About the Parallelogram Calculator
This parallelogram calculator solves the whole shape from the two adjacent side lengths and the interior angle between them. It returns the area, the perimeter, the height measured onto each side, the length of both diagonals and the second interior angle.
Use it for geometry homework, for checking a slanted plot of land or a sheared panel, or anywhere you know the sides and the lean but not the height. Rectangles, rhombuses and squares are all special parallelograms, so the same calculator works for them too — just use a 90° angle or equal sides.
Angles are entered in degrees and must be between 0° and 180°. Opposite angles of a parallelogram are equal and neighbouring angles add up to 180°, so it does not matter which of the two angles you enter: the area and perimeter come out the same.
With the default inputs, the area is 51.9615. Change any value above to recalculate instantly.
How to use the parallelogram calculator
- 1Enter the base (side a) and the adjacent side b.
- 2Enter the angle between those two sides in degrees.
- 3Read the area, perimeter and the height onto each side.
- 4Use the diagonal lengths for bracing, cutting or layout checks.
Formula and method
The area of a parallelogram is base × height. When you know the sides instead of the height, the height onto side a is b·sin θ, so the area becomes a·b·sin θ. The perimeter is simply twice the sum of the two different side lengths.
Each diagonal splits the parallelogram into two triangles, so the law of cosines gives the diagonal lengths: √(a² + b² + 2ab·cos θ) and √(a² + b² − 2ab·cos θ). A useful check is the parallelogram law: the squares of the two diagonals add up to 2(a² + b²).
- a, b
- Adjacent side lengths
- θ
- Interior angle between sides a and b
- h
- Perpendicular height onto side a
- d
- Diagonal lengths
Worked examples
Sides 10 and 6 at 60°
The height onto the base is 6 × sin 60° ≈ 5.196, so the area is 10 × 5.196 ≈ 51.96. The diagonals are √(136 ± 60), i.e. 14 and about 8.72, and the neighbouring angle is 180° − 60° = 120°.
Right angle: an 8 × 5 rectangle
At 90° sin θ = 1 and cos θ = 0, so the area is just 8 × 5 = 40 and both diagonals equal √(64 + 25) ≈ 9.43 — exactly what you expect for a rectangle.
Sides 12 and 7 at 45°
The height is 7 × sin 45° ≈ 4.95, giving an area of about 59.40. The steep lean makes the diagonals very different: about 17.66 and 8.61.
Frequently asked questions
How do you find the area of a parallelogram?+
Multiply the base by the perpendicular height (A = b × h). If you only know the two sides and the angle between them, use A = a × b × sin θ instead.
Are the diagonals of a parallelogram equal?+
Only when the parallelogram is a rectangle (or square). In general the diagonals differ in length but always bisect each other, and their squares sum to 2(a² + b²).
What do the angles of a parallelogram add up to?+
All four interior angles add up to 360°. Opposite angles are equal and any two neighbouring angles add up to 180°, so knowing one angle gives you all four.
Is a rhombus a parallelogram?+
Yes. A rhombus is a parallelogram with four equal sides, a rectangle is one with four right angles, and a square is both. The formulas on this page apply to all of them.
Why is the slanted side not the height?+
Height is measured perpendicular to the base. The slanted side is longer than the height unless the angle is 90°, which is why the area uses b·sin θ rather than b.