Area of a Parallelogram Calculator
Calculate the area of a parallelogram from base and height, from two sides and the included angle, or from two diagonals and the angle between them — plus the perimeter and a step-by-step formula wherever the given values allow it.
Input
Base and height alone can't determine the other side — fill this in to also get the perimeter.
Output
| Property | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/area-of-a-parallelogram-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"method": "base-height",
"unit": "cm",
"base": "12",
"height": "5"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `area-of-a-parallelogram-calculator` tool (Area of a Parallelogram Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/area-of-a-parallelogram-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Area of a Parallelogram Calculator — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
Also available with
Guides
A parallelogram's area can be worked out from whatever you happen to have measured — base and height, two sides and the angle between them, or two diagonals and the angle between them. This calculator covers all three, and adds the perimeter alongside the area wherever the numbers you entered make it derivable.
The formulas
Base & height (b, h) Area = b × h
Two sides & included angle (a, b, θ) Area = a × b × sin(θ)
Perimeter = 2(a + b)
Two diagonals & angle between them (d₁, d₂, θ) Area = ½ × d₁ × d₂ × sin(θ)
Side a = √((d₁/2)² + (d₂/2)² − 2(d₁/2)(d₂/2)cos(θ))
Side b = √((d₁/2)² + (d₂/2)² + 2(d₁/2)(d₂/2)cos(θ))
Perimeter = 2(a + b)Worked example: two sides of 8 cm and 5 cm with a 60° angle between them give an area of about 34.64 cm² and a perimeter of 26 cm.
How to use it
- Pick which values you know from the dropdown.
- Enter the measurements the calculator asks for — the fields update automatically.
- Pick a unit (millimeters through yards) — this labels the results only, no conversion is applied.
- The area (plus perimeter and a step-by-step formula, where derivable) updates instantly as you type.
FAQ
Why doesn't base & height give me a perimeter? Base and height alone tell you the area, but not the length of the slanted side — a parallelogram with the same base and height can be tall-and-narrow or short-and-wide. Fill in the optional "slant side" field to also get the perimeter.
How is the side length derived from the diagonals and angle? The two diagonals bisect each other, splitting the parallelogram into triangles with sides d₁/2, d₂/2 and the given angle between them — the law of cosines then gives each side length directly.
Does the unit dropdown convert my measurement? No. It labels the output (e.g. "cm" vs "in") but performs no conversion — enter every measurement in the same unit, and the results come back in that unit.
What if my angle is 0° or 180°? That would collapse the parallelogram into a straight line, so the calculator only accepts angles strictly between 0° and 180°.
Is this the same as the area & perimeter calculator? No — the area & perimeter calculator covers 9 shapes with one method per shape (base + side + height for its parallelogram mode). This tool is the dedicated parallelogram solver with three input methods and derived side lengths.
Privacy
Everything runs locally in your browser — the measurements you enter are never uploaded or stored anywhere.