Understanding the Difference Between Flooring and Truncating in Python

Reducing a float (a number with a decimal) to an int (a whole number) is a pretty common task in programming. In Python, you can achieve this by flooring or truncating the number with the floor and trunc methods, respectively.

Both methods are part of the math module and perform a similar function. But there is a subtle difference between the two: floor will round down to the nearest whole number, while trunc rounds towards 0.

Intro to Flooring

The floor method will round a number down to the nearest whole number. This is useful in cases where you receive a non-whole number and, for what ever reason, don’t want the fraction:

import math


math.floor(2.6) # 2
math.floor(3.2) # 3
math.floor(9.7) # 9

The key point here is that floor will always round down, as opposed to true rounding. In true rounding, we would expect the first and last examples in the snippet above to be 3 and 10, because the decimal is above 0.5.

Intro to Truncating

What about trunc, then? Truncating a number, removes the decimal in the direction of 0. We can see how trunc behaves by looking at a similar set of examples:

import math


math.trunc(2.6) # 2
math.trunc(3.2) # 3
math.trunc(9.7) # 9

From these examples, we can see that trunc, like floor, is not rounding. If it were, the first and last examples would again be 3 and 10, respectively, but we get 2 and 9.

However, we’re getting the same result using trunc as we did using floor. So, how are they different? Well, the trunc method is removing the decimal towards 0. In these examples, that does not give us a different result. But there are cases where it will.

Seeing The Difference

From the examples so far, it would be impossible to tell that floor and trunc have different behavior so let’s look at another example:

import math

math.floor(-2.6) # -3
math.trunc(-2.6) # -2

Flooring a number will always round it down, while truncating will always round it towards 0. So when we floor -2.6, we get -3; when we truncate -2.6, we get -2.

When we truncate a negative number, we effectively round that number up. That’s what I mean by “rounding towards 0”!

Conclusion

The difference between the two is very subtle – so much so that you can’t really tell the difference from the first two examples. This is one of those small differences that you can always look up. And you may have to look it up when the subtle difference in behavior causes a bug!