A walkthrough, end to end.
- 1
Enter three values: 3 sides (SSS), 2 sides + included angle (SAS), 2 angles + 1 side (ASA / AAS).
- 2
The calculator uses the law of cosines and the law of sines to solve for the rest.
- 3
Result includes all three sides, all three angles, area, and perimeter.
Law of Cosines + Law of Sines
Law of cosines: c² = a² + b² − 2ab·cos(C). Used when SSS or SAS. Law of sines: a/sin(A) = b/sin(B) = c/sin(C). Used after one angle is known to find the others. Area: ½ab·sin(C) when two sides and included angle known.
What you can do with this.
SSS — three sides known
Sides 5, 7, 9. Use law of cosines to find each angle: cos(A) = (b²+c²−a²)/(2bc). The calculator does all three angles automatically.
SAS — two sides + angle between
Sides a=8, b=6, included angle C=45°. Third side c = √(8² + 6² − 2·8·6·cos 45°) = ~5.7. Then law of sines for remaining angles.
ASA — two angles + side between
Angles A=50°, B=60°, side c=10 (between them). Third angle = 180−50−60 = 70°. Then law of sines: a = c·sin(A)/sin(C).
Triangle area
Always computed as part of the result. Heron's formula for SSS: A = √(s(s−a)(s−b)(s−c)) where s = perimeter/2. SAS: A = ½ab·sin(C). The calculator handles both.
Right triangle special case
Right triangle: one angle is 90°. SSS solver still works. Pythagorean theorem (a² + b² = c²) is the special case for SSS where C=90°. See the Pythagorean and Right Triangle calculators for that exact case.
Surveyor / land measurement
Triangle solving is the foundation of triangulation. Surveyors measure 2 sides and one angle (or 1 side and 2 angles) to find unknowns — exactly what this calculator does.
Carpentry / construction
Roof rafters, truss design — all triangle math. Knowing rise + run + pitch lets you compute exact rafter length via the same triangle solver.
Triangle calculator 2026 — what's current
AR / smartphone apps measure angles via camera + sensors. For computed solving from known measurements, the calculator is fastest and exact.
Frequently asked.
Acronyms for which inputs you have. SSS: 3 sides. SAS: 2 sides + angle between them. ASA: 2 angles + side between. AAS: 2 angles + side not between. Each is solvable; SSA is ambiguous (can have 0, 1, or 2 valid triangles).
Triangle inequality: each side must be less than the sum of the other two. If you enter invalid combinations, the calculator returns an error.
Degrees for angles. Sides are unit-agnostic — keep all sides in the same unit.
No. Calculations run entirely in your browser.