Surface Area of a Triangle Calculator

A surface area of a triangle calculator works out the area of a triangle from the values you enter, such as base and height, three sides, or two sides and the included angle. You get the area in square units (like cm² or ft²) instantly, with the formula used shown so you can check the result.

Formula

The most common formula for the area of a triangle is:

Area = ½ × base × height

In symbols: A = ½ × b × h

• A = area of the triangle (square units, e.g., m², cm², ft²)
• b = length of the base (any side you choose as the base, in linear units, e.g., m, cm, ft)
• h = perpendicular height from the base to the opposite vertex (same linear unit as the base)

The height must be measured at a right angle to the base. This formula works for any triangle—scalene, isosceles, equilateral, or right-angled—as long as you know the base and its corresponding perpendicular height.

Worked Example

Using the default values from the calculator above (base = 6 m, height = 4 m):

1. Write down the formula: A = ½ × b × h
2. Plug in the numbers: A = ½ × 6 × 4
3. Multiply 6 × 4 = 24
4. Take half of 24: A = 12

The area is 12 m². The calculator shows the same result with two decimal places: 12.00 m².

Other Ways to Find the Area

Sometimes you don’t have the base and height. Here are other common formulas:

• Heron’s formula – when you know all three sides (a, b, c). First compute the semi-perimeter s = (a+b+c)/2, then area = √[s(s−a)(s−b)(s−c)].
• SAS formula – when you know two sides and the included angle. Area = ½ × a × b × sin(C), where C is the angle between sides a and b.
• Equilateral triangle – area = (√3/4) × side².
• Right triangle – the two legs are the base and height, so area = ½ × leg1 × leg2.

Most triangle area calculators offer at least the base-height option and often Heron’s formula. Choose the one that matches the data you have.

How to Choose the Right Input

Before you use a triangle area calculator, decide which values you know. The most straightforward is base and height, but many real problems give you only the side lengths. In that case, use Heron’s formula. If you have two sides and the angle between them, use the SAS formula. Some calculators let you pick the method from a dropdown—select the one that fits your measurements.

Make sure all your inputs are in the same unit. If the base is in meters and the height in centimeters, convert one first. The area will come out in square units of whatever unit you used (e.g., m × m = m²).

Common Mistakes and How to Avoid Them

• Using a slanted side as the height. The height must be perpendicular to the base. For a right triangle, the height is one of the legs; for other triangles, you often need to draw the altitude.
• Mixing units. Always convert to the same unit before multiplying. For example, 2 m and 50 cm should become 2 m and 0.5 m, not 2 and 50.
• Forgetting the ½. The area of a triangle is half the area of a rectangle with the same base and height. Skipping the ½ doubles your answer.
• Rounding too early. If you use Heron’s formula, keep the semi-perimeter and square root unrounded until the final step to avoid errors.
• Using the wrong angle in the SAS formula. The angle must be the one between the two known sides, not any angle.

Why the Formula Works

A triangle is exactly half of a rectangle (or parallelogram) that shares the same base and height. If you draw a diagonal across a rectangle, you get two congruent right triangles, each with half the rectangle’s area. For non-right triangles, you can still construct a rectangle around the triangle, and the triangle occupies half of it. That’s why the ½ appears in the formula.

This geometric reasoning also explains why the area is always in square units: you are multiplying two lengths together.

Limits of the Base-Height Formula

The base-height formula is simple, but it requires you to know the perpendicular height. In many real-world situations (like measuring a piece of land), you can measure the sides directly but not the height. That’s when Heron’s formula becomes essential. Also, the base-height formula does not work if you only know the three sides—you need to compute the height first, which is possible but involves extra steps. Always check which data you actually have before choosing a formula.

Frequently Asked Questions

Can I use this calculator for any type of triangle?

Yes, the base-height formula works for all triangles—right, acute, obtuse, scalene, isosceles, or equilateral—as long as you correctly identify the base and the perpendicular height to that base.

What if I only know the three side lengths?

Use Heron’s formula. Many triangle area calculators have a separate mode for that. If yours doesn’t, you can compute the semi-perimeter and apply the formula manually.

What units will the area be in?

The area is always in square units of the input unit. If you enter base and height in centimeters, the area is in square centimeters (cm²). If you enter feet, the area is in square feet (ft²).

How do I find the height if I only have the sides?

You can use Heron’s formula to find the area first, then rearrange the area formula to solve for height: h = (2 × area) / base. Or, for a right triangle, the height is one of the legs.

What is the difference between base and height?

The base is any side you choose, and the height is the perpendicular distance from that base to the opposite vertex. You can pick any side as the base—the area will be the same regardless.

Is the area of a triangle always half of a rectangle?

Yes, every triangle can be paired with a rectangle (or parallelogram) of the same base and height, and the triangle’s area is exactly half of that shape’s area. That is why the formula includes ½.

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in b | Base | m | 6 | 0
in h | Height | m | 4 | 0
out area | Area | m² | 0.5 * b * h | 2