Python math and random Modules

Two of the most useful tools in the standard library are the Python math and random modules. math handles calculations that go beyond +, -, * and /, like square roots and rounding up. random brings chance into your programs: rolling dice, shuffling playlists, drawing raffle winners. Both come with Python, so you only need an import to start.

The Python math module

Import the module once, then call its functions with the math. prefix:

import math

print(math.sqrt(144))       # square root
print(math.pi)              # the constant pi
print(math.pow(2, 10))      # 2 to the power of 10
print(math.factorial(5))    # 5 x 4 x 3 x 2 x 1
print(math.gcd(24, 36))     # greatest common divisor

12.0
3.141592653589793
1024.0
120
12

Notice that math.sqrt() and math.pow() always return a float, while factorial() and gcd() return whole numbers (ints). If you want an int power, use the ** operator instead: 2 ** 10 gives 1024.

Commonly used math functions

How do you round up and down in Python?

The built-in round() goes to the nearest number. When you need a specific direction, use math.ceil() (think "ceiling", up) or math.floor() (think "floor", down):

import math

price = 4.25
print(round(price))
print(math.ceil(price))
print(math.floor(price))

print(math.floor(-2.5))
print(int(-2.5))

4
5
4
-3
-2

Look at the last two lines. For negative numbers, floor() goes down to -3, while int() just chops off the decimals and gives -2. They only agree for positive numbers.

Real-world example: rounding prices up

Three friends split a $100 dinner bill. $100 / 3 is $33.333..., and if everyone pays $33.33, the restaurant is a cent short. Rounding each share up to the next cent fixes it:

import math

bill = 100
friends = 3

share = math.ceil(bill / friends * 100) / 100
print("Each person pays:", share)

cupcakes = 50
boxes = math.ceil(cupcakes / 12)
print("Boxes needed:", boxes)

Each person pays: 33.34
Boxes needed: 5

The trick of multiplying by 100, rounding up, then dividing by 100 works for rounding up to any number of cents.

Real-world example: equal gift bags with gcd

You have 24 chocolates and 36 candies and want to make identical gift bags with nothing left over. The greatest common divisor tells you the most bags you can make:

import math

chocolates = 24
candies = 36

bags = math.gcd(chocolates, candies)
print("Bags:", bags)
print("Each bag gets", chocolates // bags, "chocolates and", candies // bags, "candies")

Bags: 12
Each bag gets 2 chocolates and 3 candies

The Python random module

The random module picks values by chance. Here are the functions you'll use most:

What does random.seed() do?

Computers can't flip real coins. The random module uses a formula that produces numbers that look random, starting from a value called the seed. Normally the seed comes from the current time, so you get different results each run. If you set the seed yourself, you get the same sequence every time:

import random

random.seed(42)
print(random.random(), random.randint(1, 6), random.randint(1, 6))

random.seed(42)
print(random.random(), random.randint(1, 6), random.randint(1, 6))

0.6394267984578837 1 6
0.6394267984578837 1 6

Same seed, same results. That's very useful for testing and for tutorials like this one: every example below sets a seed, so if you copy it exactly, you'll see exactly the output shown. Remove the random.seed() line and your results will change each time you run the program.

Random numbers: randint() and random()

Real-world example: a dice game

Two players each roll two dice. The higher total wins. randint(1, 6) includes both 1 and 6, just like a real die:

import random

random.seed(12)

for player in ["Mia", "Leo"]:
    die1 = random.randint(1, 6)
    die2 = random.randint(1, 6)
    print(f"{player} rolled {die1} and {die2}: total {die1 + die2}")

Mia rolled 4 and 3: total 7
Leo rolled 6 and 5: total 11

For random decimal numbers, use random.random() (0 to 1) or random.uniform() (any range):

import random

random.seed(3)
print(random.random())
print(round(random.uniform(10, 20), 2))

0.23796462709189137
15.44

Picking from a list: choice(), shuffle() and sample()

choice(): one random item

Can't decide what to have for dinner? Let Python pick:

import random

random.seed(8)
menu = ["pizza", "tacos", "sushi", "pasta", "curry"]
print("Tonight we're having", random.choice(menu))

Tonight we're having tacos

shuffle(): mix a list in place

shuffle() changes the original list and returns None, just like the list method sort():

import random

random.seed(4)
playlist = ["Song A", "Song B", "Song C", "Song D", "Song E"]
result = random.shuffle(playlist)

print(playlist)
print(result)

['Song D', 'Song E', 'Song A', 'Song C', 'Song B']
None

sample(): several items, no repeats

Real-world example: drawing raffle winners

A charity raffle needs 3 different winners. sample() never picks the same entry twice, and it leaves the original list unchanged:

import random

random.seed(21)
entries = ["Ava", "Ben", "Chen", "Dana", "Eli", "Fatima", "Gus", "Hana"]

winners = random.sample(entries, 3)
print("Winners:", winners)
print("Entries left as they were:", len(entries))

Winners: ['Chen', 'Dana', 'Fatima']
Entries left as they were: 8

It works with a range too. Here's a lottery ticket with 6 different numbers from 1 to 49, sorted:

import random

random.seed(99)
ticket = sorted(random.sample(range(1, 50), 6))
print(ticket)

[12, 13, 15, 25, 26, 39]

Common mistakes with math and random

1. Assigning the result of shuffle()

import random

cards = ["A", "K", "Q"]
cards = random.shuffle(cards)
print(cards)

None

shuffle() works in place and returns None. Call it on its own line: random.shuffle(cards).

2. Forgetting randint() includes the top number

Unlike range(1, 6), which stops at 5, random.randint(1, 6) can return 6. For a die, that's what you want; just don't write randint(1, 7).

3. Taking the square root of a negative number

import math

print(math.sqrt(-9))

ValueError: math domain error

4. Asking sample() for more items than exist

import random

print(random.sample(["red", "blue"], 3))

ValueError: Sample larger than population or is negative

Practice exercise

import math
import random

random.seed(7)
heads = 0
for flip in range(1, 6):
    side = random.choice(["Heads", "Tails"])
    print(f"Flip {flip}: {side}")
    if side == "Heads":
        heads += 1
print("Total heads:", heads)

radius = 14 / 2
area = math.pi * radius ** 2
print("Pizza area:", math.floor(area), "sq in")

Flip 1: Tails
Flip 2: Heads
Flip 3: Tails
Flip 4: Heads
Flip 5: Heads
Total heads: 3
Pizza area: 153 sq in

What's next?

You can now calculate and randomize like a pro. Next, learn to work with calendars, clocks and countdowns in Python dates and times with datetime.