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The modulo operator % in Python

What % does in Python and where it's useful: even or odd, every Nth item, wrapping around a list or a clock, splitting seconds with divmod, digits, FizzBuzz, and how it treats negative numbers.

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% is the modulo operator: the remainder after division. The number operations post introduced it in a few lines.

Every example ran with Python 3.13, checked against the binary arithmetic operations reference and the divmod() docs.

What % does

a % b is what’s left over when you divide a into groups of b:

print(17 % 5, 10 % 2, 3 % 7, 0 % 4)

2 0 3 0

17 is three groups of 5 plus 2. 3 is smaller than 7, so all of it is left over.

% goes hand in hand with floor division //. The docs give the identity x == (x//y)*y + (x%y): the quotient times the divisor, plus the remainder, gives back the original number.

Even or odd

A number is even when dividing it by 2 leaves nothing:

number = 7
if number % 2 == 0:
    print(number, "is even")
else:
    print(number, "is odd")

7 is odd

The same idea works for any divisor. n % 3 == 0 means “n divides by 3”.

Every Nth item

Inside a loop, % picks every Nth step:

for i in range(1, 11):
    if i % 3 == 0:
        print(i, end=" ")
print()

3 6 9

In real code this is “save every 100 rows” or “print progress every 1,000 items”: if i % 1000 == 0:.

Wrapping around

The result of x % n is always between 0 and n - 1 (for positive n). That makes it perfect for going around in a circle, like days of the week:

days = ["Sun", "Mon", "Tue", "Wed", "Thu", "Fri", "Sat"]
today = 5
print(days[(today + 3) % 7])
print(days[(today - 8) % 7])

Mon
Thu

Today is index 5 (Friday). Three days later is index 8, and 8 % 7 is 1, Monday. Eight days back is index -3, and -3 % 7 is 4, Thursday. The index never falls off the list. A 24-hour clock works the same way.

%= keeps an angle between 0 and 359:

angle = 350
angle += 20
angle %= 360
print(angle)

10

Splitting units with divmod

To turn seconds into hours, minutes and seconds, you need both the quotient and the remainder. divmod(x, y) returns both as a pair, (x // y, x % y):

total_seconds = 3725
minutes, seconds = divmod(total_seconds, 60)
hours, minutes = divmod(minutes, 60)
print(f"{hours}:{minutes:02}:{seconds:02}")

1:02:05

The :02 pads with a zero to two digits, as shown in the f-strings post.

Digits of a number

% 10 gives the last digit of a whole number. % 100 gives the last two. Combine it with // to get any digit:

n = 4096
print(n % 10, n % 100, n // 10 % 10)

6 96 9

FizzBuzz

The interview exercise tests % and elif order: print the numbers from 1 to 15, but “Fizz” for multiples of 3, “Buzz” for multiples of 5, and “FizzBuzz” for multiples of both:

for n in range(1, 16):
    if n % 15 == 0:
        print("FizzBuzz")
    elif n % 3 == 0:
        print("Fizz")
    elif n % 5 == 0:
        print("Buzz")
    else:
        print(n)

1 2 Fizz 4 Buzz Fizz 7 8 Fizz Buzz 11 Fizz 13 14 FizzBuzz

(Output shown on one line to save space.) The n % 15 check must come first, or 15 would match n % 3 == 0 and print “Fizz”, as explained in the if/elif post.

Negative numbers

Here Python differs from C, Java and JavaScript. The docs say the result of % “always yields a result with the same sign as its second operand (or zero)”:

print(-7 % 3, 7 % -3, -7 % -3)
print(-7 // 3, -7 == (-7 // 3) * 3 + (-7 % 3))

import math
print(math.fmod(-7, 3))

2 -2 -1
-3 True
-1.0

-7 // 3 rounds down to -3, and -3 * 3 + 2 is -7, so the remainder is 2. In C or JavaScript, -7 % 3 is -1. math.fmod() gives that behavior, and the math docs recommend fmod() for floats and % for integers.

Python’s rule is the reason the wrap-around trick works with negative indexes, and why n % 2 == 1 is a correct odd check even for negative n:

print(-3 % 2 == 1, -3 % 2)

True 1

In C, -3 % 2 is -1, so the same check would fail.

Floats

% works on floats too, but float rounding can show up in the result:

print(7.5 % 2, 5 % 0.1)

1.5 0.09999999999999973

5 % 0.1 isn’t 0 because 0.1 can’t be stored exactly. Use % with whole numbers when you can.

Common mistakes

  • Dividing by zero. 5 % 0 raises ZeroDivisionError: integer modulo by zero, the same as 5 / 0.
  • Confusing % with percent. 50 % 10 is 0, not “5”. For a percentage, multiply: part / total * 100.
  • Mistaking % in strings for modulo. "%s is %d years old" % ("Dana", 30) is the old string formatting. With a string on the left, % formats text; use f-strings instead.

What’s next

Next in the series: loops with for and while, where % and conditions do most of their work.

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