Triangle calculator for SSS, SAS and ASA/AAS
Choose the measurements you know and enter their values. HitEquals solves every side and angle, then reports area, perimeter, semiperimeter and triangle type.
Inputs used by this calculator
Triangle Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Known measurements | Three sides — SSS | Three sides — SSS · Two sides and included angle C — SAS · Angles A and B plus side c — ASA/AAS | Chooses which Triangle Calculator method or unknown the engine evaluates. |
| Side a | 3 | 0.000001 to 1000000000 | Supplies the side a quantity used by the published equation or result breakdown. |
| Side b | 4 | 0.000001 to 1000000000 | Supplies the side b quantity used by the published equation or result breakdown. |
| Side c | 5 | 0.000001 to 1000000000 | Supplies the side c quantity used by the published equation or result breakdown. |
| Angle A (degrees) | 50 | 0.000001 to 179.999999 | Supplies the angle a (degrees) quantity used by the published equation or result breakdown. |
| Angle B (degrees) | 60 | 0.000001 to 179.999999 | Supplies the angle b (degrees) quantity used by the published equation or result breakdown. |
| Included angle C (degrees) | 90 | 0.000001 to 179.999999 | Supplies the included angle c (degrees) quantity used by the published equation or result breakdown. |
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 are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.