Triangle Base Area Calculator & Formula

This calculator works out the area of a triangle when you enter its base and height. You provide the base length and the perpendicular height, and it returns the area in square units. It uses the standard formula Area = 0.5 × base × height.

Formula

The area of a triangle is given by:

Area = ½ × base × height

where:

• base (b) is the length of one side of the triangle, in metres (m), centimetres (cm), feet (ft), or any consistent unit.
• height (h) is the perpendicular distance from that base to the opposite vertex, measured at a right angle to the base, in the same unit.

The result is in square units: m², cm², ft², etc. If you mix units (e.g., base in metres and height in centimetres), the answer will be wrong unless you convert first.

Worked Example

Using the default values from the calculator above:

• Base = 10 m
• Height = 5 m

Step 1: Multiply the base by the height: 10 × 5 = 50

Step 2: Divide by 2 (or multiply by 0.5): 50 ÷ 2 = 25

So the area is 25 m². The calculator shows the same result, rounded to 2 decimal places.

Why the Height Must Be Perpendicular

A common mistake is using a slanted side length instead of the true height. The height is always measured at a 90° angle to the base. In a right triangle, the height is simply one of the legs. In an obtuse triangle, the height may lie outside the triangle—extend the base line and measure from the vertex down to that extended line. As long as you use the perpendicular distance, the formula works for any triangle: acute, obtuse, right, or equilateral.

When to Use This Calculator

You might need the triangle area for:

• Finding the area of a triangular plot of land or a room.
• Calculating material needed for a triangular sign, sail, or roof section.
• Solving geometry homework problems.
• Estimating surface area for painting or tiling a triangular surface.

If you only know the three side lengths, use Heron’s formula instead: Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2. If you know two sides and the included angle, use Area = ½ × a × b × sin(C).

Common Mistakes and How to Avoid Them

• Mixing units: Always convert both base and height to the same unit before multiplying. For example, 2 ft × 6 in should become 2 ft × 0.5 ft = 1 ft².
• Using the wrong height: The height must be perpendicular to the base you chose. You can pick any side as the base, but the height must correspond to that side.
• Forgetting to divide by 2: The formula is ½ × base × height, not base × height. That extra factor of 2 is what distinguishes a triangle from a rectangle.
• Rounding too early: If you round intermediate values, your final answer may be off. Keep full precision until the end, then round as needed.

Limits of the Formula

The base-times-height formula only works when you know the perpendicular height. If you only know the side lengths or angles, you need a different formula. Also, the formula assumes a flat, Euclidean triangle—it does not apply to spherical triangles (e.g., on the Earth’s surface) or curved surfaces. For very large land areas, you might need geodesic calculations that account for Earth’s curvature.

Frequently Asked Questions

Can I use any side as the base?

Yes. Any of the three sides can be the base. Just make sure you measure the height perpendicular to that side. The area will be the same no matter which side you choose, because the formula is mathematically equivalent for all three pairings.

What if the triangle is not right-angled?

The formula works for any triangle. The key is that the height must be perpendicular to the base. For an obtuse triangle, the height may fall outside the triangle—imagine extending the base line and dropping a perpendicular from the opposite vertex to that extended line.

How do I find the height if I only know the side lengths?

Use Heron’s formula to find the area first, then rearrange the area formula: height = (2 × area) / base. For example, if the area is 25 m² and the base is 10 m, the height is (2 × 25) / 10 = 5 m.

What units does the area come out in?

The area is always the square of whatever unit you used for base and height. If you enter base and height in metres, the area is in square metres (m²). If you enter feet, you get square feet (ft²). To convert between square units, multiply by the square of the linear conversion factor (e.g., 1 ft = 0.3048 m, so 1 ft² = 0.0929 m²).

Is there a difference between height and altitude?

No, in geometry they are the same thing. Both refer to the perpendicular distance from a vertex to the opposite side (or its extension).

Can this calculator handle very large or very small triangles?

Yes, as long as you enter numbers in a consistent unit. For very small triangles, use millimetres or inches; for very large ones, use metres or kilometres. The calculator does not impose practical limits, but be mindful of rounding errors if you enter extremely large or small numbers.

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in b | Base | m | 10 | 0
in h | Height | m | 5 | 0
out area | Area | m² | 0.5 * b * h | 2