🔺 Triangle Solver — SSS, SAS, ASA/AAS & Right Triangle

This triangle solver works out every missing angle, side, area, and perimeter of a triangle no matter which three measurements you start with. Choose SSS if you know all three sides, SAS if you know two sides and the angle between them, ASA/AAS if you know two angles and a side, or Right Triangle if you know two legs or a leg and the hypotenuse. Behind the scenes it applies the Law of Cosines, Law of Sines, Heron's formula, and the Pythagorean theorem automatically, and also classifies the result — scalene, isosceles, or equilateral by side length, and acute, right, or obtuse by angle — so you get the complete picture in one place.

What This Calculator Measures

For every mode, the solver finds the three interior angles, the three side lengths, the perimeter (their sum), and the area — using Heron's formula for SSS, the ½ab·sin(C) formula for SAS and ASA/AAS, and ½ × base × height for right triangles. It then classifies the triangle by comparing side lengths to each other and the largest angle to 90°.

Who Should Use This Calculator

Geometry, trigonometry, and precalculus students who want a single tool covering every triangle case, construction and roofing professionals working out rafter lengths and pitch angles, land surveyors solving triangular parcels, DIYers and hobbyists building triangular frames or supports, and anyone who has three triangle measurements — of any kind — and wants the full solution without picking which formula applies.

Why a General Triangle Solver Matters

Real triangles rarely arrive labeled with "use the Law of Cosines here." Knowing which of SSS, SAS, ASA/AAS, or a right-triangle shortcut applies to your specific set of known values — and then executing the correct formula without error — is exactly the kind of repetitive, mistake-prone task a single unified solver removes, while also adding the area, perimeter, and classification most standalone formula calculators skip.

Real-World Applications

Contractors compute rafter length and roof pitch angles from known rise, run, and slope measurements. Land surveyors solve triangular parcel boundaries from measured sides and angles. Engineers verify truss and gusset geometry across all four input cases in one tool. Students check geometry and trigonometry homework covering every triangle type. Hobbyists and makers design triangular braces, shelving brackets, and frames with confidence in the final dimensions.

Tips for Accurate Results

• Pick the tab that matches what you actually measured — mixing up SAS's "included" angle with a non-included one gives an incorrect result with no warning.
• In Right Triangle mode, double-check whether you're entering two legs or a leg and the hypotenuse — the hypotenuse is always the longest side, opposite the right angle.
• Use the classification result (e.g. "isosceles, right") as a quick sanity check — if it doesn't match your intuition about the shape, re-check your inputs.

Reading the results together: the two classifications (side-based and angle-based) are independent — a triangle can be, for example, isosceles and right, or scalene and obtuse, in any combination except that an equilateral triangle is always acute.

Typical ranges: all sides must be positive, all angles must fall strictly between 0° and 180° and sum to 180°, and area and perimeter must both be positive.

Manual verification: once you have all three sides and angles, recompute the area a second way (e.g. Heron's formula from the sides, or ½ab·sin(C) from two sides and an angle) — both should agree closely, confirming the solved triangle is internally consistent.

How do I know which side to label a, b, or c before entering my measurements?

Each mode's input labels are fixed, so you simply match your known values to the labeled fields on the active tab. In SSS mode enter your three side lengths into the a, b, and c boxes. In SAS mode enter the two sides you know as a and b and the angle between them as angle C. In ASA/AAS mode enter angle A, angle B, and side a (the side opposite angle A). The labels only name the measurements; swapping them just renames the angles in the result, so a labeling mix-up cannot change the solved triangle.

Why must the angle in SAS mode be the included angle between the two known sides?

The Law of Cosines, c = sqrt(a^2 + b^2 - 2ab*cos(C)), is only valid when C is the angle that sits directly between sides a and b. If you enter an angle that lies opposite one of the two sides instead, that is no longer the SAS case. It is the SSA configuration, which can be ambiguous, and it is handled by our dedicated Law of Sines Calculator rather than by this solver.

Which side of the solved triangle is opposite which angle?

By convention, side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C. This pairing gives you a built-in sanity check: in any triangle the longest side always faces the largest angle, so if the result lists side c as the longest, angle C should be the largest one as well.

Can I enter angles in degrees and radians, or only degrees?

Only degrees. Every angle field across the SSS, SAS, ASA/AAS, and Right Triangle tabs expects degrees, and all angle results are reported in degrees too. If your measurement is in radians, convert it first by multiplying by 180/pi; for example, pi/3 radians equals 60 degrees.

Why is the hypotenuse always the longest side of a right triangle?

The hypotenuse is the side opposite the 90 degree angle, and a larger angle always faces a longer side. Because the other two angles of a right triangle sum to 90 degrees, each is smaller than the single 90 degree angle, so the hypotenuse has to be longer than both legs. This is also why Leg + Hypotenuse mode rejects an input where the hypotenuse is not strictly longer than the given leg.

Why does the solver reject my input when the two ASA angles add up to 180 degrees or more?

Every triangle's three angles must sum to exactly 180 degrees. If angle A plus angle B already equals or exceeds 180 degrees, no room is left for a positive third angle, so no triangle can exist. The solver returns a clear error for this case instead of producing an impossible result.