# Parallelogram Calculator

Calculate parallelogram area, perimeter, and diagonals from sides, height, and angle. Free online parallelogram calculator with instant results.

## What this calculates

Calculate the area, perimeter, and diagonals of any parallelogram. Provide the two side lengths plus either the height or the included angle for complete results.

## Inputs

- **Side a (base)** — The base of the parallelogram.
- **Side b** — The adjacent side of the parallelogram.
- **Height** — The perpendicular height from base to opposite side.
- **Angle (degrees)** — The angle between sides a and b, in degrees.

## Outputs

- **Area** — The area of the parallelogram.
- **Perimeter** — The total length of all four sides.
- **Diagonal p** — The length of diagonal p.
- **Diagonal q** — The length of diagonal q.

## Details

A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides are equal, opposite angles are equal, and the diagonals bisect each other.

Parallelogram Formulas

- Area (from height): A = base x height

- Area (from angle): A = a x b x sin(angle)

- Perimeter: P = 2 x (a + b)

- Diagonals: p = sqrt(a^2 + b^2 - 2ab x cos(angle)), q = sqrt(a^2 + b^2 + 2ab x cos(angle))

Special Cases

A rectangle is a parallelogram with all right angles. A rhombus is a parallelogram with all sides equal. A square is both a rectangle and a rhombus. Understanding parallelograms helps you work with all these special shapes.

## Frequently Asked Questions

**Q: How do I calculate the area of a parallelogram?**

A: There are two common methods. If you know the base and height: A = base x height (where height is the perpendicular distance). If you know two sides and the included angle: A = a x b x sin(angle). For a parallelogram with base 8, side 5, and angle 60 degrees: A = 8 x 5 x sin(60) = 40 x 0.866 = 34.64.

**Q: What are the properties of a parallelogram?**

A: A parallelogram has several key properties: opposite sides are parallel and equal in length; opposite angles are equal; consecutive angles are supplementary (sum to 180 degrees); diagonals bisect each other; and the area equals base times height. These properties make parallelograms predictable and useful in engineering and design.

**Q: How do I find the diagonals of a parallelogram?**

A: Use the law of cosines. For a parallelogram with sides a and b and included angle theta: the shorter diagonal p = sqrt(a^2 + b^2 - 2ab x cos(theta)) and the longer diagonal q = sqrt(a^2 + b^2 + 2ab x cos(theta)). The diagonals bisect each other but are generally not equal.

**Q: Is every rectangle a parallelogram?**

A: Yes, every rectangle is a special case of a parallelogram where all angles are 90 degrees. Similarly, every square is both a rectangle and a rhombus, which are both parallelograms. The hierarchy is: square is a subset of rectangle, which is a subset of parallelogram, which is a subset of quadrilateral.

**Q: What is the difference between a parallelogram and a trapezoid?**

A: A parallelogram has two pairs of parallel sides, while a trapezoid has exactly one pair of parallel sides (under the exclusive definition). This means all parallelograms have more symmetry: opposite sides are equal, opposite angles are equal, and diagonals bisect each other. Trapezoids generally lack these properties unless they are isosceles.

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Source: https://vastcalc.com/calculators/math/parallelogram
Category: Math
Last updated: 2026-04-21