๐ Triangle Calculator
Enter the lengths of a triangle's three sides to automatically calculate its area (via Heron's formula), perimeter, and all three interior angles. Useful for checking math homework or for dimension calculations in DIY and design projects.
How to use
- Enter the lengths of the three sides (a, b, c).
- The area, perimeter, and angles are calculated automatically.
- An error is shown if the three sides you entered can't form a valid triangle.
How the calculation works
This tool calculates a triangle's perimeter, area and three angles from the lengths of its three sides. It first checks the triangle inequality (any two sides must add up to more than the third) and reports an error for lengths that cannot form a triangle. The area comes from Heron's formula, which needs only the three sides: s = (a + b + c) รท 2 (half the perimeter) Area = โ(s(s โ a)(s โ b)(s โ c)) The angles come from the law of cosines: cos A = (bยฒ + cยฒ โ aยฒ) รท 2bc A is the angle opposite side a. B is found the same way, and C = 180ยฐ โ A โ B.
Worked example
Sides 3, 4 and 5 Perimeter: 12 s = 6 Area: โ(6 ร 3 ร 2 ร 1) = โ36 = 6 Angles: 36.87ยฐ, 53.13ยฐ, 90.00ยฐ (a right triangle) Sides 7, 8 and 9 Area: about 26.83 Angles: 48.19ยฐ, 58.41ยฐ, 73.40ยฐ 1, 2 and 3 do not form a triangle (1 + 2 = 3), so they give an error.
Things to be aware of
- Angle A is opposite side a, B opposite b and C opposite c.
- If the largest angle is 90ยฐ, it is a right triangle; if more than 90ยฐ, obtuse.
- Use the same unit for all sides. The area is in that unit squared (cmยฒ, for example).
FAQ
How is the area calculated?
It uses Heron's formula, which computes a triangle's area directly from the lengths of its three sides.
What does the "invalid" message mean?
It appears when the three side lengths you entered can't form a triangle (the sum of two sides is less than or equal to the third side). Double-check your side lengths.
What units does this use?
No specific unit is assumed โ the result is shown in the same unit you entered (e.g. enter cm and you'll get an area in cmยฒ and a perimeter in cm).