Triangle Side and Angle Calculator

SSS – Find All Angles (Given 3 Sides)

SAS – Find Missing Side & Angles (2 Sides + 1 Angle)

ASA – Find Missing Sides (2 Angles + 1 Side)

AAS – Find Missing Sides (2 Angles + 1 Opposite Side)

Triangles are among the most important shapes in mathematics, architecture, and engineering. Whether you’re a student learning geometry, a teacher creating class material, or a professional designing structures, you often need to calculate unknown sides and angles from the known values.

Doing this manually can be time-consuming and error-prone. That’s where the Triangle Side and Angle Calculator comes in.

This free online tool lets you quickly solve any triangle by calculating missing sides and angles using formulas like the Law of Sines, Law of Cosines, and the Triangle Angle Sum theorem. It’s fast, accurate, and easy to use—even for beginners.

📐 What Is the Triangle Side and Angle Calculator?

The Triangle Side and Angle Calculator is a web-based geometry solver that helps you find unknown sides and angles of a triangle from the values you know.

It supports solving all triangle cases, including:

  • ASA (Angle-Side-Angle)
  • AAS (Angle-Angle-Side)
  • SAS (Side-Angle-Side)
  • SSA (Side-Side-Angle)
  • SSS (Side-Side-Side)

Using this calculator, you can:

  • Find unknown angles if you know the sides
  • Find unknown sides if you know the angles
  • Solve both right triangles and non-right triangles
  • Get results instantly with a single click

⚙️ How to Use the Triangle Side and Angle Calculator

Here’s a simple step-by-step guide:

1. Select the Known Values

  • Identify what information you have about your triangle.
  • This can be:
    • Two angles and one side (AAS or ASA)
    • Two sides and the included angle (SAS)
    • Three sides (SSS)
    • One right angle and any other side/angle combination (Right triangle case)

2. Enter Known Sides

  • Enter the known side lengths in their respective fields (Side A, Side B, Side C).
  • Use any unit (cm, m, in, etc.) — just make sure all sides use the same unit.

3. Enter Known Angles

  • Enter the known angles in degrees (Angle A, Angle B, Angle C).
  • Ensure the angles are realistic (each between 0° and 180°).

4. Click “Calculate”

  • Press the Calculate button.
  • The tool will use the correct trigonometric laws to solve the triangle automatically.

5. View the Results

  • The calculator displays:
    • All missing side lengths
    • All missing angle measures
    • The triangle’s perimeter
    • The triangle’s area (optional feature)

6. Reset or Copy Results (Optional)

  • Click Reset to clear all fields and start over.
  • Click Copy Results to save your outputs to the clipboard.

💡 Practical Examples

Let’s see two real examples to understand how this works:

🧮 Example 1: ASA Case

Known values:

  • Angle A = 50°
  • Angle B = 60°
  • Side c = 8 cm

Step 1: Find missing angle Angle C=180°−(50°+60°)=70°\text{Angle C} = 180° - (50° + 60°) = 70°Angle C=180°−(50°+60°)=70°

Step 2: Use the Law of Sines to find remaining sides: asin⁡A=csin⁡C⇒a=c×sin⁡Asin⁡C\frac{a}{\sin A} = \frac{c}{\sin C} \quad\Rightarrow\quad a = \frac{c \times \sin A}{\sin C}sinAa​=sinCc​⇒a=sinCc×sinA​ a=8×sin⁡50°sin⁡70°≈6.48 cma = \frac{8 \times \sin 50°}{\sin 70°} \approx 6.48 \text{ cm}a=sin70°8×sin50°​≈6.48 cm b=8×sin⁡60°sin⁡70°≈7.39 cmb = \frac{8 \times \sin 60°}{\sin 70°} \approx 7.39 \text{ cm}b=sin70°8×sin60°​≈7.39 cm

Result:

  • a ≈ 6.48 cm
  • b ≈ 7.39 cm
  • c = 8 cm
  • A = 50°, B = 60°, C = 70°

🧮 Example 2: SAS Case

Known values:

  • Side a = 7 cm
  • Side b = 9 cm
  • Angle C = 120°

Use the Law of Cosines: c2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab\cos Cc2=a2+b2−2abcosC c2=72+92−2(7)(9)cos⁡120°=49+81+63=193c^2 = 7^2 + 9^2 - 2(7)(9)\cos 120° = 49 + 81 + 63 = 193c2=72+92−2(7)(9)cos120°=49+81+63=193 c≈13.89 cmc \approx 13.89 \text{ cm}c≈13.89 cm

