Triangle Calculator

Category: Geometry
- March 20, 2025
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This calculator helps you solve triangle problems by finding unknown sides, angles, area, perimeter, and more based on the information you provide.

Choose what you know about your triangle, input the values, and the calculator will determine all other properties.

Select what you know about your triangle

units
? The length of side a opposite to angle A.
units
? The length of side b opposite to angle B.
units
? The length of side c opposite to angle C.

Advanced Options

About Triangles

A triangle is a polygon with three sides and three angles. The sum of all internal angles in any triangle is always 180° (or π radians).

Triangle Types Based on Sides:
  • Equilateral Triangle: All three sides are equal in length, and all angles are equal (60° each).
  • Isosceles Triangle: Two sides are equal in length, and the angles opposite to these sides are equal.
  • Scalene Triangle: All three sides have different lengths, and all angles are different.
Triangle Types Based on Angles:
  • Acute Triangle: All three angles are less than 90°.
  • Right Triangle: One angle is exactly 90° (a right angle).
  • Obtuse Triangle: One angle is greater than 90°.
Triangle Solution Methods:
  • SSS (Side-Side-Side): When all three sides are known.
  • SAS (Side-Angle-Side): When two sides and the included angle are known.
  • ASA (Angle-Side-Angle): When two angles and the included side are known.
  • AAS (Angle-Angle-Side): When two angles and a non-included side are known.
  • SSA (Side-Side-Angle): When two sides and a non-included angle are known (the ambiguous case).
Key Triangle Formulas:

Area:

  • Area = (1/2) × base × height
  • Area = (1/2) × a × b × sin(C) (using two sides and the included angle)
  • Area = √(s(s-a)(s-b)(s-c)) (Heron's formula, where s is the semiperimeter)

Law of Sines:

sin(A)/a = sin(B)/b = sin(C)/c

Law of Cosines:

c² = a² + b² - 2ab × cos(C)
cos(C) = (a² + b² - c²)/(2ab)
Additional Properties:
  • Perimeter: The sum of all three sides (a + b + c).
  • Semiperimeter (s): Half the perimeter, s = (a + b + c)/2.
  • Heights: The perpendicular distance from a vertex to the opposite side.
  • Medians: Lines from a vertex to the midpoint of the opposite side.
  • Incircle: The circle that is tangent to all three sides of the triangle.
  • Circumcircle: The circle that passes through all three vertices of the triangle.
  • Inradius (r): The radius of the incircle, r = Area/s.
  • Circumradius (R): The radius of the circumcircle, R = (abc)/(4×Area).

Triangle Calculator: Solve Any Triangle Instantly

The Triangle Calculator is a tool that helps you determine missing sides, angles, area, and perimeter of a triangle based on the values you provide. Whether you have three sides, two sides and an angle, or other known measurements, this calculator simplifies the process.

How the Triangle Calculator Works

The calculator uses mathematical formulas such as the Law of Sines, Law of Cosines, and Heron's Formula to compute unknown properties of a triangle. By selecting what you know about the triangle and entering the values, you can get instant results.

Law of Sines:

\(\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}\)

Law of Cosines:

\(c^2 = a^2 + b^2 - 2ab \cdot \cos(C)\)

Heron's Formula for Area:

\(\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}\)

where \( s \) is the semiperimeter: \( s = \frac{a + b + c}{2} \).

How to Use the Triangle Calculator

  1. Select the type of information you have about the triangle (e.g., three sides, two sides and an angle, etc.).
  2. Enter the known values into the corresponding input fields.
  3. Choose the desired precision for decimal places.
  4. Click the "Calculate" button to get the missing sides, angles, and other properties.
  5. If needed, enable "Show Calculation Steps" to see how the results were derived.

Features of the Triangle Calculator

  • Supports various triangle types: scalene, isosceles, equilateral, and right triangles.
  • Allows different input options, including sides, angles, perimeter, and area.
  • Provides quick calculations using trigonometric formulas.
  • Displays a visual representation of the triangle.
  • Includes an option to show step-by-step solutions.
  • Handles special cases like ambiguous SSA triangles.

Why Use a Triangle Calculator?

This calculator is useful for students, engineers, architects, and anyone working with geometry. It saves time by eliminating manual calculations and helps verify answers quickly. Whether for homework, design, or real-world measurements, this tool provides accurate results instantly.

Frequently Asked Questions (FAQ)

What if I don’t know all the sides?

The calculator can work with various input types. If you know two sides and an included angle, or two angles and a side, you can still find the missing values.

Can this calculator handle right triangles?

Yes! It includes a special mode for right triangles, allowing you to input legs, hypotenuse, or angles to find the missing measurements.

How accurate are the results?

The results are precise and can be adjusted for decimal places. The calculations are based on well-established trigonometric formulas.

Is this calculator useful for real-world applications?

Absolutely! Whether you're calculating roof angles, land measurements, or any other geometric problem, this tool provides quick and reliable answers.

Does the Triangle Calculator show how the calculations are done?

Yes! You can enable the "Show Calculation Steps" option to see the formulas used and how the results were determined.

Conclusion

The Triangle Calculator is a practical and powerful tool for solving triangles effortlessly. It helps users quickly find unknown sides, angles, area, and other properties using reliable mathematical formulas. Whether for education, construction, or general problem-solving, this calculator makes geometry easy.