Parallelogram Calculator: Area, Perimeter, Sides and Angles
Find every missing measurement of a parallelogram by entering two known values such as side lengths, angles, height or area.
Calculate Parallelogram Values
| Variable | Value |
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Units are shown for reference only and do not affect the calculation result.
How the parallelogram calculator works
The parallelogram calculator solves for every unknown side, angle, diagonal, height, perimeter and area once you enter any two known values. A parallelogram is a four sided shape with two pairs of parallel sides, and knowing just two measurements is enough to determine the rest using trigonometric identities.
Required inputs
Required inputs depend on the calculation type you select. Common combinations include both side lengths, a side and an angle, a side and the height, or the area together with one side. The calculator automatically shows only the fields needed for your chosen combination.
Parallelogram area formula explained
The parallelogram area formula is area equals base times height, or K equals b times h. When the height is unknown, area can also be found from two adjacent sides and the included angle using K equals a times b times the sine of angle A. Both formulas give the same result because height equals a times sine A.
Worked example for area
Worked examples make the formula easy to apply. If side a is 6 units, side b is 10 units, and angle A is 60 degrees, then height equals 6 times sine 60, which is about 5.2 units. Area then equals 10 times 5.2, giving approximately 51.96 square units.
Parallelogram perimeter formula
The parallelogram perimeter formula adds all four sides together. Since opposite sides are equal in length, the formula simplifies to P equals 2a plus 2b. For a parallelogram with sides of 6 and 10 units, the perimeter equals 2 times 6 plus 2 times 10, which totals 32 units.
Diagonals and angles of a parallelogram
Diagonals of a parallelogram are calculated using the law of cosines because each diagonal forms a triangle with two known sides and the angle between them. The shorter diagonal p equals the square root of a squared plus b squared minus 2ab cosine A, while the longer diagonal q equals the square root of a squared plus b squared plus 2ab cosine A.
Angle relationships
Angle relationships in a parallelogram follow two simple rules. Opposite angles are always equal, so angle A equals angle C and angle B equals angle D. Adjacent angles are supplementary, meaning angle A plus angle B always equals 180 degrees or pi radians.
Reference table of parallelogram formulas
| Quantity | Formula |
|---|---|
| Area (K) | K = b × h = a × b × sin(A) |
| Perimeter (P) | P = 2a + 2b |
| Height (h) | h = a × sin(A) |
| Diagonal p | p = sqrt(a² + b² minus 2ab cos A) |
| Diagonal q | q = sqrt(a² + b² + 2ab cos A) |
| Angle B | B = 180° minus A |
Frequently asked questions
The area of a parallelogram equals base times height, written as K equals b times h. You can also calculate area using two sides and the angle between them with the formula K equals a times b times sine of angle A.
The perimeter of a parallelogram equals two times the sum of both side lengths, written as P equals 2a plus 2b. Simply add side a and side b together, then multiply the result by two.
Yes, opposite angles in a parallelogram are always equal. Angle A equals angle C, and angle B equals angle D. Adjacent angles are supplementary, meaning angle A plus angle B equals 180 degrees.
The height of a parallelogram is found using h equals a times sine of angle A, where a is the slanted side length and A is the angle between sides a and b. Height can also be found by dividing area by base, h equals K divided by b.
The diagonals of a parallelogram are found using the law of cosines. Diagonal p equals the square root of a squared plus b squared minus 2ab cosine A, and diagonal q equals the square root of a squared plus b squared plus 2ab cosine A.
A rectangle is a special type of parallelogram where all four interior angles equal 90 degrees. A general parallelogram has opposite sides parallel and equal, but its angles can be any value as long as opposite angles match and adjacent angles add to 180 degrees.