Triangle Calculator

Solve triangle problems step by step. Enter three side lengths to compute area, perimeter, angles, and other geometric properties. Ideal for students learning trigonometry and geometry.

Side A

Side B

Side C

Result

Please check your inputs.

📖 How to Use This Tool

Enter the lengths of all three sides (a, b, c) in the input fields. Make sure they are positive numbers and satisfy the triangle inequality (each side less than the sum of the other two).

Click the 'Calculate' button to process your triangle data.

View the detailed results including area, perimeter, all three interior angles, and other properties like inradius and circumradius.

Follow the step-by-step breakdown showing how each value was computed (e.g., semiperimeter, Heron’s formula, Law of Cosines).

Use the results to check your homework, verify geometry problems, or explore relationships between side lengths and angles.

📝 What Is Triangle Calculator?

A Triangle Calculator is an interactive online tool that solves any triangle when you input its three side lengths. It instantly calculates the area, perimeter, all interior angles, and additional geometric properties like the inradius, circumradius, and altitude lengths. This transforms complex trigonometry and geometry problems into clear, step-by-step solutions.

For students learning trigonometry and geometry, this tool removes tedious manual calculations and reduces errors. Instead of spending time on arithmetic, you can focus on understanding why the formulas work. It also helps you verify your own work, experiment with different side lengths, and see how changing one side affects the entire triangle.

Whether you are studying for an exam, completing homework, or just curious about triangle properties, the Triangle Calculator provides an immediate, visual, and educational aid. It turns abstract formulas into concrete results, making learning more engaging and effective.

🧮 Formula

This tool primarily uses two key formulas:

1. **Heron’s Formula for Area:** Area = √[ s × (s – a) × (s – b) × (s – c) ] where s = (a + b + c) / 2 (the semiperimeter), and a, b, c are the side lengths. 2. **Law of Cosines for Angles:** For angle C opposite side c: cos(C) = (a² + b² – c²) / (2ab). Similarly, angles A and B are found by rotating the sides. The area formula comes first from the semiperimeter. Then each angle is computed using the Law of Cosines. All intermediate steps are shown so you can follow the logic.

💡 Tips for Best Results

✨📐 Always check the triangle inequality before calculating: the sum of any two sides must be greater than the third. Otherwise no triangle exists.

✨🧮 Use the tool to double-check your homework step by step – it shows the work so you can learn from your mistakes.

✨🔍 Experiment with special triangles like 3‑4‑5 or 5‑12‑13 to build confidence in the calculator and understand patterns.

✨📝 Pay attention to the units: keep all side lengths in the same unit (e.g., cm) to get correct area and perimeter values.

❓ Frequently Asked Questions

Can I enter any three numbers as side lengths?

No. The three numbers must satisfy the triangle inequality: the sum of any two sides must be greater than the third. If they don't, the tool will show an error message because a real triangle cannot have those lengths.

What happens if I input an invalid side (e.g., zero or negative)?

The calculator requires positive numbers. If you enter zero or a negative value, it will display a warning and ask you to correct the input. Always use lengths greater than zero.

Does the calculator show angles in degrees or radians?

By default, the angles are displayed in degrees. If you need radians, you can convert manually (multiply degrees by π/180). Some versions of the tool may offer a toggle between the two units.