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Triangle Area Calculator
Triangle area from base and height, or from three sides.
Triangle area
How it works
Base & height: area = (base × height) ÷ 2 Three sides: s = (a + b + c) ÷ 2, area = √(s × (s − a) × (s − b) × (s − c))
Worked example: a base of 10 and a height of 6 give (10 × 6) ÷ 2 = 30 square units. The same triangle by sides 3, 4 and 5: s = (3 + 4 + 5) ÷ 2 = 6, so area = √(6 × 3 × 2 × 1) = √36 = 6 square units, with a perimeter of 12.
Frequently asked questions
When do I use Heron's formula?
When you know all three sides but not the height. The height of a triangle is hard to measure directly, while the sides are usually the numbers you actually have.
What if the three sides cannot form a triangle?
Then the number under the square root is negative — for example sides 1, 2 and 10. The calculator shows a note instead of a number, because no such triangle exists.
Is the height always the vertical side?
No. The height is the perpendicular distance from the base to the opposite corner. On a slanted triangle it falls inside or outside the shape, but the formula still uses it the same way.
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