Solve any triangle from sides and angles (SSS, SAS, ASA, AAS, SSA, right) with a scaled diagram
Choose what you know
Enter all three side lengths a, b and c.
Triangle diagram
Drawn to scale with vertices, side lengths and angles labelled.
Sides
Side a
3
Side b
4
Side c
5
Angles
Angle A (°)
36.87°
Angle B (°)
53.13°
Angle C (°)
90°
Angle A (rad)
0.6435
Angle B (rad)
0.9273
Angle C (rad)
1.5708
Other measurements
Area
6
Perimeter
12
Inradius
1
Circumradius
2.5
Height to side a
4
Type
Right triangle
What is the triangle calculator?
This triangle calculator solves a triangle completely from a small set of known measurements. Give it three sides (SSS), two sides and the included angle (SAS), two angles and a side (ASA or AAS), two sides and a non-included angle (SSA), or two parts of a right triangle, and it returns every remaining side and angle, the area, the perimeter, the three heights, and the inscribed and circumscribed circle radii. A diagram is drawn to scale so you can see the shape, with vertices, side lengths and angle measures labelled. It is built for geometry and trigonometry students, but is just as useful for carpentry, surveying and design.
How to use this calculator
1. Pick the mode that matches what you already know: SSS, SAS, ASA, AAS, SSA or right triangle.
2. Type the required side lengths and angles into the fields shown (angles are in degrees).
3. The result updates instantly — no button to press.
4. Read off the missing sides and angles, the area and perimeter, and the extra measurements; the diagram shows the solved triangle to scale.
The formulas behind the answer
Law of sines: a / sin A = b / sin B = c / sin C. Use it when you know an angle and its opposite side (ASA, AAS, SSA).
Law of cosines: c² = a² + b² − 2ab·cos C (and the symmetric forms). Use it for SSS to find each angle and for SAS to find the third side.
Heron's formula for the area from three sides: with s = (a+b+c)/2, area = √(s(s−a)(s−b)(s−c)). Equivalently area = ½·a·b·sin C.
For a right triangle the Pythagorean theorem a² + b² = c² gives the missing side.
Example: sides 3, 4, 5 form a right triangle with angles 90°, 53.13° and 36.87°, area 6 and perimeter 12.
Reading the results
The three angles always add to 180°; if they do not, the inputs cannot form a triangle. A triangle is valid only when each side is shorter than the sum of the other two (the triangle inequality). When one angle equals 90° the triangle is right-angled and the longest side is the hypotenuse. In the SSA case watch for the ambiguous warning: two different triangles may satisfy your numbers, so confirm which one matches your problem. The inradius and circumradius describe the inscribed and circumscribed circles and are handy in construction and design.
Frequently asked questions
Why do I get a "triangle inequality" error? ▾
Three lengths only form a triangle if each one is less than the sum of the other two. Sides like 1, 1 and 5 fail because 1 + 1 is not greater than 5, so no triangle can close. Adjust the lengths until each side is shorter than the other two combined.
Can I enter angles in radians? ▾
Inputs are in degrees, which is what most homework uses. The results, however, report each angle in both degrees and radians, so you can copy whichever your problem needs.
What is the ambiguous (SSA) case? ▾
With two sides and an angle opposite one of them, the geometry sometimes allows two triangles — one with an acute angle and one with its obtuse supplement. The calculator detects this, shows both, and labels the second as the alternative solution.
Does it handle right triangles directly? ▾
Yes. Choose the right-triangle mode and enter any two of the two legs and the hypotenuse. The calculator applies the Pythagorean theorem and basic trigonometry to find the third side and both acute angles.