Triangle Calculator
Calculate Area, Angles, Sides & Perimeter
Professional triangle calculator for geometry problems. Calculate area using base and height, three sides (Heron's formula), or two sides and an angle. Solve right triangles with the Pythagorean theorem.
Used by students
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Step-by-step solutions
Triangle Calculator
Calculate triangle properties including area, perimeter, sides, and angles
Calculate area using base and height (most common method)
Quick Presets
Calculation Results
Triangle properties, measurements, and calculations
Enter valid measurements to see the calculation results
Triangle Geometry Fundamentals
Master the essential concepts and formulas for triangle calculations.
Area Formulas
Base x Height / 2 is the simplest formula. Heron's formula uses all three sides: sqrt(s(s-a)(s-b)(s-c)) where s is the semi-perimeter.
Pythagorean Theorem
For right triangles: a² + b² = c². The square of the hypotenuse equals the sum of squares of the other two sides.
Triangle Types
Equilateral (all sides equal), Isosceles (two sides equal), Scalene (no sides equal), Right (one 90 degree angle).
Angle Sum Property
The interior angles of any triangle always sum to 180 degrees. This fundamental property helps solve for unknown angles.
Trigonometric Ratios
Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent. Essential for solving triangles.
Law of Cosines
c² = a² + b² - 2ab cos(C). Generalization of Pythagorean theorem for any triangle. Used when you know SAS or SSS.
Common Special Triangles
3-4-5 Right Triangle
- Sides: 3, 4, 5 units
- Right angle opposite to 5
- Area = 6 square units
- Perimeter = 12 units
- Most common Pythagorean triple
45-45-90 Triangle
- Angles: 45, 45, 90 degrees
- Isosceles right triangle
- Sides ratio: 1 : 1 : sqrt(2)
- Hypotenuse = leg x sqrt(2)
- Half of a square diagonal
30-60-90 Triangle
- Angles: 30, 60, 90 degrees
- Sides ratio: 1 : sqrt(3) : 2
- Short leg opposite to 30
- Half of an equilateral triangle
- Common in geometry problems
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