Solve any triangle from three known values.
Give three values (including at least one side) and the rest follow. A 3-4-5 triangle has area = 6 and is a right triangle.
Enter three known values — three sides (SSS), two sides and the included angle (SAS), two angles and the included side (ASA), two angles and a non-included side (AAS) or two sides and a non-included angle (SSA) — and the calculator finds every side and angle, the area, perimeter, semi-perimeter, inradius, circumradius, heights and the triangle type. In the SSA ambiguous case it shows both solutions.
It uses the law of cosines, the law of sines and Heron's formula. For right triangles see the Right Triangle Calculator and Pythagorean Theorem Calculator; for area formulas the Area Calculator.
The calculator applies the standard method step by step.
| Measure | Value |
|---|---|
| Side a | 3 |
| Side b | 4 |
| Side c | 5 |
| Angle A | 36.86989765° |
| Angle B | 53.13010235° |
| Angle C | 90° |
| Area | 6 |
| Perimeter | 12 |
| Semi-perimeter | 6 |
| Inradius | 1 |
| Circumradius | 2.5 |
| Height to side a | 4 |
| Type | Scalene, right |
| Sides | Area |
|---|---|
| 3-4-5 (SSS) | Area = 6 |
| Equilateral side 2 | Area = 1.73205081 |
| 5-12-13 | Area = 30 |
| 6-8-10 | Area = 24 |
| 7-8-9 | Area = 26.83281573 |
Identify what you know (SSS, SAS, ASA, AAS or SSA), then use the law of cosines or sines to find the rest. This calculator does it for you.
Two sides and a non-included angle can fit zero, one or two triangles. The calculator shows both when two exist.
Use Heron's formula: area = √(s(s − a)(s − b)(s − c)) where s is half the perimeter.
Each side must be shorter than the sum of the other two, otherwise no triangle exists.
Look at the largest angle: under 90° acute, exactly 90° right, over 90° obtuse.
The radius of the circle that fits inside the triangle touching all sides, and of the circle passing through all three vertices.
It uses the standard method: law of cosines c² = a² + b² − 2ab cos C law of sines a ÷ sin A = b ÷ sin B = c ÷ sin C The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