Use Law of Sines to find other angles: sin⁡Aa=sin⁡Cc\frac{\sin A}{a} = \frac{\sin C}{c}asinA​=csinC​ sin⁡A=asin⁡Cc=7sin⁡120°13.89≈0.436\sin A = \frac{a \sin C}{c} = \frac{7 \sin 120°}{13.89} \approx 0.436sinA=casinC​=13.897sin120°​≈0.436 A≈25.9°,B=180°−(120°+25.9°)=34.1°A \approx 25.9°,\quad B = 180° - (120° + 25.9°) = 34.1°A≈25.9°,B=180°−(120°+25.9°)=34.1°

Result:

  • a = 7 cm
  • b = 9 cm
  • c ≈ 13.89 cm
  • A ≈ 25.9°, B ≈ 34.1°, C = 120°

⚡ Key Features of the Triangle Side and Angle Calculator

  • ✅ Solve all triangle types (ASA, AAS, SAS, SSA, SSS, right triangles)
  • ✅ Find missing sides and angles instantly
  • ✅ Uses Law of Sines, Law of Cosines, and angle sum theorem
  • ✅ Validates input to prevent impossible triangles
  • ✅ Displays all triangle dimensions clearly
  • ✅ Supports both desktop and mobile devices
  • ✅ Completely free and requires no login

📌 Common Use Cases

The Triangle Side and Angle Calculator is useful in many fields:

  • Students solving geometry or trigonometry problems
  • Teachers preparing diagrams and math questions
  • Architects and civil engineers working with building layouts
  • Surveyors calculating triangular plot boundaries
  • DIY enthusiasts designing triangular furniture or decor
  • Mathematicians verifying manual calculations

💡 Tips for Best Results

  • Always use the same unit for all sides.
  • Enter angles in degrees.
  • Ensure the triangle angle sum = 180° when entering two known angles.
  • Double-check side values to follow the triangle inequality rule.
  • For more accuracy, use at least two decimal places when entering values.
  • Use the copy results feature to save outputs for your work or reports.

❓ Frequently Asked Questions (FAQ)

Here are 20 commonly asked questions and answers:

1. What does the Triangle Side and Angle Calculator do?
It solves any triangle by finding missing sides and angles from known values.

2. Which triangle types does it support?
It supports all triangle types—right, acute, obtuse, scalene, isosceles, and equilateral.

3. What formulas does it use?
It uses the Law of Sines, Law of Cosines, and the angle sum theorem.

4. Is it free to use?
Yes, it’s 100% free and web-based.

5. Can I use decimals?
Yes, you can input decimals such as 5.75 or 12.30.

6. Which units should I use?
Use any consistent unit (cm, m, in, ft) for all sides.

7. Does it calculate the area too?
Yes, if enough data is provided, it can also calculate the area.

8. Can it calculate perimeter?
Yes, it sums all sides to find the perimeter.

9. Does it work on mobile devices?
Yes, it’s mobile-responsive and works on all screens.

10. Does it need the internet?
Yes, you must be online to use it.

11. Can I copy the results?
Yes, click the “Copy Results” button to copy outputs to your clipboard.

12. What if I enter impossible values?
It will show an error indicating the triangle is invalid.

13. How many known values do I need to start?
At least three known values (with at least one side) are needed to solve a triangle.

14. Can I use angles greater than 180°?
No, each angle must be between 0° and 180° and the total must be 180°.

15. Can it solve right triangles?
Yes, it handles right triangles automatically using trigonometry.

16. What is the Law of Sines?
asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}sinAa​=sinBb​=sinCc​

17. What is the Law of Cosines?
c2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab\cos Cc2=a2+b2−2abcosC

18. Does it store my data?
No, it doesn’t collect or store any personal or input data.

19. Who can use this tool?
Students, teachers, engineers, architects, surveyors, and hobbyists.

20. How accurate are the results?
It gives results up to two decimal places using precise math formulas.

✅ Conclusion

The Triangle Side and Angle Calculator is an essential tool for anyone dealing with triangles. It removes the need for manual calculations and gives fast, accurate, and reliable results for any triangle type.

Whether you’re a student solving homework problems, a teacher building lesson plans, or a professional working with technical designs, this calculator saves time and ensures precision.