Triangle Calculator

Provide 3 values including at least one side. Angles can be in degrees or radians (e.g., pi/2).

Free Triangle Calculator – Solve Any Triangle

Need to solve a triangle? Our Triangle Calculator instantly computes sides, angles, area, and more, helping students, engineers, and mathematicians with geometry problems.

What is a Triangle Calculator?

A Triangle Calculator is an online tool that solves triangles based on three inputs (at least one side). It calculates:

  • Sides and angles
  • Area and perimeter
  • Heights and medians
  • Inradius and circumradius

How Does the Triangle Calculator Work?

The calculator uses geometric laws:

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

Law of Cosines: c² = a² + b² - 2ab cos(C)

Area: (1/2) × a × b × sin(C) or Heron's formula

Example: Sides a=3, b=4, c=5
Angles: A≈36.87°, B≈53.13°, C≈90°
Area≈6, Perimeter=12

Why Use Our Triangle Calculator?

  • Instant – Results in seconds
  • Accurate – Uses standard geometric formulas
  • Flexible – Handles SSS, SAS, ASA, AAS, SSA cases
  • Insightful – Provides detailed properties
  • Accessible – Use on any device

Uses in Daily Life

  • Education: Solve geometry homework
  • Engineering: Structural design calculations
  • Surveying: Land measurement
  • Architecture: Design and planning
  • Science: Physics and trigonometry problems

How to Use Our Triangle Calculator

  1. Enter three values (at least one side)
  2. Specify angle unit (degrees or radians)
  3. Click Calculate for results

Results include:
✔ Sides and angles
✔ Area, perimeter, heights, medians
✔ Inradius and circumradius

Manual Calculations vs Triangle Calculator

  • Manual: Complex trigonometry, error-prone
  • Calculator: Fast, accurate, user-friendly

Fun Facts About Triangles

  • Sum of angles is always 180°
  • Equilateral triangles have three equal sides and angles
  • Right triangles follow Pythagorean theorem: a² + b² = c²
  • Triangles are fundamental in computer graphics
  • Used in ancient architecture (e.g., pyramids)

Frequently Asked Questions (FAQs)

Q1: What inputs are needed?
Ans: Three values, including at least one side.

Q2: Can it handle any triangle type?
Ans: Yes, including scalene, isosceles, equilateral, right, acute, and obtuse.

Q3: How accurate are the results?
Ans: Highly accurate using standard geometric formulas.

Q4: What is the SSA ambiguous case?
Ans: SSA may yield two possible triangles; our calculator handles the valid case.

Exploring Triangles

Triangles are fundamental shapes in geometry, defined by three sides and angles. They are classified by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse).

Key Formulas

  • Area: (1/2) × base × height or (1/2) × a × b × sin(C)
  • Heron’s Formula: √[s(s-a)(s-b)(s-c)], s = (a+b+c)/2
  • Inradius: r = Area / s
  • Circumradius: R = a / (2 sin(A))

Source: Geometric principles, 2025.

Conclusion

Our Free Triangle Calculator simplifies solving triangles for education, engineering, or design. Enter three values to get instant results.
Try it now!

This content is independently researched and authored based on geometric principles, 2025.

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Triangle Tips

  • Ensure at least one side is provided for valid results.
  • Use "pi" for radian inputs (e.g., pi/2 for 90°).
  • Verify triangle inequality: Sum of two sides must exceed the third.