Triangle Calculator
Calculate triangle area, perimeter, angles, and height. Supports all triangle types: right, equilateral, isosceles, and scalene.
1x² − 5x + 6 = 0
Discriminant = 1
two real roots
x = (−b ± √(b²−4ac)) / 2a
x₁ = 3
x₂ = 2
About the Triangle Calculator
Triangles are the most fundamental polygon in geometry — every polygon can be decomposed into triangles, and triangle calculations underpin engineering, architecture, navigation, and physics. Our triangle calculator solves for any unknown sides or angles given sufficient information, supporting SSS, SAS, ASA, AAS, and right triangle configurations.
Formula
Pythagorean: a² + b² = c² | Area = ½ × base × height | Heron's: A = √(s(s−a)(s−b)(s−c))
How It Works
For right triangles: use the Pythagorean theorem (a² + b² = c²) and trigonometric functions (sin, cos, tan). For any triangle: use the Law of Sines (a/sin A = b/sin B = c/sin C) and Law of Cosines (c² = a² + b² − 2ab cos C). Area = ½ × base × height, or using Heron's formula when three sides are known: A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2.
Tips & Best Practices
- ✓The sum of all interior angles of any triangle = 180°.
- ✓The longest side of a triangle is always opposite the largest angle.
- ✓Special right triangles: 3-4-5, 5-12-13, 8-15-17 have integer side lengths.
- ✓45-45-90 triangle: legs are equal, hypotenuse = leg × √2.
- ✓30-60-90 triangle: sides in ratio 1 : √3 : 2.
Who Uses This Calculator
Engineers calculating structural loads, surveyors determining land areas, students completing trigonometry coursework, architects designing roof pitches, and game developers calculating collision geometry all use triangle calculations.
Optimised for: USA · Canada · UK · Australia · Calculations run in your browser · No data stored
Frequently Asked Questions
How do you find the area of a triangle?
Area = ½ × base × height. For a triangle with base 10 and height 6, area = 30 square units.