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Parallelogram calculator

This parallelogram calculator works from two sides and the angle; a rhombus needs one side and the angle, or both diagonals. With a = 10, b = 6 and α = 30° the area is 30 and the perimeter 32, with the calculation steps.

Example: Shape and inputs: Parallelogram: sides a, b and angle · Side a 10 · Side b 6 · Angle α 30 ° → Result: Area A = 30 · Circumference C = 32. Source: Wikipedia – Parallelogramm. Updated: .

Any length unit; areas in its square, volumes in its cube.
°
Between sides a and b, greater than 0° and less than 180°
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Result

Result
Area A = 30 · Circumference C = 32
All measures
  • Side a: 10
  • Side b: 6
  • Angle α: 30°
  • Angle β (180° − α): 150°
  • Area A: 30
  • Circumference C: 32
  • Height on a: 3
  • Height on b: 5
  • Diagonal e: 15.48945
  • Diagonal f: 5.663652
Calculation steps
  • A = a · b · sin(α) = 10 · 6 · sin(30°) = 30
  • C = 2 · (a + b) = 2 · (10 + 6) = 32
  • Height on a = b · sin(α) = 3
  • e = √(a² + b² + 2 · a · b · cos(α)) = 15.48945
  • f = √(a² + b² − 2 · a · b · cos(α)) = 5.663652

How it is calculated

A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides are equal in length, opposite angles are equal, and neighbouring angles add up to 180°. A rhombus is the special case with four equal sides.

The formulas

How to use it

Choose the shape and enter the measures. Example: a = 10, b = 6 and α = 30° give A = 10 · 6 · sin 30° = 30, P = 32, ha = 3 and the diagonals e = 15.49 and f = 5.66. Check: e² + f² = 2 · (a² + b²). The unit is up to you; the area is in the square of the chosen unit.

Frequently asked questions

How do you calculate the area of a parallelogram?

A = base times height, A = a · ha. With the angle: A = a · b · sin(α). For 10, 6 and 30° that is 30.

How do you calculate the perimeter of a parallelogram?

P = 2 · (a + b). For a = 10 and b = 6 that gives 32.

How do you calculate a rhombus?

With equal sides a = b: A = a² · sin(α), or from the diagonals A = e · f ÷ 2. Choose “Rhombus” for this.

How do you find the height of a parallelogram?

ha = b · sin(α) stands perpendicular to side a. Likewise hb = a · sin(α).

How long are the diagonals?

e = √(a² + b² + 2ab·cos α) and f = √(a² + b² − 2ab·cos α). They bisect each other but, unlike in a rectangle, differ in length.

Sources and legal basis

As of: · Editorial policy

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