Area Of Triangle Calculator

What this calculator does

You have a triangle, you know its base and its height, and you want the area inside it. The base is any one side you choose to measure along. The height is the straight-up distance from that base to the corner opposite it.

Type the two in, pick your units, and the tool gives you the area.

Using the calculator

1. Type the base and pick its unit.
2. Type the height and pick its unit.
3. Press Calculate.

Both values need to be positive. One thing to get right: the height is the perpendicular distance, straight up from the base to the far corner, not the length of a slanting side. On a leaning triangle those two are different, and it is the perpendicular one the formula wants.

The formula | area = ½ × base × height

The area of a triangle is:

area = ½ × base × height

Multiply the base by the height, then halve it. Any of the three sides can play the part of the base, as long as the height you pair with it is measured straight out to the opposite corner.

Why a triangle is half a rectangle

So where does the halving come from? Take any triangle and draw the rectangle that just boxes it in, the same base along the bottom, the same height up the side. The triangle fills exactly half of that rectangle, and the other half is the empty corners around it.

The rectangle's area is base × height. The triangle is half of it, so area = ½ × base × height. Euclid worked this out more than two thousand years ago, and it is the easiest way to remember why the ÷ 2 is there.

Units, mixed units, and rounding

The area comes out in square units of the base's unit, since you are multiplying a length by a length. The base and height can even be in different units: the tool converts the height into the base's unit first, then gives the area in that unit squared. A tidy result is shown in full, and a long decimal is rounded to three places.

A worked example | base 6 cm, height 4 cm

Say the base is 6 cm and the height is 4 cm.

1. Multiply the two: 6 × 4 = 24.
2. Halve it: 24 ÷ 2 = 12.

So the area is 12 cm². And the mixed units work the same way: a base of 10 cm with a height of 50 mm becomes 10 cm by 5 cm, giving ½ × 10 × 5 = 25 cm².

When to use this, and when to use the others

This tool is the right one when you have the base and the perpendicular height. If you do not, there are sister tools for the other cases. Know the three side lengths instead, or two sides and an angle? The triangle area calculator covers Heron's formula and the angle methods. Got a triangle with all three sides equal? The area of equilateral triangle calculator does it from the single side.

Questions people ask

What is the area of a triangle with base 6 and height 4?

It is 12 square units. Multiply the base by the height and halve it: ½ × 6 × 4.

Does the height mean the length of a slanting side?

No. The height is the perpendicular distance, measured straight out from the base to the opposite corner. On a leaning triangle that is shorter than the slanting side, and it is the perpendicular distance the formula needs.

Can the base and height be in different units?

Yes. The tool converts the height into the base's unit before multiplying, and labels the area in the base's unit squared.

Why is the answer in square units?

Because area is a length times a length. A base and height in centimetres give an area in square centimetres.

What if I only know the three side lengths?

Then use the triangle area calculator, which has Heron's formula for the three-sides case. This tool needs the base and the perpendicular height.

References

A note on where this comes from. That a triangle is half of the rectangle, or parallelogram, sharing its base and height is an old result, set down by Euclid in the Elements around 300 BCE, where triangles on the same base and between the same parallels are shown to be half the parallelogram. For further reading, see Triangle.

1. Euclid, Elements, Book I, Proposition 41 (c. 300 BCE), that a triangle is half of a parallelogram on the same base and of the same height.