Area Of Parallelogram Calculator

What this calculator does

A parallelogram is a pushed-over rectangle: a four-sided shape where opposite sides are parallel and equal, but the corners lean instead of sitting square. This tool finds the area inside it from the base and the height.

Type the two in, pick your units, and you have 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 have to be positive, and the area comes out in square units of the base's unit. The base and height can be in different units, since the tool lines them up before multiplying.

The formula | area = base × height

The area of a parallelogram is:

area = base × height

The very same formula as a rectangle. That can look surprising for a leaning shape, so the next part is worth a read, because it is the whole reason the slant does not matter.

Why it matches a rectangle

Take a parallelogram and slice a right-angled triangle off the slanted end. Now slide that triangle across to the other end, where it fits perfectly into the gap. What you are left with is a plain rectangle, with the exact same base and the exact same height you started with.

Nothing was added or thrown away, just moved, so the area did not change. A parallelogram holds the same space as a rectangle on the same base and height. Leaning the rectangle over does not change how much fits inside it.

The height is the straight-across one

This is the one spot people trip on. The height is the perpendicular distance between the two parallel bases, measured straight across at a right angle. It is not the length of the slanted side.

On a parallelogram that leans a long way, the slanted side is noticeably longer than the straight-across height, and using it by mistake gives an area that is too big. Measure the height at a right angle to the base and you are fine.

Units and rounding

The area comes out in square units of the base's unit, since you are multiplying a length by a length. If the base and height are in different units, the tool converts one to match the other first. 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 base by height: 6 × 4 = 24.

So the area is 24 cm², the same as a 6 by 4 rectangle, however far the parallelogram happens to lean.

Questions people ask

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

It is 24 square units. Multiply the base by the perpendicular height: 6 × 4.

Why is the area the same as a rectangle's?

Because a parallelogram can be cut and rearranged into a rectangle with the same base and height. Sliding a triangle from one end to the other does not change the area.

Is the height the length of the slanted side?

No. The height is the straight, perpendicular distance between the two parallel bases. On a leaning parallelogram it is shorter than the slanted side.

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.

How does this relate to other shapes?

A rectangle is a parallelogram with square corners, and a triangle is exactly half of a parallelogram with the same base and height, which is why a triangle's area is ½ × base × height.

References

A note on where this comes from. That a parallelogram has the same area as a rectangle on the same base and between the same parallels is a classical result, proved by Euclid in the Elements around 300 BCE, the formal version of the cut-and-slide rearrangement above. For further reading, see Parallelogram.

1. Euclid, Elements, Book I, Proposition 35 (c. 300 BCE), that parallelograms on the same base and between the same parallels are equal in area.