diff --git a/components/calendar/Cargo.toml b/components/calendar/Cargo.toml
index 8aa62fd9e56..9967975f005 100644
--- a/components/calendar/Cargo.toml
+++ b/components/calendar/Cargo.toml
@@ -63,6 +63,10 @@ harness = false
 name = "datetime"
 harness = false
 
+[[bench]]
+name = "iso"
+harness = false
+
 [[example]]
 name = "iso_date_manipulations"
 
diff --git a/components/calendar/benches/iso.rs b/components/calendar/benches/iso.rs
new file mode 100644
index 00000000000..184ba0ce2f6
--- /dev/null
+++ b/components/calendar/benches/iso.rs
@@ -0,0 +1,20 @@
+// This file is part of ICU4X. For terms of use, please see the file
+// called LICENSE at the top level of the ICU4X source tree
+// (online at: https://github.com/unicode-org/icu4x/blob/main/LICENSE ).
+
+use criterion::{black_box, criterion_group, criterion_main, Criterion};
+use icu_calendar::{DateTime, Iso};
+
+fn overview_bench(c: &mut Criterion) {
+    c.bench_function("iso/from_minutes_since_local_unix_epoch", |b| {
+        b.iter(|| {
+            for i in -250..250 {
+                let minutes = i * 10000;
+                DateTime::<Iso>::from_minutes_since_local_unix_epoch(black_box(minutes));
+            }
+        });
+    });
+}
+
+criterion_group!(benches, overview_bench,);
+criterion_main!(benches);
diff --git a/components/calendar/src/helpers.rs b/components/calendar/src/helpers.rs
new file mode 100644
index 00000000000..44e98d4a61a
--- /dev/null
+++ b/components/calendar/src/helpers.rs
@@ -0,0 +1,69 @@
+// This file is part of ICU4X. For terms of use, please see the file
+// called LICENSE at the top level of the ICU4X source tree
+// (online at: https://github.com/unicode-org/icu4x/blob/main/LICENSE ).
+
+/// Calculate `(n / d, n % d)` such that the remainder is always positive.
+pub fn div_rem_euclid(n: i32, d: i32) -> (i32, i32) {
+    debug_assert!(d > 0);
+    let (a, b) = (n / d, n % d);
+    if n >= 0 || b == 0 {
+        (a, b)
+    } else {
+        (a - 1, d + b)
+    }
+}
+
+#[test]
+fn test_div_rem_euclid() {
+    assert_eq!(div_rem_euclid(i32::MIN, 1), (-2147483648, 0));
+    assert_eq!(div_rem_euclid(i32::MIN, 2), (-1073741824, 0));
+    assert_eq!(div_rem_euclid(i32::MIN, 3), (-715827883, 1));
+
+    assert_eq!(div_rem_euclid(-10, 1), (-10, 0));
+    assert_eq!(div_rem_euclid(-10, 2), (-5, 0));
+    assert_eq!(div_rem_euclid(-10, 3), (-4, 2));
+
+    assert_eq!(div_rem_euclid(-9, 1), (-9, 0));
+    assert_eq!(div_rem_euclid(-9, 2), (-5, 1));
+    assert_eq!(div_rem_euclid(-9, 3), (-3, 0));
+
+    assert_eq!(div_rem_euclid(-8, 1), (-8, 0));
+    assert_eq!(div_rem_euclid(-8, 2), (-4, 0));
+    assert_eq!(div_rem_euclid(-8, 3), (-3, 1));
+
+    assert_eq!(div_rem_euclid(-2, 1), (-2, 0));
+    assert_eq!(div_rem_euclid(-2, 2), (-1, 0));
+    assert_eq!(div_rem_euclid(-2, 3), (-1, 1));
+
+    assert_eq!(div_rem_euclid(-1, 1), (-1, 0));
+    assert_eq!(div_rem_euclid(-1, 2), (-1, 1));
+    assert_eq!(div_rem_euclid(-1, 3), (-1, 2));
+
+    assert_eq!(div_rem_euclid(0, 1), (0, 0));
+    assert_eq!(div_rem_euclid(0, 2), (0, 0));
+    assert_eq!(div_rem_euclid(0, 3), (0, 0));
+
+    assert_eq!(div_rem_euclid(1, 1), (1, 0));
+    assert_eq!(div_rem_euclid(1, 2), (0, 1));
+    assert_eq!(div_rem_euclid(1, 3), (0, 1));
+
+    assert_eq!(div_rem_euclid(2, 1), (2, 0));
+    assert_eq!(div_rem_euclid(2, 2), (1, 0));
+    assert_eq!(div_rem_euclid(2, 3), (0, 2));
+
+    assert_eq!(div_rem_euclid(8, 1), (8, 0));
+    assert_eq!(div_rem_euclid(8, 2), (4, 0));
+    assert_eq!(div_rem_euclid(8, 3), (2, 2));
+
+    assert_eq!(div_rem_euclid(9, 1), (9, 0));
+    assert_eq!(div_rem_euclid(9, 2), (4, 1));
+    assert_eq!(div_rem_euclid(9, 3), (3, 0));
+
+    assert_eq!(div_rem_euclid(10, 1), (10, 0));
+    assert_eq!(div_rem_euclid(10, 2), (5, 0));
+    assert_eq!(div_rem_euclid(10, 3), (3, 1));
+
+    assert_eq!(div_rem_euclid(i32::MAX, 1), (2147483647, 0));
+    assert_eq!(div_rem_euclid(i32::MAX, 2), (1073741823, 1));
+    assert_eq!(div_rem_euclid(i32::MAX, 3), (715827882, 1));
+}
diff --git a/components/calendar/src/iso.rs b/components/calendar/src/iso.rs
index 08198fe7d29..641fd25bc14 100644
--- a/components/calendar/src/iso.rs
+++ b/components/calendar/src/iso.rs
@@ -31,6 +31,7 @@
 
