Our Parallelogram Calculator is a powerful, all-in-one tool that instantly computes the key properties of a parallelogram. Whether you are a student, teacher, professional, or DIY enthusiast, this calculator eliminates the hassle of complex manual calculations. Simply enter the values you know, and our tool will determine all missing parameters such as area, perimeter, diagonals, height, and angles with precision and detailed, step-by-step explanations.

A parallelogram is a four-sided figure (quadrilateral) with two pairs of parallel sides. Its opposite sides are equal in length, and its opposite angles are equal in measure. This fundamental shape is common in geometry, architecture, and engineering. Our calculator recognizes the various relationships between its properties, allowing you to find a solution from almost any combination of known values.

How to Use the Parallelogram Calculator

1. Select Calculation Type: Choose the quantity you want to find from the dropdown menu (e.g., “Find Area K | Given b, h” or “Find B, p, q, h, P, K | Given a, b, A”).
2. Enter Your Values: Input the known measurements into the corresponding fields. The tool will automatically request the specific values needed for your chosen calculation.
3. Choose Units: Select your preferred unit of measurement (e.g., meters, inches, feet). All results will be displayed in this unit.
4. Set Precision: Use the significant figures dropdown to control the rounding of your results.
5. Calculate: Click the “Calculate” button. The results section will instantly display all computed values in a clear, well-organized table.

The Formulas Behind the Calculations

Our calculator is built on established geometric and trigonometric formulas. It intelligently selects the correct formula based on your inputs. Below are the core formulas it utilizes.

Property	Formula	Description
Area (K)	K = b × h	Base multiplied by height.
	K = a × b × sin(A)	Product of two sides and the sine of the included angle.
Perimeter (P)	P = 2 × (a + b)	Twice the sum of two adjacent sides.
Height (h)	h = a × sin(A)	Side length multiplied by the sine of an angle.
Diagonals (p & q)	p = √(a² + b² - 2ab × cos(A))	Law of Cosines to find the shorter diagonal (p).
	q = √(a² + b² + 2ab × cos(A))	Law of Cosines to find the longer diagonal (q).
Angles	A + B = 180° A = C B = D	Adjacent angles are supplementary; opposite angles are equal.

For more complex calculations where three parameters are known (e.g., two sides and a diagonal), the calculator uses systems of these formulas to solve for all unknowns simultaneously.

Help Section: Understanding the Parameters

This section explains each parameter used in the calculator to help you input the correct values.

Parameter	Symbol	Description
Side Length a	a	The length of one side of the parallelogram.
Side Length b (Base)	b	The length of an adjacent side to a. Often used as the base for area calculations.
Height	h	The perpendicular distance between the base (b) and its opposite side. It is not the same as the side length a.
Angle A	∠A	The angle at vertex A, located between sides a and b. Angle C (∠C) is always equal to it.
Angle B	∠B	The angle at vertex B, adjacent to angle A. Angles A and B are supplementary (A + B = 180°). Angle D (∠D) is always equal to it.
Diagonal p	p	The length of the shorter diagonal connecting vertices A and C.
Diagonal q	q	The length of the longer diagonal connecting vertices B and D.
Perimeter	P	The total distance around the parallelogram.
Area	K	The amount of space enclosed within the parallelogram, in square units.

FAQs

Q1. How do you find the area of a parallelogram without the height?

A: You can calculate the area without the height if you know the lengths of two adjacent sides and the measure of the included angle. Use the formula: Area = a × b × sin(angle) .

Q2. Is a rectangle a parallelogram?

A: Yes. A rectangle is a special type of parallelogram where all interior angles are right angles (90°).

Q3. Are the diagonals of a parallelogram equal?

A: Only in special cases like rectangles and squares. In a general parallelogram, the diagonals are not equal in length, but they do bisect each other.

Q4. Can I use this calculator for a rhombus or a square?

A: Absolutely. A rhombus is a parallelogram with all sides equal, and a square is a parallelogram with all sides equal and all angles right angles. The formulas used by this calculator apply to all parallelograms, including these special types.

Q5. What if I only know the lengths of the two diagonals and one side?

Our calculator can handle this! Select the calculation type “Find A, B, b, h, P, K | Given a, p, q” from the dropdown menu and input the known values.