Triangle Area Calculator: Formula & Examples

This calculator works out the area of a triangle from the base and height you enter, returning the result in square units. You input the base length and the perpendicular height, and it gives you the area, which is half the base multiplied by the height. The tool also shows the same result using the standard formula so you can check your own working.

Formula

The area of a triangle is given by:

Area = ½ × base × height

In symbols: A = ½ × b × h

• A – area, in square units (e.g., m², cm², ft²)
• b – base, the length of one side of the triangle, in linear units (e.g., m, cm, ft)
• h – height, the perpendicular distance from the base to the opposite vertex, in the same linear units

The height must be measured at a right angle to the base. If you use a slanted side instead, the formula gives a different (incorrect) result.

Worked Example

Using the default values from the calculator: base = 6 m, height = 4 m.

1. Write down the formula: A = ½ × b × h
2. Substitute the values: A = ½ × 6 × 4
3. Multiply 6 × 4 = 24
4. Take half: 24 ÷ 2 = 12

The area is 12 m². The calculator shows the same result, rounded to 2 decimal places.

When to Use This Formula

Use the base‑height formula whenever you know the length of one side (the base) and the perpendicular distance from that side to the opposite corner. This works for any triangle – right, acute, or obtuse – as long as the height is measured at right angles to the chosen base.

Common real‑world uses:

• Floor area of a triangular room or garden plot
• Material needed for a triangular sail, banner, or roof section
• Land surveying when a parcel is triangular
• Geometry homework and exam problems

If you do not know the height, you can find it using trigonometry or Heron’s formula (which uses all three side lengths). This calculator is specifically for the base‑height method.

How to Read the Result

The result is always in square units, matching the unit you used for base and height. If you enter metres, you get square metres (m²); if you enter feet, you get square feet (ft²).

For example:

• Base 10 cm, height 5 cm → area = 25 cm²
• Base 3 ft, height 2 ft → area = 3 ft²
• Base 8 m, height 6 m → area = 24 m²

The number itself tells you how many unit squares fit inside the triangle. A triangle with base 6 and height 4 contains 12 squares of 1 m × 1 m.

Common Mistakes

• Using a slanted side as the height. The height must be perpendicular (90°) to the base. If you measure along a slanted side, you get a larger, wrong area.
• Mixing units. Convert both base and height to the same unit first. If base is in metres and height in centimetres, convert one before multiplying.
• Forgetting the ½. The area of a triangle is half the area of a rectangle with the same base and height. Leaving out the ½ doubles the answer.
• Rounding too early. If you round the height or base before multiplying, the final area can be noticeably off. Keep full precision until the end.

Limits of the Formula

The base‑height formula is simple and exact for any triangle, but it requires you to know the height. If you only know the three side lengths, you cannot directly use this formula – you would need Heron’s formula or trigonometry to find the height first.

Also, the formula assumes a flat, Euclidean triangle. On a curved surface (like the Earth’s surface for very large triangles), the area calculation is different. For everyday objects and ordinary land plots, the standard formula is accurate enough.

Frequently Asked Questions

What if the triangle is not right‑angled?

The formula works for any triangle, not just right‑angled ones. Just make sure the height is measured perpendicular to the base. For an obtuse triangle, the height may fall outside the triangle – that is fine, the formula still works.

Can I use any side as the base?

Yes, you can choose any side as the base. The height must then be measured from that side to the opposite vertex. Whichever side you choose, the area will be the same.

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

Use Heron’s formula: first calculate the semi‑perimeter s = (a+b+c)/2, then area = √(s(s‑a)(s‑b)(s‑c)). Once you have the area, you can solve for height: h = 2A / base. Or use trigonometry if you know an angle.

What units should I use for base and height?

Use the same unit for both. The area will be in that unit squared. For example, if both are in inches, the area is in square inches. If they are in different units, convert one first.

Why is the area half of base times height?

A triangle is exactly half of a rectangle with the same base and height. If you draw a diagonal across a rectangle, you get two equal triangles, each with half the rectangle’s area. That is why the ½ appears.

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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