 use crate::any_calendar::AnyCalendarKind;
 use crate::calendar_arithmetic::{ArithmeticDate, CalendarArithmetic};
+use crate::helpers;
 use crate::{types, Calendar, CalendarError, Date, DateDuration, DateDurationUnit, DateTime};
 use tinystr::tinystr;
 
@@ -313,9 +314,12 @@ impl DateTime<Iso> {
 
     /// Convert minute count since 00:00:00 on Jan 1st, 1970 to ISO Date.
     ///
+    /// # Examples
+    ///
     /// ```rust
     /// use icu::calendar::DateTime;
     ///
+    /// // After Unix Epoch
     /// let today = DateTime::try_new_iso_datetime(2020, 2, 29, 0, 0, 0).unwrap();
     ///
     /// assert_eq!(today.minutes_since_local_unix_epoch(), 26382240);
@@ -324,10 +328,20 @@ impl DateTime<Iso> {
     ///     today
     /// );
     ///
+    /// // Unix Epoch
     /// let today = DateTime::try_new_iso_datetime(1970, 1, 1, 0, 0, 0).unwrap();
     ///
     /// assert_eq!(today.minutes_since_local_unix_epoch(), 0);
     /// assert_eq!(DateTime::from_minutes_since_local_unix_epoch(0), today);
+    ///
+    /// // Before Unix Epoch
+    /// let today = DateTime::try_new_iso_datetime(1967, 4, 6, 20, 40, 0).unwrap();
+    ///
+    /// assert_eq!(today.minutes_since_local_unix_epoch(), -1440200);
+    /// assert_eq!(
+    ///     DateTime::from_minutes_since_local_unix_epoch(-1440200),
+    ///     today
+    /// );
     /// ```
     pub fn from_minutes_since_local_unix_epoch(minute: i32) -> DateTime<Iso> {
         let (time, extra_days) = types::Time::from_minute_with_remainder_days(minute);
@@ -415,8 +429,7 @@ impl Iso {
     // Lisp code reference: https://github.com/EdReingold/calendar-code2/blob/1ee51ecfaae6f856b0d7de3e36e9042100b4f424/calendar.l#L1191-L1217
     fn iso_year_from_fixed(date: i32) -> i32 {
         // 400 year cycles have 146097 days
-        let n_400 = date / 146097;
-        let date = date % 146097;
+        let (n_400, date) = helpers::div_rem_euclid(date, 146097);
 
