📐Law of Sines Calculator
Solve oblique triangles using a/sin A = b/sin B = c/sin C, including full handling of the SSA ambiguous case.
Free Law of Sines Calculator
Solve oblique triangles instantly with our free Law of Sines Calculator, using the relationship a/sin A = b/sin B = c/sin C. It handles ASA, AAS, and the trickier SSA case, computing every missing side and angle with full step-by-step working shown.
The SSA case is famous for producing zero, one, or two valid triangles depending on your numbers — this calculator detects which situation applies automatically, and when two triangles are possible, shows both solutions clearly labelled, along with an explanation of why. Impossible SSA inputs are flagged with a plain-English reason rather than a broken calculation.
Area and perimeter are computed for each valid solution, and a scaled diagram accompanies the result. No sign-up, no downloads. See the About page or the FAQ for more.
About the Law of Sines Calculator
Features
ASA / AAS / SSA modes
Switch input mode to match the data you have, with only the relevant fields shown.
Ambiguous-case detection
Automatically determines 0, 1, or 2 valid triangles for SSA using the height test.
Step-by-step working
Every unknown is derived from the Law of Sines ratio with your actual numbers shown.
Area, perimeter & diagram
Each valid solution includes its area, perimeter, and a to-scale triangle diagram.
Frequently Asked Questions
What is the Law of Sines?
A relationship in any triangle: a/sin A = b/sin B = c/sin C, used to solve for unknown sides and angles.
What data do I need?
ASA, AAS, or SSA (two sides and a non-included angle) — pick the mode matching what you know.
What is the ambiguous case?
In SSA, depending on the numbers, there can be 0, 1, or 2 valid triangles; this calculator detects and shows all valid solutions.
Why does it show two answers sometimes?
Because your SSA inputs allow two different triangles — both are shown labelled Triangle 1 and Triangle 2.
What if there's no valid triangle?
The calculator explains clearly why (e.g. the side given is too short), rather than showing an error.
Does it show the steps?
Yes, the Law of Sines setup and algebra are shown with your actual numbers.
Does it calculate area?
Yes, for each valid solution.
Can I switch between degrees and radians?
Yes, a toggle updates all values.
Is it free?
Completely free, no sign-up or limits.
Does it work on mobile?
Yes, fully responsive.