Triangle Calculator
Calculate triangle area, perimeter, angles, and missing sides using multiple methods.
Triangle Calculations
Length of the base
Perpendicular height to base
📐 Triangle Formulas
- • Area = ½ × base × height
- • Area = √[s(s-a)(s-b)(s-c)] (Heron's formula)
- • Area = ½ × a × b × sin(C)
- • Law of Cosines: c² = a² + b² - 2ab cos(C)
- • Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Triangle Results
Area
Square units
Complete Triangle
Sides
Angles
Triangle Properties
- • Has a 90° angle - Pythagorean theorem applies
- • Sum of all angles = 180°
- • Any two sides must be greater than the third
How it works
A triangle calculator finds missing sides, angles, or the area from what you know. The most common task is area from a base and its perpendicular height; angles always add to 180°, which lets you find a third angle from two.
Triangle basics
Area = ½ · base · height Angles: A + B + C = 180°
- base
- any chosen side
- height
- perpendicular distance from that side to the opposite vertex
Worked example
- Base = 6, height = 4
- Area = ½ × 6 × 4
Area = 12 square units.
Good to know
- Height must be perpendicular to the chosen base — not the slanted side length.
- For three known sides, Heron's formula gives the area; for sides and angles, use the laws of sines and cosines.
- The longest side is always opposite the largest angle.
Related Calculators
Frequently Asked Questions
How do I calculate the area of a triangle?
Common methods: 1) Base × Height ÷ 2 when you know base and height. 2) Heron's formula: √[s(s-a)(s-b)(s-c)] where s is semi-perimeter when you know all three sides. 3) (1/2)ab×sin(C) when you know two sides and included angle.
What are the different types of triangles?
By sides: Equilateral (all sides equal), Isosceles (two sides equal), Scalene (no sides equal). By angles: Acute (all angles < 90°), Right (one angle = 90°), Obtuse (one angle > 90°). Special: 30-60-90 and 45-45-90 triangles have fixed ratios.
How do I find a missing side or angle?
Use Law of Sines (a/sin(A) = b/sin(B) = c/sin(C)) when you know two angles and one side, or two sides and one opposite angle. Use Law of Cosines (c² = a² + b² - 2ab×cos(C)) when you know two sides and included angle, or all three sides.
What is the triangle inequality theorem?
The sum of any two sides must be greater than the third side. For sides a, b, c: a + b > c, a + c > b, and b + c > a. If this isn't satisfied, the three lengths cannot form a triangle. This calculator automatically checks this condition.
How do I calculate triangle height/altitude?
Height = 2 × Area ÷ Base. For any triangle with area A and base b, h = 2A/b. You can also use: h = a × sin(B) = b × sin(A) where a and b are sides and A and B are opposite angles. For equilateral triangles: h = (√3/2) × side.
What are common triangle formulas in construction and engineering?
Roof pitch: Rise/Run ratio forms right triangle. Truss calculations use triangle stability. Land surveying uses triangulation. Bridge design relies on triangular supports for strength. The 3-4-5 rule creates perfect right angles on construction sites.