Triangle Calculator

What Is a Triangle Calculator?

A Triangle Calculator is an online geometry tool for solving a triangle from known side lengths and angles. A triangle has three sides and three interior angles, and when sufficient independent measurements are known, the remaining dimensions can be calculated mathematically.

This calculator is useful for students, teachers, engineers, designers, builders and anyone working with triangle measurements. It can calculate missing sides and angles as well as the triangle's total perimeter and area.

Why Use Triangle Calculator?

The Triangle Calculator brings several common triangle calculations together in one tool, allowing you to enter the measurements you already know and obtain the remaining values without performing the trigonometry manually.

How to Use Triangle Calculator

Enter the measurements you know and leave the remaining fields empty. The calculator determines whether the supplied information is sufficient to solve a unique triangle.

1. Enter the known measurements — Enter the available side lengths and angles in the corresponding fields.
2. Check your units — Use the same unit for every side, while entering angles in degrees.
3. Calculate the triangle — Select Calculate Triangle to solve the missing measurements.
4. Review the results — View all three sides, all three angles, the perimeter, area and calculated triangle type.

How to Calculate the Sides and Angles of a Triangle

Triangle calculations depend on which measurements are known. The calculator uses standard geometric and trigonometric relationships to determine the missing values. For three known sides, the Law of Cosines can be used to calculate the angles. For two known sides and an included angle, the Law of Cosines can first determine the third side.

When two angles and one side are known, the third angle can be found because the interior angles of every triangle add up to 180 degrees. The Law of Sines can then be used to determine the remaining sides. These relationships allow a triangle to be solved without manually rearranging complex trigonometric equations.

Triangle Area Formula

Once the three side lengths are known, the area can be calculated using Heron's formula. First calculate the semiperimeter using s = (a + b + c) / 2. The area is then √[s(s − a)(s − b)(s − c)]. This approach is particularly useful when all three side lengths are available.

Triangle Perimeter Formula

The perimeter of a triangle is the total distance around its outside. It is calculated by adding the three side lengths together: P = a + b + c. The three sides must use the same unit for the result to be meaningful.

Triangle Calculator Accuracy and Limitations

The calculator uses JavaScript's mathematical functions and standard trigonometric formulas to produce numerical results. Results are rounded for display, while calculations use the underlying numerical precision available in the browser.

A triangle must satisfy the triangle inequality: the sum of any two side lengths must be greater than the third side. Its three interior angles must also be greater than zero and add to 180 degrees. If the supplied measurements do not describe a valid or uniquely solvable triangle, the calculator displays an error rather than producing an invalid result.

Frequently Asked Questions