Triangle Calculator — Sides, Angles, Area, Perimeter

Enter any three values (with at least one side). Private by design — runs locally in your browser.

Diagram & Inputs

Tip: Any three values with ≥1 side. Standard convention: side a is opposite angle A, etc.

Results

How the Triangle Calculator Works

This tool uses fundamental geometric principles to solve for missing values of a triangle. A triangle is fully defined by three of its properties, as long as at least one of them is a side. The calculator can handle several scenarios:

  • SSS (Side-Side-Side): If all three sides are known, the angles can be found using the Law of Cosines.
  • SAS (Side-Angle-Side): If two sides and the included angle are known, the third side can be found with the Law of Cosines, and the other angles with the Law of Sines.
  • ASA (Angle-Side-Angle): If two angles and the included side are known, the third angle is found by subtracting the other two from 180°, and the remaining sides are found with the Law of Sines.
  • AAS (Angle-Angle-Side): Similar to ASA, if two angles and a non-included side are known, the third angle is found first, and then the Law of Sines is used to find the other sides.
  • SSA (Side-Side-Angle): The "ambiguous case" is when two sides and a non-included angle are known. The calculator will determine if there is one solution, two solutions, or no solution and display the results accordingly.

All calculations are performed entirely in your browser using JavaScript, ensuring your inputs remain private and secure.

Formulas Used

  • Law of Cosines: a² = b² + c² − 2bc·cos(A) (and cyclic permutations)
  • Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
  • Heron’s Area (SSS): s = (a+b+c)/2, Area = √(s(s−a)(s−b)(s−c))
  • Angle sum: A + B + C = 180°

5 Fun Facts about Triangles

One point to rule them

Only an equilateral triangle makes all four classical centers (centroid, incenter, circumcenter, orthocenter) coincide—any tilt pushes them apart.

Perfect symmetry

Altitudes can wander

In an obtuse triangle, the altitude from the obtuse vertex lands outside the shape; you still get area from 1/2 · base · height using that off-board drop.

Hidden height

SSA can double your answers

Two sides and a non-included angle may describe two valid triangles—a tall one and a squat mirror—until the would-be height exceeds the long side and no solution exists.

Ambiguous case

Shortest network hides at 120°

The Fermat point of an acute triangle joins to all three vertices with 120° angles and minimizes the total length of those three connectors—like a stealthy hub for cables.

Fermat point

Curved worlds bend the rules

On a sphere, triangle angles add to more than 180°; in hyperbolic space they add to less. Our calculator sticks to flat (Euclidean) geometry.

Beyond flat planes

Triangle Calculator: FAQs

Which inputs are valid to solve a triangle?

Any three values with at least one side (SSS, SAS, ASA, AAS, or SSA). Pure angles only are insufficient.

What is the SSA ambiguous case?

With two sides and a non-included angle, geometry may permit two distinct triangles, a single triangle, or none. The tool reports all valid solutions.

Does the calculator keep my data private?

Yes. Computation is entirely client-side; nothing is uploaded.

How is the area computed?

For SSS we use Heron’s formula. If you know two sides and the included angle, area can also be found by Area = ½ab·sin(C).

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