Complete guide
Triangle calculator for SSS, SAS and ASA/AAS
Choose the measurements you know and enter their values. Calculator24 solves every side and angle, then reports area, perimeter, semiperimeter and triangle type.
Which triangle case to choose
Use SSS for three sides, SAS for two sides surrounding the known angle C, and ASA/AAS when angles A and B plus opposite side c are known.
Triangle formulas
The law of cosines generalizes the Pythagorean theorem, while the law of sines links each side with its opposite angle.
c²=a²+b²−2ab cos Ca/sin A=b/sin B=c/sin Carea=√[s(s−a)(s−b)(s−c)]Worked 3-4-5 example
The semiperimeter is 6. Heron's formula gives √(6×3×2×1)=6, and the largest angle opposite side 5 is 90 degrees.
Triangle inequality
For SSS, every pair of sides must sum to more than the remaining side. Equality would produce a flat, zero-area shape rather than a triangle.
Angle totals and classification
Interior angles total 180 degrees. The result labels an equilateral, isosceles or scalene side pattern and an acute, right or obtuse angle pattern.
Precision and measurement
Rounded construction or survey measurements can shift the solved angles. Keep appropriate significant digits and confirm critical work with the required professional method.
Supported cases
| Case | Known | Primary method |
|---|---|---|
| SSS | a, b, c | Cosines + Heron |
| SAS | a, b, C | Law of cosines |
| ASA/AAS | A, B, c | Angle sum + law of sines |
Frequently asked questions
Do triangle angles always total 180 degrees?
Yes, for a Euclidean plane triangle.
What is the triangle inequality?
Any two side lengths must add to more than the third.
Can SAS have two answers?
No. Two sides and their included angle define one triangle.
What does Heron's formula calculate?
It calculates area from the three side lengths.
Can I enter different length units?
Use one consistent unit for every side.
Why might a nearly flat triangle fail?
Rounding can make its sides violate the strict triangle inequality.
What to keep in mind
Measurements must define one nondegenerate triangle. Results inherit the precision of the entered measurements.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.