Whenever we want to quickly assess the magnitude of a change, percentages are almost always the go-to tool. With percentages, we can easily calculate the difference between two values, figure out the proportion of a quantity relative to a total, or measure the degree of change in a value.

In this article, we’ll explore how percentages and the percentage (%) sign are used in programming from both a mathematical and syntactical perspective. By the end, you should have a comprehensive understanding of percentage formulas in programming and be ready to use them confidently in your projects.

## Percentage Formulas In Programing: The Percentage Sign (%)

We’ve all encountered the word “percentage” at some point, from calculating grades in middle school to estimating discounts on our Amazon purchases. But have you ever thought of its etymology?

It turns out that the word “percentage” comes from the Latin word “per centum,” which means “by hundred.” And, as we all know, percentages are simply fractions with 100 in the denominator.

But the percentage sign has usage in more than just the mathematical concepts of estimation and comparison. In programming, the percentage sign is mainly used as a modulo operator and in arithmetic operations. However, it has various other uses in different languages. We’ll now look at these in detail.

### Modulo Operator

The modulo operator (%), also known as the remainder or “modulus” operator, is used to divide two numbers and return the remainder. It’s super handy in algorithms such as the famous FizzBuzz, where you need to check if a number is divisible by another number or not. For example, if you want to check if a number is even or odd, you can use the modulo operator like this:

num = 123358

if num % 2 == 0:

print(“The number is even”)

else:

print(“The number is odd”)

# Output: “The number is even”

With those few lines of code, we’ve quickly determined that 123358 is an even number. Whether you’re working on a complex mathematical algorithm or just need to perform some basic arithmetic divisibility test, you’ll find the modulo operator a must-have in your programming toolkit.

### Markdown, Encoding, and CSS

Markdown is another area where the percentage sign finds usage in programming. In markdown languages, the percentage sign is used for encoding special characters. For instance, if you want to insert a percentage symbol into a Markdown file, you can use the code %, where the “%” symbol is encoded as “%25”.

Similarly, URLs may contain special characters, such as spaces that need to be encoded, using percent encoding to be properly interpreted by web browsers. Example:

URL: https://www.example.com/search?q=programming languages

Encoded URL: https://www.example.com/search?q=programming%20languages

Moreover, in CSS, percentages are used for measuring relative sizes. CSS allows the use of percentage values for a wide range of properties, such as width, height, margin, padding, and font size. By using percentages, we can create responsive web designs that adjust to the size of the viewport.

For example,

.my-class {

width: 50%;

height: 100%;

margin: 0% 10% 0% 10%;

padding: 5% 2%;

}

In this example, we are using the CSS selector to apply a set of rules to an HTML element with the class name “my-class.” By using percentage values for these properties, the element will adjust its size and spacing relative to its parent container, making it more responsive to different screen sizes.

### Format Specifier

In languages like C, the percentage sign is used as a format specifier in printf() and scanf() functions. The format specifier is a special character that begins with a percentage sign followed by a character that specifies the type of value that is to be printed or scanned.

For example, the format specifier “%d” is used to print an integer value, while “%f” is used to print a floating-point value. The format specifier “%s” is used to print a string, and “%c” is used to print a single character.

The percentage sign is used in combination with these format specifiers to print or scan values of different types in C. For example, the following code prints the value of an integer variable x:

int x = 42;

printf(“The value of x is %d\n”, x);

Here, the format specifier “%d” is used to print the value of x, and the percentage sign is used to indicate the beginning of the format specifier.

When the printf() function is executed, the value of x is substituted for the format specifier “%d”, and the resulting string is printed to the console. Let’s now look at various percentage formulas in programming with some helpful examples.

## Calculations Using Percentage Formulas In Programming

### Calculating Percentage Increase/Decrease

This is a common problem when you need to calculate the percentage change in a value over time. The percentage increase or decrease formula can be expressed mathematically as:

**Percentage Change = ((New Value – Old Value) / Old Value) x 100 **

For example, let’s say you had 10 apples yesterday, but today you have 15 apples. What’s the percentage increase? The old_value is 10, and the new_value is 15. Using the formula in a Python function, we can calculate the percentage increase as:

def calculate_percent_change(old_value, new_value):

percent_change = ((new_value – old_value) / old_value) * 100

print(“The percentage increase is: ” + str(percent_change) + “%”)

#Output: The percentage increase is: 50.0%

This tells us that the number of apples has increased by 50% from yesterday to today. By calculating the percentage change, you can analyze the growth or decline of any variable over time, and make data-driven decisions accordingly.

