The 544 fiscal calendar used by Apple

Since 1999, the Saturday closest to the end of September is designated as the last day of Apple's fiscal year. For instance, 28 September 2024 (Saturday) is 2 days from 30 September 2024 and therefore it is the last day of Apple fiscal year 2024.

Apple fiscal year, \(y\)	Start, \(\alpha\)	End, \(\omega\)	\(\Omega'\)
1994	2 October 1993	30 September 1994 (Fri)
1995	1 October 1994	29 September 1995 (Fri)
1996	30 September 1995	27 September 1996 (Fri)
1997	28 September 1998	26 September 1997 (Fri)
1998	27 September 1998	25 September 1998 (Fri)
1999	26 September 1998	25 September 1999	5
2000	26 September 1999	30 September 2000	0
2001	1 October 2000	29 September 2001	1
2002	30 September 2001	28 September 2002	2
2003	29 September 2002	27 September 2003	3
2004	28 September 2003	25 September 2004	5
2005	26 September 2004	24 September 2005	6
2006	25 September 2005	30 September 2006	0
2007	1 October 2006	29 September 2007	1
2008	30 September 2007	27 September 2008	0
2009	28 September 2008	26 September 2009	4
2010	27 September 2009	25 September 2010	5
2011	26 September 2010	24 September 2011	6
2012	25 September 2011	29 September 2012	1
2013	30 September 2012	28 September 2013	2
2014	29 September 2013	27 September 2014	3
2015	28 September 2014	26 September 2015	4
2016	27 September 2015	24 September 2016	6
2017	25 September 2016	30 September 2017	0
2018	1 October 2017	29 September 2018	1
2019	30 September 2018	28 September 2019	2
2020	29 September 2019	26 September 2020	4
2021	27 September 2020	25 September 2021	5
2022	26 September 2021	24 September 2022	6
2023	25 September 2022	30 September 2023	0
2024	1 October 2023	28 September 2024	2

An easy numerical scheme to compute the last day of Apple's fiscal year is to start with September 30, and then offset it by a couple of days to reduce its day of week value to Saturday.

\begin{equation} \omega(y) = \Omega(y) - \Omega'(y) \end{equation}

where \(\Omega(y)\) = 30 December and the amount of offset, \(\Omega'(y)\) is simply:

\begin{equation} \Omega'(y) = {\rm wday}(\Omega) \; {\rm mod} \; 7 \end{equation}

The first day, on the other hand, can be expressed very easily in terms of \(\omega\), since we can take it as the previous fiscal end point plus 1 day:

\begin{equation} \alpha(y) = \omega(y - 1) + 1 \end{equation}

The fiscal year \(y(date)\) associated with a given \(date\) can be computed from

\begin{equation} y = \begin{cases} Y + 1 & \textrm{if $date > \omega(Y)$}\\ Y - 1 & \textrm{if $date < \alpha(Y)$}\\ Y & \textrm{otherwise} \end{cases} \end{equation}

where \(Y(date)\) is the Gregorian year associated with the \(date\).

The calendrical distance of a given \(date\), \(\lambda\), displaced from the fiscal inception, \(\alpha(y)\), is then

\begin{equation} \lambda = date - \alpha(y) \end{equation}

Since a full 400-year Gregorian calendar has 146,097 days or 20,871 weeks, there are 71 extra weeks to be spread out in 400 years, that is

\begin{equation} \frac{400}{\frac{146097}{7} - 52 \times 400} = 5\tfrac{45}{71} = 5.63\ldots \end{equation}

As a result, a 53rd week is added to the third fiscal period (December) of a fiscal year every 5 or 6 years. A simple way to see if a given year is a 52-week year or a 53-week year is by computing the number of days between \(\alpha(y)\) and \(\omega(y)\), that is,

\begin{equation} \mathbb{Q}_\textrm{53 weeks?}(y) = \begin{cases} \small{\rm TRUE} & \textrm{if $\omega(y) - \alpha(y) + 1 = 53\times 7$}\\ \small{\rm FALSE} & \textrm{otherwise} \end{cases} \end{equation}

library(tidyverse)

fiscal_end <- function(.year) {
  
  .end <- paste0(.year, '-9-30') %>% as_date

  .end - days(wday(.end) %% 7)
}

fiscal_start <- function(.year) {
  
  fiscal_end(.year - 1) + days(1)
}

fiscal_distance <- function(.date) {
  
  .date <- as_date(.date)
  
  y <- year(.date)
  
  if(.date > fiscal_end(y)) {
    y <- y + 1
  } else if(.date < fiscal_start(y)) {
    y <- y - 1
  }
  
  as.numeric(
    .date - fiscal_start(y)
  )
}

fiscal_year_with_53_weeks <- function(.year) {
  
  fiscal_end(.year) - fiscal_start(.year) + 1 == 53 * 7
}

The number of work week accumulated at the end of a given period in a given fiscal year can be calculated by

\begin{equation} N(P) = 4(P+2) + \left\lfloor \tfrac{P+2}{3}\right\rfloor - q \end{equation}

where the value of \(q\) is determined by

\begin{equation} q = \begin{cases} 2^3 & \textrm{if $\mathbb{Q}_\textrm{53 weeks?}(y)$ is $\small{\rm FALSE}$ or $P \in [1, 3)$}\\ 2^3 - 1 & \textrm{otherwise} \end{cases} \end{equation}

For a given \(date\), the position of the work week can be calculated by discretizing \(\lambda\) in blocks of 7:

\begin{equation} W(date) = \left \lfloor \tfrac{1}{7}\lambda \right \rfloor + 1 \end{equation}

For a given \(date\), the position of the fiscal period can be calculated by:

\begin{equation} P(date) = \left \lceil \tfrac{3}{5+4+4} (W + q')\right \rceil - 2 \end{equation}

where the value of \(q'\) is determined by

\begin{equation} q' = \begin{cases} 2^3 & \textrm{if $\mathbb{Q}_\textrm{53 weeks?}(y)$ is $\small{\rm FALSE}$ or $W \in [1, 14)$}\\ 2^3 - 1 & \textrm{otherwise} \end{cases} \end{equation}

fiscal_cweek <- function(.year, .period) {
  
  with_53 <- fiscal_year_with_53_weeks(.year)
  
  q <- ifelse(.period %in% 1:2 | !with_53, 8, 7)
  
  .period <- .period + 2

  4 * .period + floor(.period / 3) - q
}

fiscal_nweek <- function(.year, .period) {
  
  fiscal_cweek(.year, .period) - 
    fiscal_cweek(.year, .period - 1)
}

fiscal_cweek_ <- function(.date) {
  
  lambda <- fiscal_distance(.date)
  
  floor(lambda / 7) + 1
}

fiscal_period_ <- function(.year, .cweek) {
  
  with_53 <- fiscal_year_with_53_weeks(.year)
  
  q <- ifelse(.cweek %in% 1:13 | !with_53, 8, 7)
  
  ceiling((.cweek + q) * 3/13) - 2
}

fiscal_period <- function(.date) {
  
  fiscal_cweek_(.date) %>% 
    fiscal_period_
}