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How to use
This general triangle solver handles SSS, SAS, ASA/AAS and the ambiguous SSA case. It selects the appropriate sine/cosine relationships and area formulas, and it returns two solutions when the supplied SSA measurements genuinely permit two different triangles.
- Choose the input case that matches what you know.
- Enter positive side lengths and angles in degrees in the requested fields.
- Calculate; the solver validates the geometry before returning results.
- For SSA, check whether one or two solutions are shown because that data pattern can be ambiguous.
How it is calculated
Example
In SSS mode, sides 5, 6 and 7 give perimeter 18 and area about 14.6969. The same inputs also determine all three angles, the inradius and the circumradius.
Important notes
Lengths are unit-neutral: use one consistent length unit and the area is in that unit squared. Degenerate and extremely near-degenerate cases are rejected when floating-point precision would make the result unreliable. Mihsaba’s Pythagorean calculator remains the focused tool for right triangles; this page solves general triangles.
Worked examples and interpreting results
A triangle with side lengths 3, 4 and 5 has perimeter 12 and area 6. Heron’s formula finds its area from the three sides without requiring a separate height input.
| Case | Calculation | Result |
|---|---|---|
| Perimeter | 3 + 4 + 5 | 12 |
| Semiperimeter | 12 ÷ 2 | 6 |
| Area using Heron’s formula | √(6 × (6−3) × (6−4) × (6−5)) | 6 |
How to check the result
The sum of any two sides must exceed the third. Sides 1, 2 and 3 do not form a triangle with positive area. In the three-side mode, each input is a side length rather than an angle.
Frequently asked questions
Why can SSA return two answers?
An angle and two non-included sides can correspond to two different angles with the same sine, producing two valid triangles in some cases.
Are three angles enough?
No. Three angles determine shape but not scale, so at least one side length is required.
What is the difference between SSS and SAS?
SSS means all three sides are known; SAS means two sides and the included angle are known.