Triangle Calculator

To calculate the area of a triangle when you know all three side lengths, use Heron's formula. First, calculate the semi-perimeter (s) by adding all three sides and dividing by 2: s = (a+b+c)/2. Then apply the formula: Area = √[s(s-a)(s-b)(s-c)]. This method works for any triangle type - scalene, isosceles, or equilateral. Our calculator does this automatically when you enter the three sides.

Heron's formula is a mathematical method to calculate the area of a triangle when you know the lengths of all three sides (SSS method). The formula is: Area = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter. It's particularly useful when you don't know the triangle's height or any angles. Named after Hero of Alexandria, this formula has been used since ancient times and is perfect for side-side-side triangle calculations.

The calculator uses the Law of Cosines to find each angle. For angle A opposite side a, the formula is: cos(A) = (b²+c²-a²)/(2bc). This process is repeated for all three angles. The Law of Cosines relates the sides of a triangle to the cosine of one of its angles, making it perfect for SSS triangle calculations. Once we have the cosine value, we use the inverse cosine function to get the angle in degrees.

Yes! The calculator automatically classifies your triangle by comparing side lengths: Equilateral (all three sides equal), Isosceles (exactly two sides equal), or Scalene (no sides equal). It also classifies by angles: Acute (all angles < 90°), Right (one angle = 90°), or Obtuse (one angle > 90°). This gives you a complete understanding of your triangle's properties.

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side. This must be true for all three combinations: a+b>c, a+c>b, and b+c>a. Our calculator validates this before performing calculations to ensure the side lengths can form a valid triangle. If this condition isn't met, the sides cannot form a triangle.

Absolutely! This SSS triangle calculator works for all triangle types, including right triangles. It will calculate the area, perimeter, and all three angles. If your triangle is a right triangle, the calculator will identify it by detecting a 90-degree angle. For right triangles, you can verify the results using the Pythagorean theorem (a²+b²=c²).

You can use any unit of measurement (cm, meters, inches, feet, miles, etc.) as long as all three sides use the same unit. The calculator will return area in square units and perimeter in the same unit you input. For example, if you enter sides in centimeters, you'll get perimeter in cm and area in cm². Always ensure consistency in your units for accurate results.

If you see an error, your side lengths likely violate the triangle inequality theorem. Check that: (1) All sides are positive numbers greater than zero, (2) The sum of any two sides is greater than the third side, and (3) No single side is longer than or equal to the sum of the other two sides. Also ensure you've entered valid numeric values in all three fields.