Triangle Calculator
Calculate the sides, angles, area, and perimeter of a triangle.
Understanding Triangle Calculator
The Triangle Calculator calculates the area, perimeter, semi-perimeter, and interior angles of a triangle when all three side lengths are known. It also determines the type of triangle based on its sides and angles and verifies that the three entered lengths can form a valid triangle.
When all three sides are known, the area can be calculated using Heron's formula. The interior angles can be determined using the Law of Cosines, while the perimeter is obtained by adding the three side lengths together.
How to get a useful estimate
Triangle Calculator is intended to show the mathematical relationship behind the answer, not just return a number. Enter the quantities requested by the selected method—such as Side A, Side B, Side C—and keep their units or mathematical meaning consistent. Where this calculator offers different shapes, methods, or forms, choose the one that matches the problem before entering the values.
Reading the number correctly
For a useful check, look at the units and the scale of the answer before accepting it. A formula can be evaluated correctly while an input is still inappropriate for the problem. Repeating the calculation with a simple test value or checking the result against the expected direction of change can help identify an input mistake.
Triangle Calculator
The Triangle Calculator calculates the area, perimeter, semi-perimeter, and interior angles of a triangle when all three side lengths are known. It also determines the type of triangle based on its sides and angles and verifies that the three entered lengths can form a valid triangle.
When all three sides are known, the area can be calculated using Heron's formula. The interior angles can be determined using the Law of Cosines, while the perimeter is obtained by adding the three side lengths together.
Triangle Area
When the three sides of a triangle are known, Heron's formula provides a direct way to calculate its area. First, calculate the semi-perimeter, then substitute it into the area formula.
Here, a, b, and c are the three side lengths and s is the semi-perimeter.
Triangle Perimeter
The perimeter is the total length around the triangle. It is found by adding all three sides.
The perimeter uses the same unit as the side lengths. For example, if the sides are measured in meters, the perimeter is measured in meters. The area, however, is expressed in square meters.
Triangle Inequality
Not every three positive numbers can form a triangle. For three side lengths to create a valid triangle, the sum of any two sides must be greater than the third side.
a + c > b
b + c > a
The calculator checks these conditions before performing the remaining calculations. If any condition is not satisfied, the three lengths cannot form a valid triangle.
Triangle Classification by Sides
Triangles can be classified according to whether their side lengths are equal or different.
Isosceles: Two sides are equal.
Scalene: All three sides are different.
Triangle Classification by Angles
A triangle can also be classified according to the sizes of its interior angles.
Right: One angle is exactly 90°.
Obtuse: One angle is greater than 90°.
The three interior angles of every triangle always add up to 180°.
Finding the Angles
When all three side lengths are known, the Law of Cosines can be used to calculate the interior angles. For example, the angle opposite side a can be calculated using:
Similar formulas can be used to calculate angles B and C. The calculator converts the resulting angles from radians to degrees.
Example
Consider a triangle with side lengths of 3, 4, and 5 units.
The semi-perimeter is:
Applying Heron's formula:
Area = √36
Area = 6 square units
Because the sides satisfy the Pythagorean relationship 3² + 4² = 5², this is a right triangle.
How to Use the Calculator
Enter the lengths of sides A, B, and C. The calculator first checks whether the three values can form a valid triangle. If they are valid, it calculates the area, perimeter, semi-perimeter, and three interior angles.
The result also identifies the triangle by its side type and angle type, and shows the formulas and calculation steps used to obtain the measurements.
Understanding the Units
The calculator does not assume a specific unit. If the side lengths are entered in centimeters, the perimeter is in centimeters and the area is in square centimeters. If the sides are in feet, the perimeter is in feet and the area is in square feet.
Disclaimer
This calculator is intended for informational purposes only. While we strive for accuracy, we cannot guarantee that every result is correct for every situation.