Python round up to nearest int

For those who doesn't want to use import.

For a given list or any number:

x = [2, 2.1, 2.5, 3, 3.1, 3.5, 2.499,2.4999999999, 3.4999999,3.99999999999]

You must first evaluate if the number is equal to its integer, which always rounds down. If the result is True, you return the number, if is not, return the integer(number) + 1.

w = lambda x: x if x == int(x) else int(x)+1
[w(i) for i in z]
>>> [2, 3, 3, 3, 4, 4, 3, 3, 4, 4]

Math logic:

• If the number has decimal part: round_up - round_down == 1, always.
• If the number doens't have decimal part: round_up - round_down == 0.

So:

• round_up == x + round_down

With:

• x == 1 if number != round_down
• x == 0 if number == round_down

You are cutting the number in 2 parts, the integer and decimal. If decimal isn't 0, you add 1.

PS:I explained this in details since some comments above asked for that and I'm still noob here, so I can't comment.

When our Python program works with numerical values, every so often we have turn values with a fractional component into whole (integer) numbers. But how to do so? And what options does Python have? Let’s find out together.

IN THIS ARTICLE:

• Round numerical values up and down in Python
• Round values up and down: Python’s round() function
  • Example: round Python numbers to the nearest full integer
• Round down to the next integer: Python’s math.floor() function
  • Example: round values down to the next full integer
• Round up to the next integer: Python’s math.ceil() function
  • Example: round Python values up to whole numbers
• Round all values in a Python list or array
  • Round Python values with a list comprehension
  • Round all values with Python’s for loop
• Summary

# Round numerical values up and down in Python

When we round values, we go from a numerical value with decimal places to a whole number. With this process we do lose some precision, but the rounded value is often much easier to read and interpret.

Python has three ways to turn a floating-point value into a whole (integer) number:

• The built-in round() function rounds values up and down.
• The math.floor() function rounds down to the next full integer.
• The math.ceil() function rounds up to the next full integer.

If you just want a string or script output with a whole number, then a Python format string can perform that task too. That way you also don’t lose precision in the original value.

Let’s see how these three approaches work.

# Round values up and down: Python’s round() function

To round floating-point values up and down we use Python’s round() function (Lutz, 2013; Python Docs, n.d. a). There are two ways to use this function. The first option is to round values to a certain number of decimals. The other option turns a floating-point value into a whole number.

To do that latter, we call round() with one argument: the value to turn into an integer. For example:

round(5.4598)
# Returns: 5

The round() function rounds values of .5 towards an even integer (Python Docs, n.d. a). So .5 is round up for positive values and round down for negative values.

For instance, both round(0.5) and round(-0.5) return 0, while round(1.5) gives 2 and round(-1.5) gives -2. This Python behaviour is a bit different from how rounding usually goes.

When we give round() an integer, the function simply returns that whole number. There’s no error in that case, and so we don’t have to check if the function’s argument has a fractional value. It does need to be a number though; string values are not allowed in round().

# Example: round Python numbers to the nearest full integer

To see how the round() function works in practice, let’s consider the following mini-program:

# Some numbers to round
valueA = 3.14159265359
valueB = 1845.7409947
valueC = -100.95
valueD = 9.5432
valueE = 34.49953

# Round values to whole numbers
roundA = round(valueA)
roundB = round(valueB)
roundC = round(valueC)
roundD = round(valueD)
roundE = round(valueE)

# Output rounded values
print("Value:".ljust(15), "Rounded:")

print(str(valueA).ljust(15), roundA)
print(str(valueB).ljust(15), roundB)
print(str(valueC).ljust(15), roundC)
print(str(valueD).ljust(15), roundD)
print(str(valueE).ljust(15), roundE)

Here we first make five variables with floating-point values. Some have a lot of decimal places and others just a few.

Then we do some rounding. For that we call the round() function and provide one argument: the value to round. We store the rounded integers in the variables roundA through roundE.

Next we output the results with the print() function. For each variable we display the original value (e.g., valueA) and its rounded result (roundA). With the ljust() string method we justify that first value to the left. That aligns the values for a prettier output.

Here’s how the rounded values look:

Value:          Rounded:
3.14159265359   3
1845.7409947    1846
-100.95         -101
9.55432         10
34.49953        34

# Round down to the next integer: Python’s math.floor() function

The math.floor() function returns the floor value of its argument, which is the nearest integer less than or equal to that argument’s value (Python Docs, n.d. b).

