Parallelogram Perimeter Calculator
Find the perimeter of any parallelogram instantly. Choose from three formula modes: two side lengths, one side plus both diagonals, or base plus height plus angle. Results update as you type, with full step-by-step working shown below the answer.
Formula
Worked example
A parallelogram with sides a = 8 cm and b = 5 cm has perimeter P = 2 x (8 + 5) = 2 x 13 = 26 cm. Using the diagonal formula with a = 8, e = 10, f = 8: b = sqrt((100 + 64)/2 - 64) = sqrt(82 - 64) = sqrt(18) = 4.24, P = 2(8 + 4.24) = 24.49 cm.
What is a parallelogram?
A parallelogram is a four-sided polygon (quadrilateral) in which opposite sides are parallel and equal in length. Rectangles, rhombuses, and squares are all special cases of parallelograms. The interior angles come in two equal pairs that add up to 360 degrees, and the two diagonals bisect each other at the midpoint. Because opposite sides are always equal, you only ever need the length of two adjacent sides (a and b) to find the perimeter.
How to calculate the perimeter of a parallelogram
The most direct formula is P = 2(a + b), where a and b are the lengths of the two adjacent sides. If you do not know both side lengths directly, two alternative formulas cover the usual cases. When you know one side (a) and both diagonals (e and f), the parallelogram law gives b = sqrt((e^2 + f^2)/2 - a^2), after which P = 2(a + b). When you know the base (a), the perpendicular height (h), and the interior angle (alpha) between the base and side b, the side b = h / sin(alpha), giving P = 2(a + h / sin(alpha)). All three formulas are equivalent for a valid parallelogram.
Unit conversion and practical tips
This calculator works in both metric (centimetres, metres) and imperial (inches, feet) units. Switch the unit selector before entering your measurements and the result will display in the same unit. When measuring a physical object, measure both pairs of sides independently rather than assuming the opposite sides are perfectly equal, especially for hand-cut or manufactured parts where small deviations occur. For the diagonal formula, both diagonals must be measured to full precision: a 1 mm error in a diagonal of 20 cm can shift the computed perimeter by several millimetres.
Parallelogram perimeter vs. area
Perimeter and area are independent properties. Two parallelograms can share the same perimeter while having very different areas, because the area also depends on the height (the perpendicular distance between the two base sides), not just the side lengths. For example, a parallelogram with a = 8 cm and b = 5 cm always has perimeter 26 cm, but if the angle between sides is 90 degrees (a rectangle) the area is 40 cm^2, whereas if the angle is 30 degrees the area is 8 x 5 x sin(30) = 20 cm^2, half as large.
Parallelogram perimeter formulas
| Given | Formula | When to use |
|---|---|---|
| Two sides a and b | P = 2(a + b) | Most common; you know both pair lengths |
| Side a, diagonals e and f | P = 2a + 2√((e² + f²)/2 - a²) | Only diagonals and one side are measured |
| Base a, height h, angle | P = 2(a + h / sinα) | Height and angle are known instead of side b |
Three equivalent ways to compute the perimeter depending on which measurements are available.
Frequently asked questions
What is the formula for the perimeter of a parallelogram?
The standard formula is P = 2(a + b), where a and b are the lengths of two adjacent sides. Because opposite sides of a parallelogram are always equal, you multiply the sum of one pair by two to get the total distance around the shape.
Can I find the perimeter if I only know the diagonals?
Not without at least one side length. The parallelogram law (e^2 + f^2 = 2(a^2 + b^2)) links the two diagonals to both side lengths, so knowing e and f gives you one equation with two unknowns. If you also know one side (a), you can solve for the other (b) and then compute the perimeter.
Is the perimeter of a parallelogram the same as a rectangle with the same sides?
Yes. The perimeter depends only on the side lengths, not the angles, so a parallelogram with sides a and b has exactly the same perimeter as a rectangle with those dimensions: P = 2(a + b). The area differs because the rectangle is the maximum-area case (angle = 90 degrees).
How does the angle affect the perimeter?
The angle does not change the perimeter if you already know both side lengths a and b, because P = 2(a + b) is independent of angle. The angle only enters the calculation when you are using it to derive the unknown side b from the height: b = h / sin(angle). Once b is known, the perimeter formula is the same.
What units should I use?
Use whichever unit is most convenient for your measurements. The perimeter will be in the same unit as the inputs. This calculator lets you switch between metric and imperial at the top. Just make sure all inputs use the same unit before calculating.