Math
Parallelogram Calculator
Give the parallelogram calculator two adjacent sides and the angle between them, or a base and its height, and it returns the area, perimeter, both diagonals (from the law of cosines), the height onto each side, and both interior angles.
One side; treated as the base.
The adjacent side.
Any interior angle. Its neighbor is 180° minus this.
Pick the unit your measurements use. Area is reported in square units and volume in cubic units.
Try an example
Result
Area
—
- Perimeter
- —
- Diagonals (long, short)
- —
- Heights (onto a, onto b)
- —
- Angles
- —
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Study path
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What the parallelogram calculator solves
Give the parallelogram calculator two adjacent sides and the angle between them, or a The number being raised to a power, or the side a shape's height is measured from. and its height, and it returns the area, perimeter, both diagonals (from the law of cosines), the height onto each side, and both interior angles.
Formula
How to use it
- Choose the mode: two sides with the included angle, or base and height.
- Enter the values in one unit. In base-height mode, add the slanted side if you also want perimeter, diagonals, and angles.
- Read the area, perimeter, diagonals, heights, and angles, then open the work to see each formula.
How to read the answer
The area equals base times perpendicular height, which is the same as a·b·sin θ. The two diagonals are different unless the angle is 90° (a rectangle); the longer one lies opposite the obtuse angle. Each height is the perpendicular distance between a pair of parallel sides.
Common mistakes and edge cases
- Using the slanted side as the height. The height is perpendicular to the base and is always shorter than the slanted side (equal only for a rectangle).
- Entering an angle of 0° or 180° — the shape collapses to a line and has no area.
- Mixing up which angle you have: the calculator accepts either interior angle because sin θ = sin(180° − θ).
- In base-height mode, a slanted side shorter than the height is impossible and is rejected.
Worked examples
Sides 8 and 5 with a 60° angle
Area
34.641
Sides 4 and 3 at 90° (a rectangle)
Area
12
Base 10, height 4, slanted side 5
Area
40
Base 7.5, height 2.4, no side given
Area
18
Obtuse angle 120°
Area
31.1769
Angle 180° (degenerate)
Area
Error
Side shorter than height (impossible)
Area
Error
Frequently asked questions
What is the area of a parallelogram?+
Base times perpendicular height, A = b·h. If you know two sides and the angle between them instead, A = a·b·sin θ — both give the same number.
How do I find the diagonals of a parallelogram?+
Use the law of cosines on the triangles the diagonals form: p = sqrt(a² + b² + 2ab·cos θ) and q = sqrt(a² + b² − 2ab·cos θ), where θ is the acute angle. They are equal only for a rectangle.
What are the angles of a parallelogram?+
Opposite angles are equal and adjacent angles add to 180°. If one angle is 60°, the others are 120°, 60°, 120°.
Is a rectangle a parallelogram?+
Yes — a rectangle is a parallelogram with 90° angles. Rhombuses (all sides equal) and squares are parallelograms too.
Why are there two heights?+
Each pair of parallel sides has its own perpendicular distance. The height onto side a is b·sin θ; the height onto side b is a·sin θ. Either one times its base gives the same area.
Can I find the perimeter from base and height only?+
No. The slanted side can be any length ≥ the height, so you need it (or the angle) for the perimeter. Enter it in the optional field.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026