That sounds abstract, but is just another way of saying that math.floor() rounds down to the next whole number. So 7.8 becomes 7 and 5.4 is turned into 5. And since the function rounds down to a smaller value, -8.2 becomes -9.

Here’s a quick example of the math.floor() function:

import math

math.floor(12.75)
# Returns: 12

math.floor() only accepts one argument: the value to round down. With a small custom function we can also round down to a number of decimal places. See round down to a specific decimal amount for more.

# Example: round values down to the next full integer

To explore how the math.floor() function works in practice, let’s examine the following Python program:

import math

# Some random values
valueA = 11.2829850
valueB = 19.2545879
valueC = 0.50000001
valueD = 34.6403001
valueE = -9.9121138

# Round values down to the nearest full integer
roundA = math.floor(valueA)
roundB = math.floor(valueB)
roundC = math.floor(valueC)
roundD = math.floor(valueD)
roundE = math.floor(valueE)

# Print the results
print(valueA, "rounded =", roundA)
print(valueB, "rounded =", roundB)
print(valueC, "rounded =", roundC)
print(valueD, "rounded =", roundD)
print(valueE, "rounded =", roundE)

We first import the math module. That makes it possible to use the math.floor() function. Then we make five variables, valueA through valueE. Each holds a floating-point value.

Next we round those values down. For that we call the math.floor() function on each variable. We store the outcome in new variables (roundA through roundE).

The program’s third part outputs the variables with Python’s print() function. Here each print() statement displays the original value and its rounded down version. Here’s how that looks:

11.282985 rounded = 11
19.2545879 rounded = 19
0.50000001 rounded = 0
34.6403001 rounded = 34
-9.9121138 rounded = -10

# Round up to the next integer: Python’s math.ceil() function

The math.ceil() function returns the ceiling of its argument, which is the nearest integer greater than or equal to that argument’s value (Python Docs, n.d. b).

That’s just a way of saying that math.ceil() rounds up to a whole number: 3.2 becomes 4 and 7.75 gets turned into 8. And because the function rounds up to a greater value, -9.8 becomes -9.

Here’s a quick example of math.ceil():

import math

math.ceil(12.45)
# Returns: 13

Here’s a way to remember the difference between math.floor() and math.ceil(). As you know, each floating-point value lies between two consecutive integers. 12.45, for instance, is between 12 and 13.

Now the “ceiling” is the higher endpoint of this interval. So math.ceil() returns 13. The lower start point of that integer interval is called the “floor”. So math.floor() returns 12.

Python’s math.ceil() function always rounds up to a full integer. But with a small custom function we can also round up to a number of decimal places. See round Python values to decimal places for how.

# Example: round Python values up to whole numbers

Let’s see how math.ceil() works in practice. This example program rounds several floating-point values up to a whole number:

import math

# Some random values
valueA = 11.2829850
valueB = 19.2545879
valueC = 0.50000001
valueD = 34.6403001
valueE = -9.9121138

# Round values up to the nearest full integer
roundA = math.ceil(valueA)
roundB = math.ceil(valueB)
roundC = math.ceil(valueC)
roundD = math.ceil(valueD)
roundE = math.ceil(valueE)

# Output the results
print(valueA, "rounded =", roundA)
print(valueB, "rounded =", roundB)
print(valueC, "rounded =", roundC)
print(valueD, "rounded =", roundD)
print(valueE, "rounded =", roundE)

We first import the math module. That makes the math.ceil() function available. Then we make five different variables, named valueA through valueE. Each has a number with several decimal places.

The next part rounds those values up to a full integer. To make that happen we call the math.ceil() function on each variable. We put the values returns by that function in new variables, roundA through roundE.

The third code segment has the print() function output both the original and rounded value. Here’s what that displays:

11.282985 rounded = 12
19.2545879 rounded = 20
0.50000001 rounded = 1
34.6403001 rounded = 35
-9.9121138 rounded = -9

# Round all values in a Python list or array

Of course there are also situations where we have a bunch of values to round, rather than a single value. There are two main ways to do that: with a list comprehension or for loop. Let’s see.

# Round Python values with a list comprehension

When we have a sequence of floating-point values, one way to round them is with a list comprehension. That requires just a bit of code and runs efficiently.

