Parallelogram Area Calculator

How to Calculate the Area of a Parallelogram

A parallelogram is a four-sided figure (quadrilateral) with two pairs of parallel sides. Opposite sides are equal in length, and opposite angles are equal. Rectangles, rhombi, and squares are all special types of parallelograms.

There are three ways to calculate the area of a parallelogram, depending on the information you have. Our calculator above supports all three methods — just select the one that matches your available measurements.

Method 1: Base and Height

The most common and simplest method. The formula is:

A = b × h

The area A equals the length of the base (b) multiplied by the perpendicular height (h). The height must be measured at a right angle (90°) to the base — not along the slanted side.

Example: A parallelogram with base = 10 and height = 6.

• A = 10 × 6 = 60 square units

Method 2: Two Sides and Interior Angle

When you know the lengths of two adjacent sides and the angle between them, use trigonometry:

A = a × b × sin(α)

The area equals the product of the two side lengths multiplied by the sine of the included angle α.

Example: Side a = 7, side b = 8, angle α = 60°.

• sin(60°) = 0.866025
• A = 7 × 8 × 0.866025 = 48.50 square units

This method works because h = a × sin(α), so the formula is equivalent to b × h. When α = 90°, sin(90°) = 1, and the parallelogram becomes a rectangle.

Method 3: Diagonals and Angle Between

If you know the lengths of the two diagonals and the angle where they intersect:

A = ½ × d₁ × d₂ × sin(θ)

The area equals one-half the product of the two diagonal lengths multiplied by the sine of the angle θ between them.

Example: Diagonal d₁ = 9, diagonal d₂ = 12, angle θ = 30°.

• sin(30°) = 0.5
• A = ½ × 9 × 12 × 0.5 = 27 square units

Properties of a Parallelogram

• Opposite sides are equal and parallel
• Opposite angles are equal
• Consecutive angles are supplementary (add up to 180°)
• Diagonals bisect each other (they cross at their midpoints)
• The sum of all interior angles is 360°

Special Cases

• Rectangle: A parallelogram where all angles are 90° → A = length × width
• Rhombus: A parallelogram where all sides are equal → A = ½ × d₁ × d₂
• Square: Both a rectangle and a rhombus → A = side²

Frequently Asked Questions

What is the difference between base × height and side × side?

The base is one side of the parallelogram, but the height is the perpendicular distance to the opposite side — not the other side. In a parallelogram that isn't a rectangle, the slanted side is longer than the height. Using side × side would overestimate the area unless you multiply by sin(angle).

Do I need to know the angle to calculate area?

If you know the base and perpendicular height, no angle is needed (Method 1). If you only know the side lengths or diagonal lengths, then yes — you need an angle to use Method 2 or Method 3.

What if my angle is in radians?

Use our Angle Converter to convert radians to degrees first, or enter the angle in degrees directly. The calculator expects angles in degrees.

Is a rectangle a parallelogram?

Yes! A rectangle is a special parallelogram where all four angles are 90°. Since sin(90°) = 1, the area formula simplifies to A = base × height = length × width.

How do I find the height if I only know the sides and angle?

The height can be calculated from the side and angle: h = a × sin(α), where a is the slanted side and α is the interior angle. Then use A = base × h.