Free tool
Triangle Calculator
Enter a triangle's three sides to get its area(Heron's formula), perimeter, and type - right, acute, or obtuse - or enter two legs to find the hypotenuse of a right triangle. It runs in your browser and saves nothing.
Area & type from three sides
Enter the three side lengths (same unit).
Enter all three sides to get the perimeter, area (Heron's formula), and whether the triangle is right, acute, or obtuse.
Right triangle: find the hypotenuse
Enter the two legs; the hypotenuse comes from a² + b² = c².
Enter both legs to find the hypotenuse, area, and perimeter of the right triangle.
Worked example: the 3-4-5 triangle
Take a triangle with sides 3, 4, 5:
- Perimeter: 3 + 4 + 5 = 12, so s (half the perimeter) = 6.
- Area (Heron's formula):√(6 × (6−3) × (6−4) × (6−5)) = √(6 × 3 × 2 × 1) = √36 = 6.
- Type:3² + 4² = 9 + 16 = 25 = 5², so the longest side squared equals the sum of the other two squared - it's a right triangle.
Frequently asked questions
How do you find the area of a triangle?+
If you know the base and height, the area is one-half times base times height. If you only know the three side lengths, use Heron's formula: find s (half the perimeter), then the area is the square root of s times (s - a) times (s - b) times (s - c). For sides 3, 4, 5 the perimeter is 12, so s = 6 and the area is the square root of 6 x 3 x 2 x 1 = the square root of 36 = 6.
How do you know if a triangle is right, acute, or obtuse?+
Compare the square of the longest side with the sum of the squares of the other two. If they are equal, it's a right triangle; if the longest side squared is larger, it's obtuse; if smaller, it's acute. Example: 3, 4, 5 gives 3^2 + 4^2 = 25 = 5^2, so it's a right triangle.
How do you find the hypotenuse of a right triangle?+
Use the Pythagorean theorem: the hypotenuse c is the square root of (a^2 + b^2), where a and b are the two legs. For legs 3 and 4, c = the square root of (9 + 16) = the square root of 25 = 5.
Is this triangle calculator free?+
Yes - it's completely free, runs entirely in your browser, and stores nothing. Enter three sides for the area and type, or two legs to find the hypotenuse.
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