JDN(Y,M,D) = D - 32075
  + 1461 × (Y + 4800 + (M-14) ÷ 12) ÷ 4
  + 367 × (M - 2 - (M-14) ÷ 12 × 12) ÷ 12
  - 3 × ((Y + 4900 + (M-14) ÷ 12) ÷ 100) ÷ 4

// Add days:
newJDN = JDN(startDate) + daysToAdd
// Convert back to calendar date

Julian Day Number converts any Gregorian date to an integer, making day addition trivially simple.

function addMonths(date, n) {
  const result = new Date(date);
  const targetMonth = result.getMonth() + n;
  result.setMonth(targetMonth);

  // Clamping: if month overflowed,
  // set to last day of target month
  if (result.getMonth() !== ((targetMonth % 12) + 12) % 12) {
    result.setDate(0); // last day of prev month
  }
  return result;
}

JavaScript's Date handles most clamping automatically. Always verify month didn't overflow for Jan 31, Mar 31, etc.

function addBusinessDays(date, days) {
  let count = 0;
  const result = new Date(date);
  while (count < days) {
    result.setDate(result.getDate() + 1);
    const dow = result.getDay(); // 0=Sun, 6=Sat
    if (dow !== 0 && dow !== 6
        && !isPublicHoliday(result)) {
      count++;
    }
  }
  return result;
}

Public holidays require a country-specific list. For US: New Year's, MLK Day, Presidents Day, Memorial Day, Independence Day, Labor Day, Thanksgiving, Christmas.

function isLeapYear(year) {
  return (year % 4 === 0
    && year % 100 !== 0)
    || (year % 400 === 0);
}

// Examples:
// 2024 → true  (div by 4)
// 1900 → false (div by 100, not 400)
// 2000 → true  (div by 400)

The Gregorian calendar adds one leap day every 4 years, skips every 100, then adds it back every 400. This keeps the calendar aligned with the solar year to within 26 seconds/year.