Parallelogram Calculator
Enter any valid combination of parallelogram dimensions to instantly get area, perimeter, height, interior angles, and diagonals. Designed to be more flexible than classic single-form calculators.
parallel sides
perpendicular to base
leave blank if unknown
included angle
Area from diagonals: A = (d1 × d2 × sin φ)/2
Parallelogram formulas used
Area (base & height): \( A = b \cdot h \)
Area (sides & angle): \( A = a \cdot b \cdot \sin(\theta) \)
Perimeter: \( P = 2(a + b) \)
Height (relative to a): \( h = b \cdot \sin(\theta) \)
Diagonals: \( d_1 = \sqrt{a^2 + b^2 - 2ab\cos(\theta)} \), \( d_2 = \sqrt{a^2 + b^2 + 2ab\cos(\theta)} \)
Area (diagonals & angle φ): \( A = \frac{d_1 d_2 \sin(\varphi)}{2} \)
FAQs
Can I use any units?
Yes. As long as you use the same unit for all inputs, the output area will be in the corresponding squared unit (cm → cm², ft → ft², etc.).
Why is the perimeter missing in the diagonals tab?
To compute the perimeter we need at least one side length. Provide side a in the field labeled “Optional side a.”
When is a parallelogram a rhombus or a rectangle?
A rhombus has all sides equal. A rectangle has 90° angles. If both are true, it’s a square. The calculator shows a note when it detects these patterns.
Formula (LaTeX) + variables + units
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Area (base & height): \( A = b \cdot h \) Area (sides & angle): \( A = a \cdot b \cdot \sin(\theta) \) Perimeter: \( P = 2(a + b) \) Height (relative to a): \( h = b \cdot \sin(\theta) \) Diagonals: \( d_1 = \sqrt{a^2 + b^2 - 2ab\cos(\theta)} \), \( d_2 = \sqrt{a^2 + b^2 + 2ab\cos(\theta)} \) Area (diagonals & angle φ): \( A = \frac{d_1 d_2 \sin(\varphi)}{2} \)
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.