Triangle Calculator

Solve any triangle — SSS, SAS, AAS, ASA — with all sides, angles, area, and height.

Known values

Side a

Side b

Side c

Results

Side a

Side b

Side c

Angle A

36.8699°

Angle B

53.1301°

Angle C

90°

Area

Perimeter

Height (to c)

2.4

Solving triangles: SSS, SAS, AAS, ASA

This solver handles all four triangle configurations using the Law of Cosines (for SSS and SAS) and the Law of Sines(for AAS and ASA). Given any valid combination of known sides and angles it calculates the remaining unknowns, the area (via Heron's formula), the perimeter, and the height to side c.

For circle geometry, see the Circle Calculator. For unit conversion of the results, use the Area Converter.

Built and maintained by Meet Shah · Last updated 28 July 2026

What this tool is used for

Solving a triangle from a named case such as SSS or SAS.
Finding area and perimeter alongside the missing values.
Working out a height for a construction problem.
Identifying which named case (SSS, SAS, AAS, ASA) your known values form.
Confirming that the given values determine a unique triangle.

Frequently Asked Questions

What do SSS, SAS, AAS and ASA mean?: They name which three measurements you know. SSS is three sides, SAS is two sides with the angle BETWEEN them, ASA is two angles with the side between them, and AAS is two angles with a side not between them. Each is a congruence condition — enough to fix exactly one triangle.
Why is there no SSA option?: Because SSA does not determine a triangle. Two sides and a non-included angle can describe two valid triangles, one, or none — the ambiguous case. Offering it would mean silently picking one answer, so the tool covers only the four configurations with a unique solution.
Which formula does each mode use?: SSS and SAS use the Law of Cosines (c² = a² + b² − 2ab·cos C), which reduces to Pythagoras when C is 90° because cos 90° = 0. AAS and ASA use the Law of Sines, a/sin A = b/sin B, after deriving the third angle from the 180° sum. All four then re-solve as SSS so every output comes from one code path.
Why does it refuse some perfectly reasonable-looking sides?: The triangle inequality: each side must be shorter than the other two combined. 3, 4, 8 fails because 3 + 4 < 8 — those lengths cannot close into a triangle, and the Law of Cosines would ask for the arc-cosine of a number outside [−1, 1]. The check runs before the trigonometry, so you get a refusal rather than NaN.
How are area and height computed?: Area comes from Heron's formula, √(s(s−a)(s−b)(s−c)) with s the semi-perimeter, which needs no angle at all. The height reported is the one dropped onto side c, recovered from the area as 2 × area / c — so it is the altitude to that specific side, not the triangle's longest or shortest.

Common errors and gotchas

Hitting the ambiguous SSA case, which can describe two valid triangles.
Supplying sides that violate the triangle inequality, which describe no triangle.
Mixing degrees and radians, which produces a plausible but wrong triangle.
Assuming angles sum to 180 outside plane geometry.
Choosing the law of sines where the law of cosines is numerically better, or the reverse.