What is the formula for the area of a parallelogram?

Area = base × height, where the height is the perpendicular distance between the two parallel base edges — not the length of the slant side. If you only know the slant side (s) and the included angle (x), the perpendicular height equals s × sin(x).

Does the height mean the slant side or the vertical drop?

It means the vertical (perpendicular) drop from one base edge to the other, regardless of how tilted the parallelogram is. A slant side of 8 cm at 45° gives a perpendicular height of 8 × sin(45°) = 5.66 cm. Enter that 5.66 cm value here.

A rectangle is a parallelogram — does the formula still work?

Yes. A rectangle is a special parallelogram whose angles are all 90°, so its perpendicular height equals its actual side length. The formula A = base × height is identical to length × width for a rectangle.

Can I use this for a rhombus?

Yes. A rhombus is also a parallelogram (all four sides equal). Enter the base length and the perpendicular height between the base edges, and the same formula applies. Alternatively, a rhombus area can be computed from its two diagonals as (d1 × d2) ÷ 2.

What units does this calculator use?

Any consistent unit — centimetres, metres, inches, or feet. The area result is always in the square of whatever unit you enter. If you enter metres, the area is in m². If you enter centimetres, the area is in cm².

How do I find the height if I only know the area and base?

Select "Solve for Height" from the dropdown, then enter the area and base. The calculator rearranges the formula to h = Area ÷ base and shows you the step-by-step working.

Parallelogram Area Calculator

A parallelogram is a four-sided flat shape where opposite sides are parallel and equal in length. It is one of the fundamental quadrilaterals in geometry, appearing everywhere from architectural cross-bracing and truss designs to fabric patterns, map projections, and school coursework. Calculating its area correctly — and quickly — is a skill that comes up in construction estimates, land surveying, graphic design, and competitive mathematics alike.

This calculator handles the three most common tasks in one tool: find the area from base and height, find the base when you know the area and height, or find the perpendicular height when you know the area and base. A live SVG diagram updates as you type so you always have a visual check on the proportions.

How it works

The fundamental relationship is beautifully simple:

A = b × h

where b is the length of either parallel base and h is the perpendicular height — the shortest (right-angle) distance between the two base edges. This is not the slant side. A parallelogram can lean at any angle; the formula always uses the vertical drop, not the diagonal length.

Rearranging for the unknown:

Solve for base: b = A ÷ h
Solve for height: h = A ÷ b

The calculator shows the exact substitution so you can follow every step.

A note on perpendicular height

The most common mistake is confusing the slant side with the height. If you have a parallelogram with a slant side of length s and an included interior angle theta (in degrees), the perpendicular height is:

h = s × sin(theta)

For example, a slant side of 10 cm at 60° gives a perpendicular height of 10 × sin(60°) = 10 × 0.866 = 8.66 cm. Enter that 8.66 cm as the height here.

Worked example

Suppose a plot of land is shaped like a parallelogram. The base runs 24 metres along a road and the perpendicular width across to the back fence is 9 metres. The area is:

A = 24 × 9 = 216 m²

Now suppose you know the plot is 300 m² and is 15 m deep (height), but the frontage (base) is unclear. Switching to “Solve for Base”:

b = 300 ÷ 15 = 20 m

Base	Height	Area
5 cm	3 cm	15 cm²
12 m	7 m	84 m²
24 ft	9 ft	216 ft²
100 mm	45 mm	4 500 mm²

Every calculation happens locally in your browser — no numbers are uploaded or stored.

Formula note

The formula A = b × h is derived by imagining you slice a right triangle off one end of the parallelogram and reattach it to the other end. The resulting rectangle has width b and height h, confirming that the area equals b × h — identical to a rectangle of the same base and height. This geometric proof requires no algebra: it is a pure cut-and-rearrange argument that has been known since ancient Greece.