📐 Triangle Calculator
Solve triangles: area, angles, and missing sides from any known values.
What is this tool?
A triangle calculator is a mathematical tool that solves triangles by computing unknown sides, angles, area, and perimeter from the values you provide. Triangles are fundamental geometric shapes that appear in construction, engineering, navigation, surveying, and design. Whether you are determining the roof pitch of a building, calculating land area from survey data, or solving a geometry problem, this calculator handles multiple solution methods to fit whatever information you have available. The calculator supports four common input methods: SSS (three sides known), SAS (two sides and the included angle), ASA (two angles and the included side), and AAS (two angles and a non-included side). Using the Law of Sines, the Law of Cosines, and Heron formula, it can determine every unknown dimension and property of any triangle.How it works
The calculator uses different mathematical methods depending on what you provide. For SSS (three sides known), it uses the Law of Cosines to find angles and Heron formula for area. For SAS (two sides and the included angle), it uses the Law of Cosines to find the third side, then the Law of Sines for remaining angles. For ASA and AAS (angle-based inputs), it uses the Law of Sines throughout. Heron formula for area: s equals half the perimeter, and area equals the square root of s times (s-a) times (s-b) times (s-c), where a, b, and c are the side lengths and s is the semi-perimeter.How to use
- Enter the known side lengths and angles for your triangle. You need at least three values, with at least one side length.
- Choose your input method based on what you know: SSS for three sides, SAS for two sides and the angle between them, ASA for two angles and the side between them.
- Click Calculate to solve for all unknown sides, angles, area, and perimeter.
- Verify the results make sense: the three angles should sum to 180 degrees, and the longest side should be opposite the largest angle.
- Use the results for your construction, engineering, or geometry application. All measurements are computed to high precision.
Frequently Asked Questions
Frequently Asked Questions
How do I calculate the area of a triangle?
If you know the base and height, area equals half the base times the height. If you know all three sides, use Heron formula: compute the semi-perimeter s equals (a+b+c)/2, then area equals the square root of s times (s-a) times (s-b) times (s-c). If you know two sides and the included angle, area equals half the product of the two sides times the sine of the angle.
What is the Law of Sines?
The Law of Sines states that the ratio of each side to the sine of its opposite angle is constant throughout the triangle: a/sin(A) equals b/sin(B) equals c/sin(C). This law is used to solve triangles when you know two angles and a side, or two sides and a non-included angle.
What is the Law of Cosines?
The Law of Cosines is a generalization of the Pythagorean theorem: c squared equals a squared plus b squared minus 2ab times cosine of C. It is used when you know all three sides or two sides and the included angle. It reduces to the Pythagorean theorem when the angle is 90 degrees.
What are the types of triangles?
By sides: equilateral (all sides equal), isosceles (two sides equal), and scalene (no sides equal). By angles: acute (all angles less than 90 degrees), right (one angle equals 90 degrees), and obtuse (one angle greater than 90 degrees). The sum of angles in any triangle always equals 180 degrees.
Tips & Advice
When using the triangle calculator for construction projects like roof framing or stair stringers, always verify your results with a physical measurement before cutting materials. For surveying and land calculation, be aware that large distances on Earth surface require geodesic corrections for maximum accuracy. When solving for angles, the calculator may show results in degrees; convert to radians if needed for further calculations. For right triangles, remember the special triangle ratios: a 45-45-90 triangle has sides in the ratio 1:1:square root of 2, and a 30-60-90 triangle has sides in the ratio 1:square root of 3:2.