Getting century from year in JavaScript

In JavaScript, determining the century from a given year is a common programming task. A century represents a period of 100 years, where the 1st century includes years 1-100, the 20th century covers 1901-2000, and so on.

Understanding Century Calculation

The key insight is that centuries don't align perfectly with hundreds. For example:

• Year 1900 belongs to the 19th century (not 20th)
• Year 2000 belongs to the 20th century (not 21st)
• Year 2001 begins the 21st century

Logic and Algorithm

To find the century from a year:

1. Divide the year by 100
2. Round up to the nearest integer using Math.ceil()
3. Return the result

The Math.ceil() function automatically handles the rounding logic, ensuring years ending in 01-99 round up correctly.

Implementation

function getCentury(year) {
    return Math.ceil(year / 100);
}

// Test with various years
console.log("Year 1: Century", getCentury(1));
console.log("Year 100: Century", getCentury(100)); 
console.log("Year 101: Century", getCentury(101));
console.log("Year 1900: Century", getCentury(1900));
console.log("Year 2000: Century", getCentury(2000));
console.log("Year 2023: Century", getCentury(2023));

Year 1: Century 1
Year 100: Century 1
Year 101: Century 2
Year 1900: Century 19
Year 2000: Century 20
Year 2023: Century 21

Alternative Approach

You can also use manual calculation with conditional logic:

function getCenturyManual(year) {
    let century = Math.floor(year / 100);
    if (year % 100 !== 0) {
        century += 1;
    }
    return century;
}

// Test the alternative approach
console.log("Manual calculation for 1999:", getCenturyManual(1999));
console.log("Manual calculation for 2000:", getCenturyManual(2000));

Manual calculation for 1999: 20
Manual calculation for 2000: 20

Comparison

Practical Example

// Function to get century with descriptive output
function describeCentury(year) {
    const century = Math.ceil(year / 100);
    const suffix = century === 1 ? 'st' : century === 2 ? 'nd' : century === 3 ? 'rd' : 'th';
    return `Year ${year} belongs to the ${century}${suffix} century`;
}

console.log(describeCentury(1776));
console.log(describeCentury(2024));

Year 1776 belongs to the 18th century
Year 2024 belongs to the 21st century

Conclusion

Using Math.ceil(year / 100) provides the simplest and most reliable way to calculate centuries from years in JavaScript. This approach automatically handles edge cases and maintains O(1) time complexity for efficient computation.