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How to Round a Number Down in Python?

<div>Problem Formulation: Given a float number. How to round the float down in Python?
Here are some examples of what you want to accomplish:
<ul>
<li><code>42.52 --> 42</code></li>
<li><code>21.99999 --> 22</code></li>
<li><code>-0.1 --> -1</code></li>
<li><code>-2 --> -2</code></li>
</ul>
Solution: If you have little time, here’s the most straightforward answer:
To round a positive or negative number <code>x</code> down in Python, apply <a rel="noreferrer noopener" href="https://blog.finxter.com/daily-python-puzzle-integer-division/" data-type="post" data-id="91" target="_blank">integer division</a> <code>//</code> to <code>x</code> and divide by <code>1</code>. Specifically, the expression <code>x//1</code> will first perform normal float division and then throw away the remainder—effectively “rounding <code>x</code> down”. 
In general, there are multiple ways to round a float number <code>x</code> down in Python:
<ul>
<li>Vanilla Python: The expression <code>x//1</code> will first perform normal division and then skip the remainder—effectively “rounding <code>x</code> down”.</li>
<li>Round down: The <code>math.floor(x)</code> function rounds number <code>x</code> down to the next full integer.</li>
<li>Round down (float representation): Alternatively, <code>numpy.floor(x)</code> rounds down and returns a float representation of the next full integer (e.g., <code>2.0</code> instead of <code>2</code>).</li>
<li>Round up: The <code>math.ceil(x)</code> function rounds number <code>x</code> up to the next full integer. </li>
<li>Round up and down: The Python built-in <code>round(x)</code> function rounds <code>x</code> up and down to the closest full integer.</li>
</ul>
Let’s dive into each of those and more options in the remaining article. I guarantee you’ll get out of it having learned at least a few new Python tricks in the process!
<h2>Method 1: Integer Division (x//1)</h2>
The most straightforward way to round a positive or negative number <code>x</code> down in Python is to use <a href="https://blog.finxter.com/daily-python-puzzle-integer-division/" data-type="post" data-id="91" target="_blank" rel="noreferrer noopener">integer division</a> <code>//</code> by <code>1</code>. The expression <code>x//1</code> will first perform normal division and then skip the remainder—effectively “rounding <code>x</code> down”. 
For example:
<ul>
<li><code>42.52//1 == 42</code></li>
<li><code>21.99//1 == 21</code></li>
<li><code>-0.1//1 == -1</code></li>
<li><code>-2//1 == -2</code></li>
</ul>
This trick works for positive and negative numbers—beautiful isn’t it? <img src="https://s.w.org/images/core/emoji/13.1.0/72x72/1f33b.png" alt="?" class="wp-smiley" style="height: 1em; max-height: 1em;" />
Here are a couple of Python code examples:
<pre class="EnlighterJSRAW" data-enlighter-language="python" data-enlighter-theme="" data-enlighter-highlight="1-2" data-enlighter-linenumbers="" data-enlighter-lineoffset="" data-enlighter-title="" data-enlighter-group="">def round_down(x): return x//1 print(round_down(42.52))
# 42 print(round_down(21.99999))
# 21 print(round_down(-0.1))
# -1 print(round_down(-2))
# -2
</pre>
<img src="https://s.w.org/images/core/emoji/13.1.0/72x72/1f393.png" alt="?" class="wp-smiley" style="height: 1em; max-height: 1em;" /> Info: The double-backslash <code>//</code> operator performs integer division and the single-backslash <code>/</code> operator performs float division. An example for integer division is <code>40//11 = 3</code>. An example for float division is <code>40/11 = 3.6363636363636362</code>.
Feel free to watch the following video for some repetition or learning:
<figure class="wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio">
<div class="wp-block-embed__wrapper">
<iframe loading="lazy" title="Python Division Deep Dive" width="780" height="439" src="https://www.youtube.com/embed/WK5Q60qME-8?feature=oembed" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
</div>
</figure>
<h2>Method 2: math.floor()</h2>
To round a number down in Python, import the <code>math</code> library with <code>import math</code>, and call <code><a rel="noreferrer noopener" href="https://blog.finxter.com/python-math-functions/" data-type="post" data-id="69128" target="_blank">math.floor(number)</a></code>.
