diff --git a/src/analysis/calendar.rs b/src/analysis/calendar.rs
new file mode 100644
index 0000000..4ea7988
--- /dev/null
+++ b/src/analysis/calendar.rs
@@ -0,0 +1,37 @@
+//! Time worked per date, laid out like a wall calendar: one column per week,
+//! one row per weekday. The Insights screen colors each cell by hours.
+
+use std::collections::HashMap;
+
+use jiff::civil::{Date, Weekday};
+use jiff::{SignedDuration, ToSpan};
+
+use crate::domain::WorkDay;
+use crate::time::DateRange;
+
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub struct CalendarHeat {
+    /// One entry per week, oldest first, each holding its 7 dates starting on
+    /// the week start. A cell is `None` for dates after today.
+    pub weeks: Vec<[Option<(Date, SignedDuration)>; 7]>,
+}
+
+/// The last `week_count` weeks, ending with the week of `today`.
+pub fn calendar(days: &[WorkDay], today: Date, week_start: Weekday, week_count: usize) -> CalendarHeat {
+    let worked: HashMap<Date, SignedDuration> = days.iter().map(|day| (day.date(), day.worked())).collect();
+    let this_week = DateRange::week_of(today, week_start);
+
+    let weeks = (0..week_count)
+        .rev()
+        .map(|weeks_ago| {
+            let first = this_week.first().saturating_sub((7 * weeks_ago as i64).days());
+            std::array::from_fn(|offset| {
+                let date = first.saturating_add((offset as i64).days());
+                let time = worked.get(&date).copied().unwrap_or(SignedDuration::ZERO);
+                (date <= today).then_some((date, time))
+            })
+        })
+        .collect();
+
+    CalendarHeat { weeks }
+}
diff --git a/src/analysis/focus.rs b/src/analysis/focus.rs
new file mode 100644
index 0000000..9e66bbe
--- /dev/null
+++ b/src/analysis/focus.rs
@@ -0,0 +1,75 @@
+//! How long you stay on, and how you take breaks.
+//!
+//! A "session" is one segment: from pressing Start to pressing Pause.
+
+use jiff::SignedDuration;
+use jiff::civil::Date;
+use jiff::tz::TimeZone;
+
+use super::{days_in, median};
+use crate::domain::WorkDay;
+use crate::time::DateRange;
+
+/// Session lengths are counted in these buckets: (label, upper limit in minutes).
+pub const SESSION_BUCKETS: [(&str, i64); 6] =
+    [("<15m", 15), ("15-30m", 30), ("30m-1h", 60), ("1-2h", 120), ("2-3h", 180), ("3h+", i64::MAX)];
+
+#[derive(Debug, Clone, PartialEq)]
+pub struct Focus {
+    pub sessions: usize,
+    /// How many sessions fall in each of [`SESSION_BUCKETS`].
+    pub session_counts: [usize; SESSION_BUCKETS.len()],
+    pub median_session: Option<SignedDuration>,
+    pub longest_session: Option<(Date, SignedDuration)>,
+    /// Sessions that lasted at least the "long session" setting: long
+    /// stretches without a break (hyperfocus).
+    pub long_sessions: usize,
+    pub days_worked: usize,
+    pub breaks: usize,
+    pub median_break: Option<SignedDuration>,
+    /// Work days where work went on past midnight.
+    pub past_midnight: usize,
+}
+
+impl Focus {
+    pub fn sessions_per_day(&self) -> f64 {
+        if self.days_worked == 0 { 0.0 } else { self.sessions as f64 / self.days_worked as f64 }
+    }
+}
+
+pub fn focus(days: &[WorkDay], range: DateRange, zone: &TimeZone, long_session: SignedDuration) -> Focus {
+    let worked_days: Vec<&WorkDay> = days_in(days, range).filter(|day| !day.is_empty()).collect();
+
+    let sessions: Vec<(Date, SignedDuration)> = worked_days
+        .iter()
+        .flat_map(|day| day.segments().iter().map(|segment| (day.date(), segment.duration())))
+        .collect();
+    let breaks: Vec<SignedDuration> = worked_days
+        .iter()
+        .flat_map(|day| day.breaks().map(|(end, next_start)| next_start.duration_since(end)))
+        .collect();
+
+    let mut session_counts = [0; SESSION_BUCKETS.len()];
+    for (_, length) in &sessions {
+        let minutes = length.as_mins();
+        let bucket = SESSION_BUCKETS.iter().position(|(_, limit)| minutes < *limit).unwrap_or(0);
+        session_counts[bucket] += 1;
+    }
+
+    let past_midnight = worked_days
+        .iter()
+        .filter(|day| day.last_end().is_some_and(|end| end.to_zoned(zone.clone()).date() > day.date()))
+        .count();
+
+    Focus {
+        sessions: sessions.len(),
+        session_counts,
+        median_session: median(sessions.iter().map(|(_, length)| *length).collect()),
+        longest_session: sessions.iter().copied().max_by_key(|(_, length)| *length),
+        long_sessions: sessions.iter().filter(|(_, length)| *length >= long_session).count(),
+        days_worked: worked_days.len(),
+        breaks: breaks.len(),
+        median_break: median(breaks),
+        past_midnight,
+    }
+}
diff --git a/src/analysis/mod.rs b/src/analysis/mod.rs
new file mode 100644
index 0000000..911c8ed
--- /dev/null
+++ b/src/analysis/mod.rs
@@ -0,0 +1,82 @@
+//! Numbers about your work, computed from the work days.
