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Triangle Solver (SSS / SAS / ASA)

Select the known combination (three sides, two sides plus the included angle, or two angles plus the included side) and this tool will compute the remaining.

Need step-by-step derivations or ambiguous SSA handling? Use the advanced triangle solver.

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Known values

Used in SSS and SAS; for SAS it is one of the sides adjacent to angle C.

In SAS this is the other side adjacent to angle C.

Used in SSS and as the included side between angles A and B in ASA.

First known angle for the ASA mode.

Second known angle for the ASA mode.

SAS uses the included angle between sides a and b.

Enter your known values and click “Solve triangle” to see the computed sides, angles, area, and radii here.

FAQ

Which input combinations are supported?

You can pick SSS, SAS, or ASA. Ambiguous SSA cases are intentionally excluded to keep the output deterministic.

How do you compute the area and radii?

Once all three sides are known, the solver uses Heron’s formula for the area, then derives the circumradius with R = abc / (4S) and the inradius with r = S / s.

Do you validate impossible triangles?

Yes. The calculator checks the triangle inequality and the 180° interior-angle sum before showing any results.

What should I enter first?

Start with the minimum required inputs shown above the calculate button, then keep optional settings at their defaults for a first pass. After getting a baseline, change one parameter at a time so you can explain which assumption moved the output.

How precise are the results?

The calculator keeps internal precision and rounds only for display. Small differences can still appear if another tool uses different constants, period conventions, or rounding rules. Align assumptions before comparing final values.

How to use Triangle Calculator effectively

What this page is for

Use this page to solve triangle sides, angles, area, and related values from a valid set of inputs. Start by identifying which side-angle combination you have.

Input checks

Keep angle units and side units consistent. Ambiguous SSA cases, impossible angle sums, and inconsistent side lengths need validation before interpretation.

Workflow

A practical sequence is to solve the triangle, check whether a second solution exists, and then use area or perimeter values only after the geometry is valid.

Common mistakes

Avoid entering rounded intermediate values from another tool when exact inputs are available. Rounding can create small but confusing angle-sum differences.

How to read the result

Interpret the solution type first. If the page reports ambiguity or invalid geometry, the numeric-looking outputs are not a stable basis for downstream work.