The function returns the floor of the specified <code>number</code> that is defined as the largest integer <a rel="noreferrer noopener" href="https://blog.finxter.com/python-less-than-or-equal-to/" data-type="post" data-id="30938" target="_blank">less than or equal</a> to <code>number</code>.
<img src="https://s.w.org/images/core/emoji/13.1.0/72x72/1f4a1.png" alt="?" class="wp-smiley" style="height: 1em; max-height: 1em;" /> Note: The <code>math.floor()</code> function correctly rounds down floats to the next-smaller full integer for positive and negative integers.
Here’s a code example that rounds our five numbers down to the next-smaller full integer: 
<pre class="EnlighterJSRAW" data-enlighter-language="python" data-enlighter-theme="" data-enlighter-highlight="" data-enlighter-linenumbers="" data-enlighter-lineoffset="" data-enlighter-title="" data-enlighter-group="">import math print(math.floor(42.52))
# 42 print(math.floor(21.99999))
# 21 print(math.floor(-0.1))
# -1 print(math.floor(-2))
# -2
</pre>
The following video shows the <code>math.floor()</code> as well as the <code>math.ceil()</code> functions — feel free to watch it to gain a deeper understanding:
<figure class="wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio">
<div class="wp-block-embed__wrapper">
<iframe loading="lazy" title="Python Math floor(), ceil(), trunc(), and modf()" width="780" height="585" src="https://www.youtube.com/embed/MZb2liD3Iuw?feature=oembed" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
</div>
</figure>
<h2>Method 3: np.floor()</h2>
To round a number down in Python, import the <a rel="noreferrer noopener" href="https://blog.finxter.com/numpy-tutorial/" data-type="post" data-id="1356" target="_blank">NumPy library</a> with <code>import numpy as np</code>, and call <code>np.floor(number)</code>.
The function returns the floor of the specified <code>number</code> that is defined as the largest integer <a rel="noreferrer noopener" href="https://blog.finxter.com/python-less-than-or-equal-to/" data-type="URL" data-id="https://blog.finxter.com/python-less-than-or-equal-to/" target="_blank">less than or equal</a> to <code>number</code>.
Here’s an example:
<pre class="EnlighterJSRAW" data-enlighter-language="python" data-enlighter-theme="" data-enlighter-highlight="" data-enlighter-linenumbers="" data-enlighter-lineoffset="" data-enlighter-title="" data-enlighter-group="">import numpy as np print(np.floor(42.52))
# 42.0 print(np.floor(21.99999))
# 21.0 print(np.floor(-0.1))
# -1.0 print(np.floor(-2))
# -2.0
</pre>
Both <code>math.floor()</code> and <code>np.floor()</code> round down to the next full integer. The difference between <code>math.floor()</code> and <code>np.floor()</code> is that the former returns an integer and the latter returns a float value.
<h2>Method 4: int(x)</h2>
Use the <code><a rel="noreferrer noopener" href="https://blog.finxter.com/python-int-function/" data-type="post" data-id="22715" target="_blank">int(x)</a></code> function to round a positive number <code>x>0</code> down to the next integer. For example, <code>int(42.99)</code> rounds <code>42.99</code> down to the answer <code>42</code>. 