Here’s a mini-program that does just that:

import math

# Some random values
values = [
    3.46410162, 6.70820393, 11.04536102,
    15.29705854, 21.21320344, 31.4960315
]

# Generate new lists with values rounded
valuesRounded = [round(number) for number in values]
valuesRoundUp = [math.ceil(number) for number in values]
valuesRoundDown = [math.floor(number) for number in values]

# Output data
print("Original values:\n", values)
print("Rounded:\n", valuesRounded)
print("Rounded up to next integer:\n", valuesRoundUp)
print("Rounded down to next integer:\n", valuesRoundDown)

First we import the math module. That makes the math.ceil() and math.floor() rounding functions available. Then we make a list named values, which holds several floating-point values.

To round those values to whole numbers we make three list comprehensions. The first one executes round() for each list value. The other two execute math.ceil() and math.floor() functions on the list values.

We generate the values that those functions use with an in-line for loop: for number in values. This takes one value from the values list at a time, and makes it available through the number variable.

Those list comprehensions generate new lists. We assign those to the valuesRounded, valuesRoundUp, and valuesRoundDown variables.

The last part of the program outputs the original list and the three rounded ones. Here’s how that looks:

Original values:
 [3.46410162, 6.70820393, 11.04536102, 15.29705854, 21.21320344, 31.4960315]
Rounded:
 [3, 7, 11, 15, 21, 31]
Rounded up to next integer:
 [4, 7, 12, 16, 22, 32]
Rounded down to next integer:
 [3, 6, 11, 15, 21, 31]

In the above example we kept the original list. If you don’t need to retain those values, you can also overwrite the original list with rounded values. Here’s how a list comprehension does that:

# Round all numbers in the 'values' list,
# in place (to replace the original numbers)
values = [round(value) for value in values]

# Round all values with Python’s for loop

Of course we can also round list or array values with a regular for loop. This requires a bit more code than a list comprehension, but makes it easier to perform additional operations on each element. Plus a for loop is easier to read in complex situations.

Here’s how a Python program rounds values inside a for loop:

import math

# Some random values
values = [
    3.46410162, 6.70820393, 11.04536102,
    15.29705854, 21.21320344, 31.4960315
]

# Create the new lists
valuesRounded = []
valuesRoundUp = []
valuesRoundDown = []

# Populate new lists with rounded values
for number in values:
    valuesRounded.append(round(number))
    valuesRoundUp.append(math.ceil(number))
    valuesRoundDown.append(math.floor(number))

# Output data
print("Original values:\n", values)
print("Rounded (standard):\n", valuesRounded)
print("Rounded up to next integer:\n", valuesRoundUp)
print("Rounded down to next integer:\n", valuesRoundDown)

We again first import the math module to be able to use math.ceil() and math.floor(). Then we make a list (values) with floating-point values.

Then we make three initially empty lists: valuesRounded, valuesRoundUp, and valuesRoundDown. These are going to hold our rounded values.

To fill those lists we make a Python for loop. This loop goes through all elements in the values list. During each loop cycle the number variable holds a single element from that list.

Inside the loop we call the append() method on each of the three new lists. That way we add a new element to them. The value we add each pass through the loop is the number variable rounded with round(), math.ceil(), and math.floor(). After this loop is done, each of those three lists has a rounded value from the original list.

The program ends with several print() statements. That displays the original list and its rounded derivatives. Here’s what that output looks like:

Original values:
 [3.46410162, 6.70820393, 11.04536102, 15.29705854, 21.21320344, 31.4960315]
Rounded (standard):
 [3, 7, 11, 15, 21, 31]
Rounded up to next integer:
 [4, 7, 12, 16, 22, 32]
Rounded down to next integer:
 [3, 6, 11, 15, 21, 31]

By the way, you don’t have to make a new list when you round values. If you’re fine with losing the original data, you can also overwrite the existing list. Doing so is easy when you combine a for loop with the enumerate() function:

# Loop through the original 'values' list, and
# round the numbers (in place)
for index, value in enumerate(values):
    values[index] = round(value)

READ MORE

• Round Python values to a certain number of decimal places
• Truncate Python floating-point values to a whole number
• Truncate Python values to a certain number of decimal digits

# Summary

Python has three ways to round a floating-point value to a whole number. The round() function rounds a value up or down. A decimal digit of .5 has Python round towards an even integer. That makes it round up for positive values and down for negative ones.

The math.floor() function, on the other hand, always rounds down to the nearest full integer. math.ceil() does the opposite. That function always rounds up to a whole number.

All three functions work in the same way: provide the function with one argument, which is the floating-point value to round.

Published December 20, 2019.

« All Python math articles

How do you round to the nearest integer in Python?

Does INT round up Python?

How do you round up to the nearest integer?

Does Python round .5 up or down?