SSS Triangle Calculator

Created by Anna Szczepanek, PhD
Reviewed by Davide Borchia
Last updated: Aug 30, 2022

No matter if you're interested in solving SSS triangles or rather want to learn about the congruence of SSS triangles, this SSS triangle calculator is the perfect place to start! We'll discuss:

  • how to solve a SSS triangle, that is, how to determine the three internal angles of the triangle; and
  • how to compute the area of an SSS triangle.

With Omni's SSS triangle solver you'll become a sssuper triangle expert!

How do I solve SSS triangles?

SSS means we know all three sides of a triangle. To solve an SSS triangle:

  1. Apply the law of cosines to sides a and b to determine the angle between these sides:
    γ = acos((a² + b² − c²)/(2ab))
  2. Apply again the law of cosines to a and c to determine the angle β.
  3. Compute the remaining angle as α = 180° - β - γ .
  4. If you wish to determine the area, compute Area = ½ ab sin γ or use the Heron formula: Area=√(s(s - a)(s - b)(s - c)), where s = (a + b + c)/2.

Triangle with sides and angles

🙋 Computing acos may be non-obvious, you'll need to use trigonometric resources or specialized software. Or, which is the best choice, use Omni's SSS triangle solver!

How to use this SSS triangle calculator?

Using our SSS triangle calculator is pretty straightforward! Just enter the data you have (the lengths of the three sides of your triangle), and the results will appear immediately! For your convenience, the area and perimeter also get calculated by default.

Are SSS triangles congruent?

Yes! If all three sides of one triangle have their lengths equal to the lengths of the corresponding three sides of another triangle, then these two triangles are congruent by the SSS triangle congruence criterion.

Omni's triangle resources

Do you have some other data than the three side lengths? You may need one of the other triangle criterions, like, for instance, SAS, AAA, AAS! We've covered all of them (and more!):

FAQ

What is the formula for an SSS triangle area?

The quickest formula for the area of a triangle with sides a, b, and c is the Heron's formula:
Area=√(s(s-a)(s-b)(s-c)), where s is the semi-perimeter of the triangle; that is one-half of its perimeter: s = ½(a+b+c).

How do I calculate a SSS triangle with sides 2 3 4?

  1. Apply the law of cosines to sides 2 and 3 to determine the angle between these sides:
    γ = acos((2² + 3² - 4²)/(2 × 2 × 3)) =104.48°
  2. Apply the law of cosines again to sides a and c to determine the angle β between theses sides.
    β = acos((2² + 4² - 3²)/(2 × 2 × 4)) =46.57°
  3. Compute the remaining angle α as α = 180° - 104.48° - 46.57° = 28.95°.
Anna Szczepanek, PhD
Triangle area: triangle with base and height





a
cm
b
cm
c
cm
Results
α
deg
β
deg
γ
deg
Area
cm²
Perimeter
cm
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