Triangle Calculator
Solve any triangle — enter any combination of sides and angles and get all missing values, area, and perimeter.
Law of Cosines (SSS/SAS): a² = b² + c² − 2bc×cos(A). Law of Sines (AAS/ASA): a/sin(A) = b/sin(B) = c/sin(C). Area = ½ab×sin(C). Angles in any triangle sum to 180°.
Triangle Geometry by Curriculum
| Curriculum | Coverage | Key formulas tested |
|---|---|---|
| 🇺🇸 US SAT/ACT | Right triangles only (mostly) | Pythagorean theorem, SOHCAHTOA |
| 🇺🇸 US AP Calc/Pre-Calc | All triangle types | Sine rule, cosine rule, area = ½ab sin C |
| 🇬🇧 UK GCSE | All triangle types | Sine rule, cosine rule, area formula |
| 🇬🇧 UK A-Level Further Maths | Proof-level coverage | Deriving sine/cosine rules, applications |
| 🌍 IB Mathematics | All triangle types | Sine rule, cosine rule, ambiguous case |
| 🇯🇵 Japan (高校数学II) | All triangle types | 正弦定理/余弦定理 (same formulas) |
| 🇩🇪 Germany (Gymnasium) | All triangle types | Sinussatz, Kosinussatz |
| 🇮🇳 India (CBSE/ISC) | All triangle types | Sine and cosine formulas |
Frequently Asked Questions
What is the Law of Sines?
a/sin(A) = b/sin(B) = c/sin(C), where a, b, c are side lengths and A, B, C are the opposite angles. Use it when you know two angles and one side (AAS/ASA).
What is the Law of Cosines?
a² = b² + c² − 2bc·cos(A). It generalises the Pythagorean theorem. Use it when you know 3 sides (SSS) or 2 sides and the included angle (SAS).
What is the ambiguous case (SSA)?
When you know 2 sides and a non-included angle, there can be 0, 1, or 2 valid triangles. This is the ambiguous case. This calculator handles SSS, SAS, and AAS which are all unambiguous.
What are the triangle inequality conditions?
For a valid triangle: a + b > c, a + c > b, and b + c > a. The calculator checks this automatically and shows an error if the values cannot form a triangle.
Related Calculators
Cite this page APA · MLA · BibTeX
APA
WorldCalculators.org. (n.d.). Triangle Calculator — Solve Any Triangle (SSS, SAS, AAS). https://worldcalculators.org/calculators/triangle/
MLA
“Triangle Calculator — Solve Any Triangle (SSS, SAS, AAS).” WorldCalculators.org, worldcalculators.org/calculators/triangle/.
BibTeX
@misc{worldcalculatorscalculatorstriangle,
title = {Triangle Calculator — Solve Any Triangle (SSS, SAS, AAS)},
author = {{WorldCalculators.org}},
year = {n.d.},
howpublished = {\url{https://worldcalculators.org/calculators/triangle/}}
} Figures change when tax years or guidance change. Cite the date shown and link the page so readers see the current version.