Triangle Calculator
Solve sides, angles, area and more
Triangle Calculator: Solve Sides, Angles and Area
This free triangle calculator solves a triangle from the values you already know. Enter three sides, two sides and the angle between them, two angles and the side between them, or any two sides of a right triangle, and it fills in the missing sides and angles. It also gives the area, perimeter, all three heights, the inradius and the circumradius, and draws the triangle so you can see the result.
Quick answer: a triangle with sides 6, 8 and 10 has angles of 36.87°, 53.13° and 90°, an area of 24 and a perimeter of 24. Because 6² + 8² equals 10², it is a right triangle. Pick the tab that matches what you know, type your numbers, and the answer updates as you type.
Four Ways to Solve a Triangle
A triangle is fixed by three well-chosen measurements. With SSS you know all three sides, and the angles follow from the law of cosines. With SAS you know two sides and the angle between them, which gives the third side and the other two angles. With ASA you know two angles and the side between them, so the third angle is simply 180° minus the other two and the sides come from the law of sines. The right triangle tab needs just two sides, because the right angle supplies the missing information.
Triangle Formulas Used
Sides are named a, b and c, and each is opposite the angle with the matching capital letter. These are the formulas the calculator applies.
The height to a side is twice the area divided by that side. The inradius is the area divided by s, and the circumradius is a × b × c divided by four times the area.
Worked Examples
| Method | You know | The calculator finds |
|---|---|---|
| SSS | Sides 6, 8, 10 | Angles 36.87°, 53.13°, 90° · area 24 |
| SAS | a = 5, B = 60°, c = 8 | b = 7 · A = 38.21° · C = 81.79° · area 17.321 |
| ASA | A = 40°, b = 10, C = 60° | B = 80° · a = 6.527 · c = 8.794 · area 28.263 |
| Right triangle | Legs 3 and 4 | Hypotenuse 5 · angles 36.87° and 53.13° · area 6 |
For the 6, 8, 10 triangle the three heights are 8, 6 and 4.8, the inradius is 2 and the circumradius is 5. In any right triangle the circumradius is half the hypotenuse, which is why it comes out as 5 here.
Types of Triangle
By sides, a triangle is equilateral when all three sides are equal, isosceles when two are equal and scalene when none are. By angles, it is acute when all angles are under 90°, right when one is exactly 90° and obtuse when one is over 90°. The calculator names the type from your result, such as a right scalene triangle.
Limits and Things to Know
Two sides and an angle that is not between them (SSA) can describe two different triangles, or none, so that case is not offered here. Angles are entered in degrees, and the length unit you pick only labels the results. The sides must satisfy the triangle inequality, so the two shorter sides have to add up to more than the longest. For building or cutting work, measure the real piece before you rely on a calculated size.
Who Can Use This Calculator?
Students use it to check geometry and trigonometry homework, and teachers use the diagram to explain how sides and angles relate. Carpenters, roofers and DIY builders use it for rafters, bracing and corner cuts, and the roofing calculator and area calculator help once the dimensions are known. For other calculations on the same page of homework, the scientific calculator covers sine, cosine and square roots.
How to Use This Triangle Calculator
Choose what you know
Pick SSS, SAS, ASA or Right triangle. The labels on each tab show which sides and angles to enter.
Enter your values
Type the numbers and choose a length unit if you want one. For a right triangle, leave one side empty to find it.
Read the solved triangle
The type, sides, angles, area, heights and radii appear at once, with a diagram of the triangle.
Try an example
Tap an example under the button to fill the boxes, or use Clear to start again.