Triangle Calculator
A triangle with sides 3, 4 and 5 has an area of 6, a perimeter of 12 and a right angle of 90 degrees.
How to use
- Choose what you know: three sides (SSS), two sides and the angle between them (SAS), or two angles and the side between them (ASA).
- Enter the three values. The labels show which side or angle each box means.
- Read all three sides, all three angles, the area, the perimeter and whether the triangle is equilateral, isosceles or scalene, and right, acute or obtuse.
How it works
Side a is opposite angle A, side b opposite B and side c opposite C. Angles are in degrees.
SSS: the angles come from the law of cosines, cos A = (b² + c² − a²) ÷ 2bc. The three sides must satisfy the triangle inequality: any two sides add up to more than the third.
SAS: the missing side is c = √(a² + b² − 2ab cos C), then the other angles follow.
ASA: the third angle is 180° minus the other two. The sides follow from the law of sines, a ÷ sin A = b ÷ sin B = c ÷ sin C.
Area = ½ × a × b × sin C, which gives the same result as Heron's formula.
FAQ
Why does it say the sides cannot form a triangle?
Two sides must together be longer than the third. Sides 1, 2 and 3 fail because 1 + 2 is not more than 3: they would lie flat on one line.
What does SAS mean?
Side, angle, side. You know two sides and the angle between them. In the tool, enter side a, then the angle C between a and b, then side b.
Why are two angles alone not enough?
Two angles fix the shape but not the size. Add one side, ideally the one between them, to get a single triangle. That is the ASA mode.
How do I tell if a triangle is right-angled?
Check whether the largest angle is 90°. The result line says right, acute or obtuse. For sides, a² + b² = c² means a right angle at C.