Give the three side lengths of a triangle and this tool works out its area, perimeter, all three interior angles, and whether it is scalene, isosceles or equilateral — and right, acute or obtuse. Everything is computed in your browser with no sign-up.
Enter three sides to solve the triangle.
How it works
The area comes from Heron’s formula: with s as half the perimeter, area = √(s(s−a)(s−b)(s−c)). This works from the sides alone, so you never need the height. The perimeter is simply the sum of the three sides.
Each angle is found with the law of cosines — for the angle opposite side a, cos A = (b² + c² − a²) ÷ (2bc) — and the third angle is whatever makes the three add up to 180°. The result is classified by its sides (equal sides) and by its largest angle (exactly 90° is right, more is obtuse, less is acute).
A set of three lengths only forms a triangle if each side is shorter than the sum of the other two — the triangle inequality. If your values fail that test the tool says so instead of returning an impossible shape. Sides can be in any single unit; the area comes out in that unit squared.
Practical examples
The 3-4-5 right triangle
Enter 3, 4 and 5. The area is 6, the perimeter is 12, and the angle opposite the longest side is exactly 90° — so it is a scalene right triangle, the classic set-square shape.
An equilateral triangle
Enter 5, 5, 5. All three angles come out at 60°, it is classified equilateral and acute, and the area is about 10.8253.
Checking a plot of land
Measure the three sides of a triangular garden — say 8 m, 11 m and 15 m — and read the area straight off (about 42.85 m²), without needing to measure a perpendicular height.
Frequently asked questions
What is Heron’s formula?
It gives a triangle’s area from its three side lengths alone. Compute s = (a+b+c)/2, then area = √(s(s−a)(s−b)(s−c)). It is ideal when you can measure the sides but not the height.
How are the angles calculated?
By the law of cosines. For each angle, cosine = (sum of the squares of the two adjacent sides − square of the opposite side) ÷ (2 × product of the adjacent sides). The tool converts the result to degrees.
What is the triangle inequality?
A rule that any side must be shorter than the sum of the other two. If it is not — for example sides 1, 2 and 3 — the “triangle” collapses into a line and has no area, so the tool rejects it.
What is the difference between scalene, isosceles and equilateral?
Scalene has three different side lengths, isosceles has two equal sides, and equilateral has all three equal (and all angles 60°). The tool reports which one your sides make.
How do I know if my triangle is right-angled?
Its largest angle will be exactly 90°, which happens when the sides satisfy a² + b² = c² (a Pythagorean set like 3-4-5). The tool labels it “right”; more than 90° is obtuse and less is acute.
Can I enter angles instead of sides?
Not here — this tool takes three sides (the SSS case). Angles alone do not fix a triangle’s size, and other combinations (two sides and an angle) need a different solver.
What units does it use?
Any single length unit you like. The perimeter shares that unit and the area is in its square — enter metres and you get m², enter inches and you get square inches.
Why are the angles shown with decimals?
Most triangles have irrational angle measures, so they are rounded to two decimal places. The three still add up to 180° apart from a tiny rounding difference.
Is my data uploaded anywhere?
No. The calculation is entirely local to your browser; nothing you type is sent or stored.
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