Triangle Calculator

Triangle Calculator: Solve Any Triangle Online

A triangle is a fundamental geometric shape with three sides and three angles. The sum of the interior angles of any triangle always equals 180 degrees. Triangles are classified by their side lengths (equilateral, isosceles, or scalene) and by their angles (acute, right, or obtuse). Our triangle calculator solves for all missing sides, angles, area, perimeter, and other properties when you provide any three values including at least one side length.

This calculator uses the Law of Sines and Law of Cosines to solve triangles. The Law of Sines states that the ratio of a side length to the sine of its opposite angle is constant for all three sides. The Law of Cosines relates the sides of a triangle to the cosine of one of its angles. Together, these laws make it possible to solve any triangle given sufficient information.

How to Use the Triangle Calculator

Simply enter any three values about your triangle. You can mix sides and angles, but at least one value must be a side length. The calculator will automatically detect which case applies (SSS, SAS, ASA, AAS, or SSA) and compute all missing information. For example, entering side a=3, side b=4, and side c=5 will solve a right triangle with angles approximately 36.87 degrees, 53.13 degrees, and 90 degrees.

Triangle Properties

The calculator computes the following properties: all three side lengths (a, b, c), all three interior angles (A, B, C), area (using Heron's formula), perimeter, semi-perimeter, inradius (radius of the inscribed circle), circumradius (radius of the circumscribed circle), and all three median lengths. These properties are useful in geometry, engineering, architecture, and many other fields.

Common Triangle Types

Understanding triangle types helps in identifying the shape you are working with. An equilateral triangle has all sides equal and all angles 60 degrees. An isosceles triangle has two equal sides and two equal angles. A scalene triangle has all sides and angles different. A right triangle has one 90-degree angle. An obtuse triangle has one angle greater than 90 degrees, and an acute triangle has all angles less than 90 degrees.

Frequently Asked Questions

How do I solve a triangle?

To solve a triangle, you need at least three pieces of information, with at least one being a side length. Our calculator handles all common cases including SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), AAS (two angles and non-included side), and SSA (two sides and non-included angle).

What is the Law of Sines?

The Law of Sines states that the ratio of a side length to the sine of its opposite angle is equal for all three sides of a triangle: a/sin(A) = b/sin(B) = c/sin(C). This is useful for finding missing sides when you know two angles and a side.

What is the Law of Cosines?

The Law of Cosines relates the sides of a triangle to the cosine of one of its angles: a squared = b squared + c squared - 2bc x cos(A). It is particularly useful for finding the third side when you know two sides and the included angle (SAS).

How is the area of a triangle calculated?

The area can be calculated using several methods. Heron's formula uses all three sides: area = sqrt(s(s-a)(s-b)(s-c)) where s is the semi-perimeter. Alternatively, area = (1/2) x base x height, or area = (1/2)ab x sin(C) when two sides and the included angle are known.

What is the inradius and circumradius of a triangle?

The inradius is the radius of the largest circle that fits inside the triangle. It is calculated as area divided by semi-perimeter. The circumradius is the radius of the circle that passes through all three vertices of the triangle, calculated as a / (2 x sin(A)).

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