Here’s an example for positive numbers where <code>int()</code> will round down:
<pre class="EnlighterJSRAW" data-enlighter-language="python" data-enlighter-theme="" data-enlighter-highlight="" data-enlighter-linenumbers="" data-enlighter-lineoffset="" data-enlighter-title="" data-enlighter-group="">print(int(42.52))
# 42 print(int(21.99999))
# 21
</pre>
However, if the number is negative, the function <code>int()</code> will round up! Here’s an example for negative numbers:
<pre class="EnlighterJSRAW" data-enlighter-language="python" data-enlighter-theme="" data-enlighter-highlight="" data-enlighter-linenumbers="" data-enlighter-lineoffset="" data-enlighter-title="" data-enlighter-group="">print(int(-0.1))
# 0 print(int(-2))
# -2
</pre>
Before I show you how to overcome this limitation for negative numbers, feel free to watch my explainer video on this function here:
<figure class="wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio">
<div class="wp-block-embed__wrapper">
<iframe loading="lazy" title="Python int() Function" width="780" height="439" src="https://www.youtube.com/embed/JKDzKWtlaQE?feature=oembed" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
</div>
</figure>
<h2>Method 5: int(x) – bool(x%1)</h2>
You can also use the following vanilla Python snippet to round a number <code>x</code> down to the next full integer:
<ul>
<li>If <code>x</code> is positive, round down by calling <code>int(x)</code>.</li>
<li>If <code>x</code> is negative, round up by calling <code>int(x) - bool(x%1)</code>. </li>
</ul>
Explanation: Any non-zero expression passed into the <code><a rel="noreferrer noopener" href="https://blog.finxter.com/python-bool/" data-type="post" data-id="17841" target="_blank">bool()</a></code> function will yield <code>True</code> which is represented by integer 1. 
The <a rel="noreferrer noopener" href="https://blog.finxter.com/python-modulo/" data-type="post" data-id="104" target="_blank">modulo</a> expression <code>x%1</code> returns the decimal part of <code>x</code>. 
<ul>
<li>If it is non-zero, we subtract <code>bool(x%1) == 1</code>, i.e., we round down. </li>
<li>If it is zero (for whole numbers), we subtract <code>bool(x%1) == 0</code>, i.e., we’re already done.</li>
</ul>
Here’s what this looks like in a simple Python function:
<pre class="EnlighterJSRAW" data-enlighter-language="python" data-enlighter-theme="" data-enlighter-highlight="1-4" data-enlighter-linenumbers="" data-enlighter-lineoffset="" data-enlighter-title="" data-enlighter-group="">def round_down(x): if x<0: return int(x) - bool(x%1) return int(x) print(round_down(42.52))
# 42 print(round_down(21.99999))
# 21 print(round_down(-0.1))
# -1 print(round_down(-2))
# -2
</pre>
Alternatively, you can use the following slight variation of the function definition:
<pre class="EnlighterJSRAW" data-enlighter-language="python" data-enlighter-theme="" data-enlighter-highlight="3" data-enlighter-linenumbers="" data-enlighter-lineoffset="" data-enlighter-title="" data-enlighter-group="">def round_down(x): if x<0: return int(x) - int(x)!=x return int(x)</pre>
<h2>Method 6: round()</h2>
This method is probably not exactly what you want because it rounds a number up and down, depending on whether the number is closer to the smaller or larger next full integer. However, I’ll still mention it for comprehensibility.
<hr class="wp-block-separator"/>
Python’s built-in <code><a href="https://blog.finxter.com/python-round-a-simple-guide-with-video/" data-type="post" data-id="23673" target="_blank" rel="noreferrer noopener">round()</a></code> function takes two input arguments: 
<ul>
<li>a <code>number</code> and </li>
<li>an optional <code>precision</code> in decimal digits. </li>
</ul>
It rounds the number to the given precision and returns the result. The return value has the same type as the input number—or integer if the <code>precision</code> argument is omitted. 
Per default, the precision is set to 0 digits, so <code>round(3.14)</code> results in <code>3</code>.
Here are three examples using the <code>round()</code> function—that show that it doesn’t exactly solve our problem.
<pre class="EnlighterJSRAW" data-enlighter-language="python" data-enlighter-theme="" data-enlighter-highlight="" data-enlighter-linenumbers="" data-enlighter-lineoffset="" data-enlighter-title="" data-enlighter-group="">import math print(round(42.42))
# 42 print(round(21.00001))
# 21 print(round(-0.1))
# 0
</pre>
Again, we have a video on the <code>round()</code> function — feel free to watch for maximum learning!
<figure class="wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio">
<div class="wp-block-embed__wrapper">
<iframe loading="lazy" title="Python round() — A Helpful Interactive Guide" width="780" height="439" src="https://www.youtube.com/embed/B3P3dXpLoTk?feature=oembed" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
</div>
</figure>
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