Triangles are one of the most fundamental shapes in geometry, appearing everywhere from mathematics and architecture to engineering and design. Understanding the properties of a triangle—such as its angles, sides, perimeter, and area—is essential for students, teachers, architects, and professionals across many fields.

Triangle Side & Angle Calculator

Side A:

Side B:

Side C:

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Easily calculate triangle angles, area, and perimeter with our Triangle Calculator. Quick, accurate, and simple to use online tool.

Triangle Side & Angle Calculator – Find Angles, Area & Perimeter Instantly

Introduction

Instead of manually applying formulas like the law of cosines or Heron’s formula, you can now quickly solve triangle-related problems using our Triangle Side & Angle Calculator. This powerful online tool instantly computes:

All three angles (A, B, C)
The perimeter of the triangle
The area of the triangle

With just three side lengths, the calculator gives accurate results in seconds, saving you time and effort.

How the Triangle Calculator Works

The Triangle Side & Angle Calculator works by applying well-known mathematical principles:

Law of Cosines – Used to calculate the angles of the triangle when all three sides are known.
- Formula: cos⁡(A)=b2+c2−a22bc\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}cos(A)=2bcb2+c2−a2 (and similarly for angles B and C).
Perimeter – Simply the sum of all three sides.
- Formula: P=a+b+cP = a + b + cP=a+b+c
Area (Heron’s Formula) – Uses the semi-perimeter (half of the perimeter) to calculate area.
- Formula: A=s(s−a)(s−b)(s−c)A = \sqrt{s(s-a)(s-b)(s-c)}A=s(s−a)(s−b)(s−c) where s=a+b+c2s = \frac{a+b+c}{2}s=2a+b+c.

These calculations are performed instantly in the background when you enter the triangle’s side lengths and click the Calculate button.

How to Use the Triangle Side & Angle Calculator

Using the calculator is simple and intuitive:

Enter the side lengths
- Input values for Side A, Side B, and Side C in the respective fields.
- Make sure the values are positive numbers greater than zero.
Click "Calculate"
- The tool will process your input using trigonometric formulas.
View Results
- The calculator displays:
  - Angle A, Angle B, Angle C (in degrees)
  - Perimeter (sum of all sides)
  - Area (calculated with Heron’s formula)
Reset if needed
- Use the Reset button to clear inputs and start a new calculation.

Example of Triangle Calculation

Example 1:

Suppose you have a triangle with side lengths:

Side A = 5 units
Side B = 7 units
Side C = 10 units

Step 1: Perimeter P=5+7+10=22P = 5 + 7 + 10 = 22P=5+7+10=22

Step 2: Semi-perimeter (s) s=222=11s = \frac{22}{2} = 11s=222=11

Step 3: Area (Heron’s Formula) A=11(11−5)(11−7)(11−10)=11×6×4×1=264≈16.25A = \sqrt{11(11-5)(11-7)(11-10)} = \sqrt{11 \times 6 \times 4 \times 1} = \sqrt{264} \approx 16.25A=11(11−5)(11−7)(11−10)=11×6×4×1=264≈16.25

Step 4: Angles (Law of Cosines)

Angle A ≈ 28.96°
Angle B ≈ 44.42°
Angle C ≈ 106.62°

The calculator will instantly provide these results without manual computation.

Benefits of Using the Triangle Calculator

Accuracy – Avoids mistakes that often occur during manual calculations.
Speed – Get results in seconds instead of spending time solving equations.
Convenience – No need to memorize complex formulas.
Educational Use – Great for students learning geometry and trigonometry.
Professional Applications – Helpful in construction, surveying, and design.

Applications of Triangle Calculations

Education – Assisting students with homework and learning geometry.
Engineering & Architecture – Calculating angles and dimensions in design.
Surveying & Navigation – Determining distances and directions.
Art & Design – Ensuring proportional accuracy in patterns and structures.

20 Frequently Asked Questions (FAQs)

Q1: What is a triangle calculator?
A triangle calculator is an online tool that computes triangle angles, perimeter, and area based on given side lengths.

Q2: Which formulas does this calculator use?
It uses the law of cosines for angles and Heron’s formula for area.

Q3: Do I need all three sides to use this calculator?
Yes, this tool requires all three sides to calculate angles, area, and perimeter.

Q4: Can I use decimals instead of whole numbers?
Yes, the calculator accepts both integers and decimal values.

Q5: What happens if the sides don’t form a valid triangle?
The calculator alerts you if the given sides violate the triangle inequality rule.

Q6: What is the triangle inequality rule?
The sum of any two sides must be greater than the third side.

Q7: Does this calculator work for right-angled triangles?
Yes, it works for all valid triangles, including right, acute, and obtuse.

Q8: Can I calculate triangle height with this tool?
Currently, the tool gives angles, perimeter, and area—not height.

Q9: Is the calculator suitable for students?
Absolutely, it’s designed for both learning and practical use.

Q10: What unit are the results in?
Results are in the same unit you enter for the side lengths (cm, m, inches, etc.).

Q11: Can I calculate an equilateral triangle?
Yes, just enter the same value for all three sides.

Q12: Does it support negative or zero values?
No, sides must be positive numbers greater than zero.

Q13: Will the tool round off values?
Yes, results are rounded to two decimal places for clarity.

Q14: Can I use this calculator offline?
No, it works online within your browser.

Q15: Is this tool free to use?
Yes, the Triangle Calculator is completely free.

Q16: Can I use it for professional projects?
Yes, it’s accurate enough for professional and academic use.

Q17: How do I reset my inputs?
Click the Reset button to clear all values.

Q18: Does it work on mobile devices?
Yes, it is mobile-friendly and works on all devices.

Q19: Can I calculate obtuse triangles?
Yes, the calculator correctly computes angles even if one is greater than 90°.

Q20: Why should I use this instead of manual calculation?
It saves time, prevents mistakes, and simplifies learning.

Conclusion

The Triangle Side & Angle Calculator is an efficient and user-friendly tool for solving triangle problems instantly. Whether you’re a student learning geometry, a teacher preparing lessons, or a professional in engineering or design, this calculator provides quick and reliable results.