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<title>Paper Sizes</title>
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<h1 class="center">Paper Sizes</h1>
<p>Did you know that international paper sizes (like A3, A4, etc) are based on the <a href="../square-root.html">square root of 2</a>?</p>
<p>Because the square root of 2 has this cool property:</p>
<p class="center larger"><b>1</b> &times; &radic;2 &times; &radic;2 = <b>2</b></p>
<p>Which lets us have this: </p>
<p class="center"><img src="images/paper-size-root2.svg" alt="paper sizes root 2"><br>
</p>
<p></p>
<p>So we can have sheets that have exactly the same <a href="../algebra/proportions.html">proportions</a> (their ratio of side lengths are the same) and <b>also</b> fit in each other perfectly: </p>
<p class="center"><img src="images/paper-size-a4-a3.svg" alt="paper sizes A4 A3"><br>
<span class="larger">Two <b>A4</b>s make an <b>A3</b><br>
and have the same proportions</span> </p>
<p>This makes things really efficient:</p>
<ul>
<li>Don't have any A3? Tape two A4's together.</li>
<li>Don't have any A5? Cut an A4 in half. </li>
</ul>
<p><b>And</b> because they have the same proportions, any artwork or document can be resized to fit on any sheet:</p>
<p class="center"><img src="images/paper-size-resize.svg" alt="paper size resize"></p>
<p>Another benefit is that you can print something out at 70% size and fit 2 pages side-by-side on just one sheet like this: </p>
<p class="center"><img src="images/paper-size-70.svg" alt="paper size resize"></p>
<p>Why 70%? Because 1/&radic;2 = <b>0.7071...</b> which is close to <b>70%</b></p>
<p>A similar enlargement is &radic;2 = <b>1.4142...</b> which is close to <b>140%</b></p>
<h2>Sizes</h2>
<p>The popular A4 size is 210 mm wide by 297 mm high: </p>
<p class="center"><img src="images/paper-size-a4.svg" alt="paper sizes"><br>
</p>
<p>With a width of 210 the height is: <span class="larger">210 &times; &radic;2 &asymp; 297</span></p>
<p>&nbsp;</p>
<p>Here are all the sizes cut from an <b>A0</b> sheet (which has an <a href="../measure/metric-area.html">area</a> of <b>1.0 m<sup>2</sup></b>):</p>
<p class="center"><img src="images/paper-sizes.svg" alt="paper sizes"></p> <p>Lastly here are the official sizes:</p>
<div class="simple">
<table align="center">
<tr>
<th height="21" align="center">size </th>
<th align="center">mm &times; mm</th>
<th align="center">about the size of a</th>
<th align="center">&nbsp;</th>
<th align="center">area</th>
</tr>
<tr>
<td height="21" align="center">A0</td>
<td align="center">841 &times; 1189</td>
<td align="center"><i>table top</i></td>
<td align="center">&nbsp;</td>
<td align="left">1.0 m<sup>2</sup></td>
</tr>
<tr>
<td height="21" align="center" >A1</td>
<td align="center">594 &times; 841</td>
<td align="center">&nbsp;</td>
<td align="center">&nbsp;</td>
<td align="left">0.5 m<sup>2</sup></td>
</tr>
<tr>
<td height="21" align="center" >A2</td>
<td align="center">420 &times; 594</td>
<td align="center"><i>monitor</i></td>
<td align="center">&nbsp;</td>
<td align="left">0.25 m<sup>2</sup></td>
</tr>
<tr>
<td height="21" align="center" >A3</td>
<td align="center">297 &times; 420</td>
<td align="center">&nbsp;</td>
<td align="center">&nbsp;</td>
<td align="left">0.125 m<sup>2</sup></td>
</tr>
<tr>
<td height="21" align="center" >A4</td>
<td align="center">210 &times; 297</td>
<td align="center"><i>writing sheet</i></td>
<td align="center">&nbsp;</td>
<td align="left">0.0624 m<sup>2</sup></td>
</tr>
<tr>
<td height="21" align="center" >A5</td>
<td align="center">148 &times; 210</td>
<td align="center">&nbsp;</td>
<td align="center">&nbsp;</td>
<td align="left">0.0311 m<sup>2</sup></td>
</tr>
<tr>
<td height="21" align="center" >A6</td>
<td align="center">105 &times; 148</td>
<td align="center">&nbsp;</td>
<td align="center">&nbsp;</td>
<td align="left">0.0155 m<sup>2</sup></td>
</tr>
<tr>
<td height="21" align="center" >A7</td>
<td align="center">74 &times; 105</td>
<td align="center"><i>note</i></td>
<td align="center">&nbsp;</td>
<td align="left">0.00777 m<sup>2</sup></td>
</tr>
<tr>
<td height="21" align="center" >A8</td>
<td align="center">52 &times; 74</td>
<td align="center">&nbsp;</td>
<td align="center">&nbsp;</td>
<td align="left">0.003848 m<sup>2</sup></td>
</tr>
<tr>
<td height="21" align="center" >A9</td>
<td align="center">37 &times; 52</td>
<td align="center">&nbsp;</td>
<td align="center">&nbsp;</td>
<td align="left">0.001924 m<sup>2</sup></td>
</tr>
<tr>
<td height="21" align="center" >A10</td>
<td align="center">26 &times; 37</td>
<td align="center"><i>stamp</i></td>
<td align="center">&nbsp;</td>
<td align="left">0.000962 m<sup>2</sup></td>
</tr>
</table>
</div>
<p>Note: you can think of the &quot;A-number&quot; as how many folds (or cuts-in-half) away from an A0 we are. So an A3 needs 3 folds of an A0, and so is &frac12;&times;&frac12;&times;&frac12; = 1/8th the size.</p>
<p>&nbsp;</p>
<div class="related">
<a href="../algebra/proportions.html">Proportions</a>
<a href="../square-root.html">Square Root</a>
<a href="index.html">Geometry Index</a>
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