### Calculating the Percentage of a Total

We can also find ourselves needing to calculate the percentage of a quantity with respect to a total. For example, you might want to know what percentage of the total apples in a basket are green. The formula for calculating the percentage of the total is:

**Percentage of Total = (Quantity / Total) x 100**

Let’s say we have a basket of 50 apples, and 15 of them are green. We can calculate the percentage of green apples using Python as such:

def calculate_percent_total(quantity, total):

percent_total = (quantity/total) * 100

print(“The percentage of green apples is: ” + str(percent_total) + “%”)

#Output: The percentage of green apples is: 30.0%

So, 30% of the apples in the basket are green and the rest aren’t. This method can be useful in situations like calculating the percentage of sales for a particular product, the percentage of male or female employees in a company, or the percentage of students who passed a particular exam.

Next up, let’s see how we can use a percentage formula to calculate the magnitude of change in a given quantity.

### Calculating the Magnitude of Change

Sometimes we may need to express the change in a quantity in terms of percentage, but also take into account the magnitude of the change.

For example, if we’re comparing the populations of two cities over time, we might want to know not only the percentage change but also the actual difference in population size. We can use the following formula to calculate the magnitude change:

**Magnitude Change = ((New Value – Old Value) / Old Value) x 100**

To calculate the magnitude change as a percentage, we can simply multiply the result by 100. Let’s say City A had a population of 500,000 in 2020 and a population of 550,000 in 2021, while City B had a population of 700,000 in 2020 and a population of 750,000 in 2021. We can use this formula in Python to calculate the magnitude change for both cities:

def calculate_magnitude_change(old_value, new_value):

magnitude_change = ((new_value – old_value) / old_value) * 100

return magnitude_change

city_a_magnitude = calculate_magnitude_change(500000, 550000)

city_b_magnitude = calculate_magnitude_change(700000, 750000)

print(“City A population magnitude change: ” + str(city_a_magnitude) + “%”)

print(“City B population magnitude change: ” + str(city_b_magnitude) + “%”)

#Output:

#City A population magnitude change: 10%

#City B population magnitude change: 7.14%

We can see that City A’s population increased by 10% while City B’s population increased by 7.14%. By using the magnitude change formula, we can also see that City A’s population increased by 50,000.

Meanwhile, City B’s population increased by 50,000, as well, even though City A’s percentage increase was higher. This formula can be useful in various situations where we need to compare the change in magnitude of two or more variables over time.

### Calculating Percentage Error

The formula for calculating percentage error compares an experimental value with its expected value and expresses it as a percent value, or simply the accuracy of a measurement with respect to an estimate.

The formula we could use in this case is as follows:

**Percentage Error = (Actual Value – Estimated Value) / Actual Value x 100**

For example, let’s say we want to measure the temperature of a room using a thermometer. We measure it to be 25°C, but the actual temperature is 20°C. We can calculate the percentage error using Python like so:

def calculate_percent_error(actual_value, estimated_value):

percent_error = ((estimated_value – actual_value) / actual_value) * 100

print(“The percentage error is: ” + str(percent_error) + “%”)

calculate_percent_error(20, 25)

#Output: The percentage error is: 25.0%

This tells us that our estimate was off by 25%, which means our thermometer isn’t very accurate. This formula can be used in various situations such as measuring the accuracy of predictions made by machine learning models or estimating the performance of a new product on the market.

You may notice that this formula looks similar to the magnitude change formula. That’s because the two are related concepts: the magnitude change formula measures the absolute change in a quantity while the percentage error formula measures the relative change with respect to an estimate.

## Percentage Formulas In Programing: Percentages and Fractions

Sometimes, we may need to convert a fraction into a percentage. This can be done by multiplying the fraction by 100 and adding the “%” sign. For example, let’s say we have the fraction 3/4. To calculate its corresponding percentage, we can use Python as such:

def calculate_percentage(numerator, denominator):

percentage = (numerator / denominator) * 100

print(“The percentage is: ” + str(percentage) + “%”)

calculate_percentage(3, 4)

#Output: The percentage is: 75.0%

We can see that the fraction 3/4 corresponds to 75%. This means that three out of four parts are equal to 75%.

To convert a percentage into a fraction, divide the percentage by 100 and simplify the resulting fraction, if possible. For example, if we have the percentage 60%, we can convert it to a fraction as follows:

60% = 60/100

= 3/5

Therefore, 60% is equivalent to the fraction 3/5.

It’s important to note that when working with percentages, we need to remember that they represent a proportion or fraction of a whole, usually out of 100. So, a percentage can be converted to a fraction by dividing it by 100, and a fraction can be converted to a percentage by multiplying it by 100.

## Wrapping Up

The importance of understanding percentages cuts across people of all levels, from C-Suite executives who need to make strategic decisions based on financial reports to students who need to calculate grades.

So, regardless of one’s profession or background, having a good grasp of percentages can help in expressing ideas, making comparisons, and conveying important information.

In addition to being used for mathematical operations, the percentage sign has wide applications in programming, finding use as a format specifier, in writing markdown, and in CSS.

If you’re a programmer, therefore, mastering percentage formulas in programming would go a long way in not only improving your math proficiency but bolstering your programming chops as well.