Calcs.ToolsTriangle Calculator - Calculate Area, Perimeter & Triangle Type
Calculate triangle properties instantly with our free online calculator. Find area, perimeter, and triangle type (equilateral, isosceles, scalene) using geometry formulas. Perfect for students, teachers, and geometry problems.
Understanding Triangle Calculations
Triangles are three-sided polygons with unique geometric properties. Our calculator uses established formulas to calculate area (using Heron's formula) and perimeter, while also classifying triangles by their side lengths.
Triangle Types by Sides
- Equilateral: All three sides equal
- Isosceles: At least two sides equal
- Scalene: All sides different lengths
- Right Triangle: One 90-degree angle (detected automatically)
Area Formula
Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2 (semi-perimeter)
Frequently Asked Questions About Triangle Calculations
How do you calculate the area of a triangle?
Triangle area is calculated using Heron's formula: Area = √[s(s-a)(s-b)(s-c)] where s is the semi-perimeter (s = (a+b+c)/2) and a, b, c are the side lengths. For right triangles, you can also use Area = (base × height) ÷ 2. Our calculator automatically chooses the appropriate method.
What's the difference between perimeter and area?
Perimeter is the distance around the triangle (sum of all sides), measured in linear units. Area is the space inside the triangle, measured in square units. Perimeter tells you how much border material you need, while area tells you how much surface space the triangle occupies.
How does the calculator determine triangle type?
The calculator analyzes the side lengths: Equilateral (all sides equal), Isosceles (at least two sides equal), or Scalene (all sides different). It also checks for right triangles using the Pythagorean theorem (a² + b² = c²). The classification helps understand the triangle's geometric properties and applicable formulas.
Can I calculate triangles with angles instead of sides?
This calculator works with side lengths. For angle-based calculations, you would need the Law of Sines or Law of Cosines. If you have angles and one side, you can calculate the other sides first, then use this calculator. Consider using a trigonometric calculator for angle-based triangle problems.
What makes a triangle valid?
For three lengths to form a valid triangle, they must satisfy the triangle inequality theorem: the sum of any two sides must be greater than the third side. Our calculator validates this and will indicate if the entered side lengths cannot form a triangle.
Triangle Calculation Tips & Best Practices
- Check triangle validity: Ensure the sum of any two sides is greater than the third
- Use consistent units: All side lengths should be in the same measurement unit
- Identify triangle type: Classification helps choose the right solution approach
- Round appropriately: Consider significant figures for your application
- Verify calculations: Double-check results with manual calculations when possible
- Understand formulas: Know when to use different area calculation methods