Area of a Parallelogram Calculator

Area of a parallelogram formula

A parallelogram is a four-sided shape whose opposite sides are parallel and equal in length. Picture a rectangle pushed sideways: the base stays the same, the height stays the same, and so does the area.

A = base × heightThe height is measured at right angles to the base, not along the slanted side.

This works because the slanted triangle at one end can be cut off and moved to the other end, turning the parallelogram into a rectangle with the same base and height.

When you know two adjacent sides a and b and the angle θ between them instead of the height, the height is b × sin θ, which gives a second form:

A = a × b × sin θ

How to use the calculator

1. Choose the Metric you want the area reported in.
2. Enter the Base and pick the unit it was measured in.
3. Enter the perpendicular Height with its own unit. Units can differ between the boxes; the calculator converts both to the Metric unit first.
4. Press Calculate area.

If you only have the two side lengths and an angle, work out the height first as side × sin(angle), then enter that value. An angle of 90° turns the shape into a rectangle.

Worked examples

Straight measurements. A panel has a base of 7 cm and a perpendicular height of 3.3 cm. A = 7 × 3.3 = 23.1 cm².

Mixed units. A paving slab has a base of 250 cm and a height of 1.5 m. Converting the base to 2.5 m gives A = 2.5 × 1.5 = 3.75 m², which is what the calculator reports with Metric set to m.

From sides and an angle. A frame has sides of 8 cm and 5 cm meeting at 30°. The height is 5 × sin 30° = 2.5 cm, so A = 8 × 2.5 = 20 cm². The direct formula agrees: 8 × 5 × sin 30° = 20.

Rhombus. A rhombus is a parallelogram with four equal sides. If you know its diagonals p and q, A = p × q ÷ 2: diagonals of 6 and 8 give 24.

Common mistakes

• Using the slanted side as the height. The slanted side is always longer than the true height unless the angle is 90°, so the area comes out too large.
• Multiplying the two sides. For a non-rectangular parallelogram, a × b overstates the area by a factor of 1 ÷ sin θ.
• Mixing units without converting. Multiplying meters by centimeters gives a meaningless number. Pick the units in the selectors and let the tool convert.
• Forgetting the square. The answer is in square units. To change them, see the area unit converter.

Where parallelograms turn up

Parallelograms are everywhere once you look for slanted rectangles: a leaning wall panel, a tiled floor laid on the diagonal, the side face of a ramp, the pane of a skewed window frame, or one section of a hipped roof. In each case the usable measurements are the length of one edge and the distance straight across to the opposite edge.

Example. A roof section is a parallelogram with a 12 m eave and a perpendicular height of 4.5 m up the slope. Its area is 12 × 4.5 = 54 m². If roofing sheets cost 18 per square meter, the material for this section costs 54 × 18 = 972, before allowing for overlaps and waste.

Surveyors and designers also use the sine form when the slanted side and the angle are easier to measure than the height, as in the 8 cm and 5 cm frame example above.

Related shapes

A parallelogram with a right angle is a rectangle, and one with four equal sides and right angles is a square. Cutting a parallelogram along a diagonal produces two equal triangles, so each has half the area. A trapezoid has only one pair of parallel sides, and averaging those two bases turns it into a parallelogram-style calculation. The general area calculator covers all of these.