Triangle Calculator
Calculate area, perimeter, angles, and type of any triangle using three sides (SSS) or base and height. Free online geometry calculator with instant results.
About This Calculator
Our triangle calculator is a versatile geometry tool that computes the area, perimeter, interior angles, and classification of any triangle. You can input measurements using either the three sides (SSS) method with Heron's formula or the base and height method for quick area calculations. This calculator is ideal for students studying geometry, teachers preparing lesson materials, architects and engineers performing structural calculations, and anyone who needs to solve triangle problems quickly and accurately.
How It Works
For the SSS (three sides) method, the calculator uses Heron's formula: A = √(s(s-a)(s-b)(s-c)) where s is the semi-perimeter. Interior angles are computed using the Law of Cosines: cos(A) = (b² + c² - a²)/(2bc). The triangle is validated using the triangle inequality theorem, which requires that the sum of any two sides exceeds the third. For the base and height method, the calculator applies the standard formula A = ½ × base × height.
Once calculated, the tool classifies the triangle by both its side lengths (equilateral, isosceles, scalene) and its angles (acute, right, obtuse). Results include the area, perimeter, all three interior angles in degrees, and the full triangle classification.
Frequently Asked Questions
How do you find the area of a triangle using Heron's formula?
Heron's formula calculates triangle area from three side lengths: A = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2 is the semi-perimeter and a, b, c are the three sides. This formula works for any triangle, not just right triangles.
How do you classify triangles by angles?
Triangles are classified by their largest interior angle: acute triangles have all angles less than 90°, right triangles have one angle exactly 90°, and obtuse triangles have one angle greater than 90°. The sum of all three interior angles always equals 180°.
What is the triangle inequality theorem?
The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side. For sides a, b, and c: a + b > c, a + c > b, and b + c > a. If any of these conditions fails, the three side lengths cannot form a valid triangle.
How do you find angles from side lengths using the Law of Cosines?
The Law of Cosines finds angles from side lengths: cos(A) = (b² + c² - a²)/(2bc), cos(B) = (a² + c² - b²)/(2ac), cos(C) = (a² + b² - c²)/(2ab). Take the arccos of each result to get the angle in degrees.
Can you calculate triangle area from base and height?
Yes, the simplest formula is A = ½ × base × height. The base can be any side of the triangle, and the height is the perpendicular distance from the base to the opposite vertex. This formula works for all triangle types.
How do you calculate triangle perimeter?
Triangle perimeter is the sum of all three side lengths: P = a + b + c. Simply add the lengths of all three sides together to get the total distance around the triangle.
What is the difference between equilateral, isosceles, and scalene triangles?
Equilateral triangles have all three sides equal and all angles 60°. Isosceles triangles have two equal sides and two equal base angles. Scalene triangles have all three sides of different lengths and all three angles different.
Do I need units when using the triangle calculator?
The triangle calculator works with any consistent unit system. If you enter side lengths in centimeters, the area will be in square centimeters and perimeter in centimeters. Use the same unit for all inputs to get correct results.