triangle (area formulas)Wikipedia · en.wikipedia.org
- Heron's formula (area from three sides)Wikipedia · en.wikipedia.org
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.
Embed this calculator
Add this free calculator to your own site. Copy the snippet — it works anywhere you can paste HTML, and stays in sync with this page.