About this calculator
Triangle Calculator calculates the area, perimeter and three angles of a triangle based on the lengths of its sides. Use Heron's formula to calculate the area: area = √[s(s-a)(s-b)(s-c)], where s=(a+b+c)/2 is the half-perimeter. Calculate the angle using the cosine law: cos A = (b²+c²-a²)/(2bc), then use the inverse cosine function to find the angle. Our free online triangle calculator provides a simple, fast and accurate solution.
A triangle must satisfy the triangle inequality: the sum of any two sides is greater than the third side. For example, side lengths 3, 4, and 5 can form a triangle (3+4>5, 3+5>4, 4+5>3), but 1, 2, and 5 cannot (1+2<5). Triangle Calculator automatically verifies whether the three input sides form a triangle.
Using the triangle calculator is very simple and intuitive. Just enter the lengths of three sides, click the calculate button, and you'll instantly get the area, perimeter, and three angles. This tool is particularly suitable for students learning geometry, engineers performing measurement calculations, and architects designing.
What it calculates
The triangle calculator finds area, perimeter, unknown sides, and angles from side lengths, angles, or height.
Formula
- Area: A = 1/2 * base * height.
- Heron formula: A = sqrt(s(s-a)(s-b)(s-c)).
- Law of sines: a/sin A = b/sin B = c/sin C.
- Law of cosines: c^2 = a^2 + b^2 - 2ab cos C.
Inputs
- Triangle side lengths.
- Angles or height.
- A calculation mode that matches the known values.
Example
| Known | Result | Note |
|---|---|---|
| 3,4,5 | Right triangle | Satisfies Pythagorean theorem |
| base 10, height 6 | Area 30 | A = 1/2bh |
| sides a,b,c | Use Heron formula | First compute semiperimeter s |
How to interpret the result
The result describes the size and shape of the triangle. Side lengths must satisfy the triangle inequality, and interior angles sum to 180°.
Common mistakes
- Not every three side lengths form a triangle.
- Keep angle units consistent.
- SSA information can produce two possible triangles.
How to use
Using the triangle calculator is very simple. First, enter the lengths of the three sides a, b, and c in the three input boxes. You can enter any positive number, including decimals. For example, enter 3, 4, 5 (this is a right triangle).
Click the "Calculate" button. The calculator will first verify that these three sides form a triangle (satisfying the triangle inequality). If a triangle cannot be formed, an error message will be displayed.
If a triangle can be formed, the calculator will immediately show you: the perimeter (the sum of the three sides), the area (using Heron's formula), and the three angles (using the law of cosines). For example, a triangle with side lengths 3, 4, and 5 has perimeter = 12, area = 6, angle A = 90°, angle B = 53.13°, and angle C = 36.87°. Click the "Reset" button to clear all inputs and start a new calculation.
Main features
This triangle calculator has the following features: Use Heron's formula to calculate area; Use cosine theorem to calculate angles; Automatically verify triangle inequalities; Display perimeter, area and three angles at the same time; High-precision calculation (retaining 4 decimal places); Automatically detect invalid input; The interface is simple and intuitive, easy to use; The response speed is fast, and the calculation results are displayed instantly; Completely free, no registration or download required; Supports desktop and mobile device access; Suitable for students, engineers and architects.
Use cases
The triangle calculator is very useful in several scenarios. When students learn geometry, triangles are the basic shapes. You can use the triangle calculator to verify your calculations and understand Heron's formula and cosine theorem. As you complete your geometry homework, you can quickly check whether your answers are correct.
In engineering surveying, trigonometric calculations are used to measure distances and angles. For example, given the distance between three points, the angle can be calculated. In architectural design, triangles are stable structures and the area and angle of the triangle need to be calculated. In geographic information systems (GIS), triangulation networks (TINs) are used to represent terrain, and the properties of triangles need to be calculated.
In physics, the decomposition and composition of forces involves trigonometric calculations. In navigation, triangulation requires calculating triangles. In game development, collision detection, path planning, etc. involve triangle calculations. In art design, triangular composition requires calculation of proportions and angles. Whether studying, engineering or designing, the triangle calculator is a useful tool.