The formula
How it works
Solve a triangle from its three sides. Enter the lengths a, b and c, and the calculator finds all three angles, the area, the perimeter and the type of triangle.
FAQ
What if my sides don’t form a triangle?
For a valid triangle, each side must be shorter than the sum of the other two — the triangle inequality. If you enter lengths that break this rule, no triangle exists and the calculator flags it. Check the numbers, as even a small typo can make an impossible triangle.
How are the angles found?
From the law of cosines, which relates each angle to the three sides. Once one angle is found this way, the others follow, and they always add up to 180 degrees. The area comes from Heron’s formula, which needs only the side lengths, not the angles or a height.
How can I tell if a triangle is right, acute or obtuse?
Look at its largest angle: exactly 90° is a right triangle, less than 90° is acute, and more than 90° is obtuse. The calculator works this out automatically once it finds the three angles.
What does scalene, isosceles and equilateral mean?
Scalene means all three sides have different lengths, isosceles means two sides are equal, and equilateral means all three sides — and all three angles — are equal. This is independent of whether the triangle is right, acute or obtuse.
Can I solve a triangle with only two sides and an angle?
Yes, but this calculator is built for the side-side-side case where all three lengths are known. Two sides and an included angle would use the law of cosines in reverse, and other combinations use the law of sines instead.
Why doesn’t the calculator ask for units?
Because a triangle’s angles and shape only depend on the ratios between its sides, not the units used. Enter all three sides in the same unit — inches, metres, anything — and the angles will be correct; only the area and perimeter carry that unit.
How is the perimeter used once the triangle is solved?
The perimeter, simply a + b + c, is also the basis for Heron’s formula, since the semi-perimeter s is half of it. Beyond the area calculation, the perimeter is useful on its own for framing, fencing or trimming material around the triangle’s edge.
About the triangle calculator
This calculator solves a triangle completely from its three side lengths. Using the law of cosines and Heron’s formula, it finds all three interior angles, the area and the perimeter, and identifies whether the triangle is right, acute or obtuse, and whether it is scalene, isosceles or equilateral. Three sides fully determine a triangle, so no other information is needed.
How to use it
Enter the three side lengths a, b and c in any consistent unit. The calculator returns the three angles opposite those sides, the area, the perimeter and the triangle’s classification. For example, sides of 3, 4 and 5 form a right triangle with angles of about 36.9°, 53.1° and 90°, an area of 6 and a perimeter of 12.
The formula
Each angle comes from the law of cosines, for instance , applied to each side in turn. The area uses Heron’s formula, , where is half the perimeter. Because the angles must total 180°, the third can also be found by subtraction once two are known.
Where it is used
Students use it to check geometry and trigonometry homework, while builders, surveyors and designers use triangle solving to work out lengths and angles that cannot be measured directly. Triangulation — fixing a position from distances — relies on the same maths. Any time three measurements of a triangle are known and the rest are needed, this calculator supplies them.