+//!
+//! Every analysis takes the list of work days (from `Journal::snapshot`, so
+//! the session in progress counts too) and returns plain data. The Insights
+//! screen draws that data; nothing in here knows about screens.
+//!
+//! - [`overview`]: week and month totals against your targets, balance, trends.
+//! - [`calendar`]: time worked per date, for the calendar heatmap.
+//! - [`rhythm`]: when you work, by weekday and hour of the day.
+//! - [`focus`]: how long your sessions and breaks last.
+
+pub mod calendar;
+pub mod focus;
+pub mod overview;
+pub mod rhythm;
+
+use jiff::ToSpan;
+use jiff::civil::Date;
+
+use crate::domain::WorkDay;
+use crate::time::DateRange;
+
+/// How far back the Insights screen looks.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)]
+pub enum Period {
+    Weeks4,
+    #[default]
+    Weeks12,
+    Months6,
+    Year,
+    AllTime,
+}
+
+impl Period {
+    pub const ALL: [Period; 5] =
+        [Period::Weeks4, Period::Weeks12, Period::Months6, Period::Year, Period::AllTime];
+
+    pub fn label(self) -> &'static str {
+        match self {
+            Period::Weeks4 => "4 weeks",
+            Period::Weeks12 => "12 weeks",
+            Period::Months6 => "6 months",
+            Period::Year => "1 year",
+            Period::AllTime => "all time",
+        }
+    }
+
+    /// The dates covered, ending today. "All time" starts at the first work day.
+    pub fn range(self, today: Date, days: &[WorkDay]) -> DateRange {
+        let first = match self {
+            Period::Weeks4 => today.saturating_sub(27.days()),
+            Period::Weeks12 => today.saturating_sub(83.days()),
+            Period::Months6 => today.saturating_sub(6.months()).saturating_add(1.day()),
+            Period::Year => today.saturating_sub(1.year()).saturating_add(1.day()),
+            Period::AllTime => days.first().map_or(today, WorkDay::date),
+        };
+        DateRange::new(first, today)
+    }
+
+    /// One step longer (all time stays all time).
+    pub fn longer(self) -> Period {
+        let index = Period::ALL.iter().position(|p| *p == self).unwrap_or(0);
+        Period::ALL[(index + 1).min(Period::ALL.len() - 1)]
+    }
+
+    /// One step shorter (4 weeks stays 4 weeks).
+    pub fn shorter(self) -> Period {
+        let index = Period::ALL.iter().position(|p| *p == self).unwrap_or(0);
+        Period::ALL[index.saturating_sub(1)]
+    }
+}
+
+/// The work days whose date falls in `range`.
+pub fn days_in(days: &[WorkDay], range: DateRange) -> impl Iterator<Item = &WorkDay> {
+    days.iter().filter(move |day| range.contains(day.date()))
+}
+
+/// The middle value of a list (the lower middle for an even count).
+fn median<T: Ord + Copy>(mut values: Vec<T>) -> Option<T> {
+    values.sort();
+    values.get(values.len().saturating_sub(1) / 2).copied()
+}
diff --git a/src/analysis/overview.rs b/src/analysis/overview.rs
new file mode 100644
index 0000000..488cdaf
--- /dev/null
+++ b/src/analysis/overview.rs
@@ -0,0 +1,142 @@
+//! The big picture: totals against your targets, balance, and trends.
+
+use jiff::civil::{Date, Time, Weekday};
+use jiff::tz::TimeZone;
+use jiff::{SignedDuration, Timestamp, ToSpan};
+
+use super::days_in;
+use crate::domain::WorkDay;
+use crate::time::DateRange;
+use crate::time::resolve::on_date;
+
+/// Time worked in some range of dates.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)]
+pub struct Totals {
+    pub worked: SignedDuration,
+    pub days_worked: usize,
+}
+
+impl Totals {
+    fn of<'a>(days: impl Iterator<Item = &'a WorkDay>) -> Totals {
+        days.filter(|day| !day.is_empty()).fold(Totals::default(), |totals, day| Totals {
+            worked: totals.worked + day.worked(),
+            days_worked: totals.days_worked + 1,
+        })
+    }
+
+    /// Average time per day worked (not per calendar day).
