Triangle Area Calculator

Enter the base and height of a triangle to find its area. The calculator shows every step of the work with your values, plus a full explanation of the formula below.

Base (b)

Height (h)

The Triangle Area Formula

The area of any triangle is half of the product of its base and its height:

$$A = \frac{1}{2} \times b \times h$$

The height (also called the altitude) must be measured perpendicular to the base — straight up and down, not along a slanted side. In the diagram above, the dashed red line shows the height.

Why Divide by Two?

A triangle is exactly half of a rectangle with the same base and height. The area of that rectangle is $b \times h$, so the triangle's area is $\frac{1}{2} \times b \times h$.

Step-by-Step Example

A triangle has a base of $b = 12$ and a height of $h = 8$. Find the area.

Step 1 — Write the formula:

$$A = \frac{1}{2} \times b \times h$$

Step 2 — Substitute the values:

$$A = \frac{1}{2} \times 12 \times 8$$

Step 3 — Multiply the base and height:

$$A = \frac{1}{2} \times 96$$

Step 4 — Divide by 2:

$$A = 48\ \text{square units}$$

Right Triangles

For a right triangle, the two legs serve as the base and height — no separate altitude needed:

$$A = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$$

Heron's Formula (All Three Sides Known)

If you know all three side lengths $a$, $b$, $c$ but not the height, use Heron's formula. First compute the semi-perimeter:

$$s = \frac{a + b + c}{2}$$

Then the area is:

$$A = \sqrt{s(s-a)(s-b)(s-c)}$$

Example: A triangle with sides 5, 6, 7.

$$s = \frac{5+6+7}{2} = 9$$ $$A = \sqrt{9(9-5)(9-6)(9-7)} = \sqrt{9 \times 4 \times 3 \times 2} = \sqrt{216} \approx 14.70$$

Frequently Asked Questions

Does it matter which side I call the base?

No — any side can be the base, as long as the height is measured perpendicular to that side. Each choice gives the same area.

What if the triangle is obtuse?

The formula $A = \frac{1}{2}bh$ still applies. For an obtuse triangle, the height may fall outside the triangle when extended, but the value of $h$ is still the perpendicular distance from the chosen base to the opposite vertex.