How to Calculate and Format Aligned Square Roots in Python

Calculating a square root is a basic mathematical operation, but presenting that result in a specific textual format, such as aligning it with padding characters, requires string manipulation. This guide demonstrates how to calculate the square root of an integer and format the output to a specific width (30 characters) using + signs as padding.

This exercise covers math.sqrt(), Python f-string for decimal precision, and dynamic string concatenation.

Understanding the Logic

To achieve the desired output (e.g., transforming 10 into +++++++++++++++++++++++++3.162), we need to break the problem into three steps:

1. Calculation: Compute the square root of the input number.
2. Precision: Format the result to exactly 3 decimal places.
3. Padding: Calculate how many + characters are needed to make the total string length exactly 30 characters, and prepend them.

Step 1: Calculating and Formatting Decimals

First, we use the math module to get the square root. Then, we use Python's f-string formatting to handle the decimal precision.

Using math.sqrt and f-string

import math

num = 10

# ✅ Correct: Calculate square root
root = math.sqrt(num)
print(f"Raw Root: {root}")

# ✅ Correct: Format to 3 decimal places using :.3f
formatted_root = f"{root:.3f}"
print(f"Formatted: {formatted_root}")

Output:

Raw Root: 3.1622776601683795
Formatted: 3.162

note

The syntax :.3f inside an f-string tells Python to format the float as a fixed-point number with 3 digits after the decimal point.

Step 2: Implementing Dynamic Padding

Once we have the number string (e.g., "3.162", which has a length of 5), we need to fill the remaining space to reach a total width of 30.

Calculating Padding Length

We calculate the required padding by subtracting the length of our number string from the target width (30). We use max() to ensure we don't get a negative number if the string is already longer than 30.

target_width = 30
current_str = "3.162"

# ⛔️ Incorrect: Hardcoding padding often leads to alignment errors
# output = "++++++++++++++++++++" + current_str 

# ✅ Correct: Dynamically calculate needed padding
padding_needed = max(target_width - len(current_str), 0)
padding_str = "+" * padding_needed

final_output = padding_str + current_str
print(final_output)

Output:

+++++++++++++++++++++++++3.162

Complete Code Solution

Here is the complete script, encapsulated in a function and a main execution block.

import math

def format_square_root(num):
    """
    Calculates the square root of 'num', formats it to 3 decimal places,
    and pads it with '+' to a total length of 30.
    """
    # 1. Calculate the square root
    square_root = math.sqrt(num)
    
    # 2. Format to 3 decimal places (returns a string)
    formatted_output = f"{square_root:.3f}"
    
    # 3. Calculate padding (Total 30 - Length of number)
    # max(..., 0) ensures safety if the number is huge
    padding_length = max(30 - len(formatted_output), 0)
    
    # 4. Construct final string
    output = "+" * padding_length + formatted_output
    return output

if __name__ == "__main__":
    try:
        # Get user input
        user_input = int(input("Input: "))
        
        # Process and Print
        result = format_square_root(user_input)
        print("Output:", result)
        
    except ValueError:
        print("Please enter a valid integer.")

Execution Example 1

Input: 10

Output: +++++++++++++++++++++++++3.162

Execution Example 2

Input: 200

Output: ++++++++++++++++++++++++14.142

tip

While the manual padding method demonstrated above is excellent for learning string logic, Python f-string also support alignment natively. f"{square_root:+>30.3f}" would achieve a similar result in one line (> aligns right, + is the fill character).

Conclusion

Formatting numerical output often involves more than just calculation. By combining:

1. math.sqrt() for the math,
2. f"{val:.3f}" for precision,
3. "char" * count for padding,

You can create precise, strictly formatted textual reports suitable for data tables or specific UI requirements.