+    pub fn average_day(&self) -> Option<SignedDuration> {
+        let days = i32::try_from(self.days_worked).ok().filter(|days| *days > 0)?;
+        Some(self.worked / days)
+    }
+}
+
+/// When a work day started and ended, in minutes after midnight of its date.
+/// A night shift ending at 04:10 the next morning ends at minute 1690 (28:10).
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub struct DaySpan {
+    pub date: Date,
+    pub start_minute: i64,
+    pub end_minute: i64,
+}
+
+/// What the overview needs from the settings.
+#[derive(Debug, Clone, Copy)]
+pub struct Targets {
+    pub daily: SignedDuration,
+    pub week_start: Weekday,
+}
+
+#[derive(Debug, Clone, PartialEq)]
+pub struct Overview {
+    pub this_week: Totals,
+    pub last_week: Totals,
+    pub this_month: Totals,
+    /// Everything in the selected period.
+    pub period: Totals,
+    /// Over the selected period: for each day worked, time worked minus the
+    /// daily target, added up. Positive means you worked more than planned.
+    pub balance: SignedDuration,
+    /// Time worked per week, oldest first, ending with this week:
+    /// (first date of the week, total).
+    pub weeks: Vec<(Date, SignedDuration)>,
+    /// First start and last end of every day worked in the period.
+    pub spans: Vec<DaySpan>,
+}
+
+pub fn overview(
+    days: &[WorkDay],
+    today: Date,
+    period: DateRange,
+    targets: Targets,
+    zone: &TimeZone,
+    week_count: usize,
+) -> Overview {
+    let this_week = DateRange::week_of(today, targets.week_start);
+    let period_totals = Totals::of(days_in(days, period));
+
+    let balance =
+        days_in(days, period).filter(|day| !day.is_empty()).map(|day| day.worked() - targets.daily).sum();
+
+    let weeks = (0..week_count)
+        .rev()
+        .map(|weeks_ago| {
+            let week_start = this_week.first().saturating_sub((7 * weeks_ago as i64).days());
+            let week = DateRange::week_of(week_start, targets.week_start);
+            (week.first(), Totals::of(days_in(days, week)).worked)
+        })
+        .collect();
+
+    let spans = days_in(days, period).filter_map(|day| day_span(day, zone)).collect();
+
+    Overview {
+        this_week: Totals::of(days_in(days, this_week)),
+        last_week: Totals::of(days_in(days, this_week.previous())),
+        this_month: Totals::of(days_in(days, DateRange::month_of(today))),
+        period: period_totals,
+        balance,
+        weeks,
+        spans,
+    }
+}
+
+fn day_span(day: &WorkDay, zone: &TimeZone) -> Option<DaySpan> {
+    let midnight = on_date(day.date(), Time::midnight(), zone).timestamp();
+    let minutes_after_midnight = |instant: Timestamp| instant.duration_since(midnight).as_mins();
+    Some(DaySpan {
+        date: day.date(),
+        start_minute: minutes_after_midnight(day.first_start()?),
+        end_minute: minutes_after_midnight(day.last_end()?),
+    })
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::domain::{Journal, ShiftState};
+    use jiff::Zoned;
+    use jiff::civil::date;
+
+    fn at(day: i8, hour: i8) -> Zoned {
+        date(2026, 9, day).at(hour, 0, 0, 0).to_zoned(TimeZone::UTC).unwrap()
+    }
+
+    #[test]
+    fn night_shift_spans_go_past_24h() {
+        let segment = crate::domain::Segment::new(at(24, 22).timestamp(), at(25, 4).timestamp()).unwrap();
+        let journal =
+            Journal::from_parts(vec![(date(2026, 9, 24), vec![segment])], ShiftState::Idle).unwrap();
+        let days = journal.snapshot(at(26, 12).timestamp());
+        let targets = Targets { daily: SignedDuration::from_hours(8), week_start: Weekday::Monday };
+        let today = date(2026, 9, 26);
+        let result = overview(&days, today, DateRange::last_days(today, 7), targets, &TimeZone::UTC, 4);
+
+        assert_eq!(
+            result.spans,
+            vec![DaySpan { date: date(2026, 9, 24), start_minute: 22 * 60, end_minute: 28 * 60 }]
+        );
+        assert_eq!(result.this_week.worked, SignedDuration::from_hours(6));
+        assert_eq!(result.balance, SignedDuration::from_hours(-2));
+        assert_eq!(result.weeks.len(), 4);
+    }
+}
diff --git a/src/analysis/rhythm.rs b/src/analysis/rhythm.rs
new file mode 100644
index 0000000..1c0ca7a
--- /dev/null
+++ b/src/analysis/rhythm.rs
@@ -0,0 +1,88 @@
+//! When you work: time worked in each hour of each weekday.
