Parallelogram Calculator
Free parallelogram calculator that finds area, perimeter, height, diagonals and angles from multiple input sets: base & height, sides & angle, or diagonals & angle. Includes formulas, special-case detection (rectangle, rhombus) and FAQs.
Full original guide (expanded)
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.