Triangle Calculator
Free triangle calculator: solve any triangle from SSS, SAS or ASA inputs. Get missing sides, angles, area, perimeter and height instantly online.
About the Triangle Calculator
This free triangle calculator solves a complete triangle from three known measurements: three sides (SSS), two sides with the included angle (SAS), or two angles with the side between them (ASA). It returns every missing side and angle plus the area, perimeter and the height on side c — flagging impossible inputs like sides that violate the triangle inequality.
The math combines three classic results: the law of cosines c² = a² + b² − 2ab·cos C, the law of sines a/sin A = b/sin B = c/sin C, and Heron's formula Area = √(s(s−a)(s−b)(s−c)) where s is half the perimeter. Geometry students, land surveyors measuring irregular plots and engineers laying out trusses all use these routinely.
How to Use the Triangle Calculator
- 1Pick the solving mode: SSS (three sides), SAS (two sides + included angle) or ASA (two angles + the side between them).
- 2Enter the three known values — angles in degrees.
- 3Read the remaining sides, angles, area, perimeter and height instantly.
Frequently Asked Questions
How do I find the area of a triangle from three sides?
Use Heron's formula. For sides 5, 6 and 7: s = (5+6+7)/2 = 9, then Area = √(9 × 4 × 3 × 2) = √216 ≈ 14.70. The calculator also derives the angles — here 44.42°, 57.12° and 78.46° — via the law of cosines.
How does the SAS mode work?
With sides a = 8, b = 6 and included angle C = 60°, the law of cosines gives c = √(64 + 36 − 2×8×6×0.5) = √52 ≈ 7.21. The remaining angles follow from the law of cosines again, and area = ½ab·sin C = ½ × 8 × 6 × 0.866 ≈ 20.78.
Why does the calculator say my sides do not form a triangle?
Every pair of sides must sum to more than the third (the triangle inequality). Sides 2, 3 and 7 fail because 2 + 3 = 5 < 7 — the two short sides cannot reach each other. Similarly, in ASA mode the two angles must total less than 180°.
What is the difference between SSS, SAS, ASA and AAS?
They name which measurements you know, in order around the triangle: SSS is three sides, SAS two sides with the angle between them, ASA two angles with the side between them. AAS (two angles and a non-included side) can be converted to ASA since the third angle is 180° minus the other two.
Can I solve a triangle from three angles only?
No — angles fix only the shape, not the size. Triangles with angles 30°, 60°, 90° can have any scale, so at least one side length is required. That is why every mode here includes at least one side.