+//!
+//! Segments are cut at every hour boundary on the clock, so a shift from
+//! 22:30 to 01:00 adds 30 minutes to 22h and 60 minutes to 23h on its first
+//! weekday, and 60 minutes to 00h on the next one.
+
+use jiff::civil::Weekday;
+use jiff::tz::TimeZone;
+use jiff::{RoundMode, SignedDuration, Unit, ZonedRound};
+
+use super::days_in;
+use crate::domain::WorkDay;
+use crate::time::DateRange;
+
+#[derive(Debug, Clone, PartialEq)]
+pub struct Rhythm {
+    /// The weekday of each row, starting with the week start.
+    pub weekdays: [Weekday; 7],
+    /// Seconds worked: `seconds[row][hour]`.
+    pub seconds: [[i64; 24]; 7],
+    /// How many weeks the data covers (to turn totals into averages).
+    pub weeks: f64,
+}
+
+impl Rhythm {
+    /// The busiest hours of the day (all weekdays together), busiest first.
+    pub fn peak_hours(&self, count: usize) -> Vec<i8> {
+        let mut hours: Vec<(i8, i64)> = (0..24i8)
+            .map(|hour| (hour, self.seconds.iter().map(|row| row[hour as usize]).sum()))
+            .filter(|(_, seconds)| *seconds > 0)
+            .collect();
+        hours.sort_by_key(|(hour, seconds)| (std::cmp::Reverse(*seconds), *hour));
+        hours.into_iter().take(count).map(|(hour, _)| hour).collect()
+    }
+
+    /// The largest cell, to scale colors against.
+    pub fn busiest_cell(&self) -> i64 {
+        self.seconds.iter().flatten().copied().max().unwrap_or(0)
+    }
+}
+
+pub fn rhythm(days: &[WorkDay], range: DateRange, week_start: Weekday, zone: &TimeZone) -> Rhythm {
+    let weekdays: [Weekday; 7] = std::array::from_fn(|offset| week_start.wrapping_add(offset as i64));
+    let mut seconds = [[0i64; 24]; 7];
+
+    for segment in days_in(days, range).flat_map(|day| day.segments()) {
+        let mut cursor = segment.start().to_zoned(zone.clone());
+        let end = segment.end();
+        while cursor.timestamp() < end {
+            let hour_start = cursor
+                .round(ZonedRound::new().smallest(Unit::Hour).mode(RoundMode::Trunc))
+                .unwrap_or_else(|_| cursor.clone());
+            let next_hour = hour_start.timestamp() + SignedDuration::from_hours(1);
+            let piece_end = next_hour.min(end);
+
+            let row = cursor.weekday().since(week_start) as usize;
+            seconds[row][cursor.hour() as usize] += piece_end.duration_since(cursor.timestamp()).as_secs();
+            cursor = piece_end.to_zoned(zone.clone());
+        }
+    }
+
+    Rhythm { weekdays, seconds, weeks: f64::from(range.day_count()) / 7.0 }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::domain::{Journal, Segment, ShiftState};
+    use jiff::civil::date;
+
+    #[test]
+    fn night_shifts_split_across_hours_and_weekdays() {
+        let zone = TimeZone::UTC;
+        let start = date(2026, 9, 24).at(22, 30, 0, 0).to_zoned(zone.clone()).unwrap(); // Thursday
+        let end = date(2026, 9, 25).at(1, 0, 0, 0).to_zoned(zone.clone()).unwrap(); // Friday
+        let segment = Segment::new(start.timestamp(), end.timestamp()).unwrap();
+        let journal =
+            Journal::from_parts(vec![(date(2026, 9, 24), vec![segment])], ShiftState::Idle).unwrap();
+        let days = journal.snapshot(end.timestamp());
+
+        let result = rhythm(&days, DateRange::last_days(date(2026, 9, 25), 7), Weekday::Monday, &zone);
+        let (thursday, friday) = (3, 4);
+        assert_eq!(result.seconds[thursday][22], 30 * 60);
+        assert_eq!(result.seconds[thursday][23], 60 * 60);
+        assert_eq!(result.seconds[friday][0], 60 * 60);
+        assert_eq!(result.peak_hours(1), vec![0]);
+    }
+}
diff --git a/src/main.rs b/src/main.rs
index 0b0825b..0b7f45e 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -4,6 +4,7 @@
 //! then this only declares the modules written so far.
 #![allow(dead_code)]
 
+mod analysis;
 mod domain;
 mod time;