         // 100 year cycles have 36524 days
         let n_100 = date / 36524;
@@ -655,4 +668,60 @@ mod test {
         let offset = today.added(DateDuration::new(0, 1, 0, 1));
         assert_eq!(offset, today_plus_1_month_1_day);
     }
+
+    #[test]
+    fn test_iso_to_from_fixed() {
+        // Reminder: ISO year 0 is Gregorian year 1 BCE.
+        // Year 0 is a leap year due to the 400-year rule.
+        fn check(fixed: i32, year: i32, month: u8, day: u8) {
+            assert_eq!(Iso::iso_year_from_fixed(fixed), year, "fixed: {}", fixed);
+            assert_eq!(
+                Iso::iso_from_fixed(fixed),
+                Date::try_new_iso_date(year, month, day).unwrap(),
+                "fixed: {}",
+                fixed
+            );
+            assert_eq!(
+                Iso::fixed_from_iso_integers(year, month, day),
+                Some(fixed),
+                "fixed: {}",
+                fixed
+            );
+        }
+        check(-1828, -5, 12, 31);
+        check(-1827, -4, 1, 1); // leap year
+        check(-1826, -4, 1, 2);
+        check(-1462, -4, 12, 31);
+        check(-1461, -3, 1, 1);
+        check(-1460, -3, 1, 2);
+        check(-732, -2, 12, 31);
+        check(-731, -1, 1, 1);
+        check(-367, -1, 12, 31);
+        check(-366, 0, 1, 1); // leap year
+        check(-365, 0, 1, 2);
+        check(-1, 0, 12, 31);
+        check(0, 1, 1, 1);
+        check(1, 1, 1, 2);
+        check(364, 1, 12, 31);
+        check(365, 2, 1, 1);
+        check(1459, 4, 12, 30);
+        check(1460, 4, 12, 31); // leap year
+        check(1461, 5, 1, 1);
+    }
+
+    #[test]
+    fn test_from_minutes_since_local_unix_epoch() {
+        fn check(minutes: i32, year: i32, month: u8, day: u8, hour: u8, minute: u8) {
+            let today = DateTime::try_new_iso_datetime(year, month, day, hour, minute, 0).unwrap();
+            assert_eq!(today.minutes_since_local_unix_epoch(), minutes);
+            assert_eq!(
+                DateTime::from_minutes_since_local_unix_epoch(minutes),
+                today
+            );
+        }
+
+        check(-1441, 1969, 12, 30, 23, 59);
+        check(-1440, 1969, 12, 31, 0, 0);
+        check(-1439, 1969, 12, 30, 0, 1);
+    }
 }
diff --git a/components/calendar/src/lib.rs b/components/calendar/src/lib.rs
index 0124c5b0540..cf21430e5b2 100644
--- a/components/calendar/src/lib.rs
+++ b/components/calendar/src/lib.rs
@@ -124,6 +124,7 @@ mod duration;
 mod error;
 pub mod ethiopian;
 pub mod gregorian;
+mod helpers;
 pub mod indian;
 pub mod iso;
 pub mod japanese;
diff --git a/components/calendar/src/types.rs b/components/calendar/src/types.rs
index bb462b03827..a23a646cd01 100644
--- a/components/calendar/src/types.rs
+++ b/components/calendar/src/types.rs
@@ -5,6 +5,7 @@
 //! This module contains various types used by `icu_calendar` and `icu_datetime`
 
 use crate::error::CalendarError;
+use crate::helpers;
 use core::convert::TryFrom;
 use core::convert::TryInto;
 use core::fmt;
@@ -479,23 +480,8 @@ impl Time {
     /// Takes a number of minutes, which could be positive or negative, and returns the Time
     /// and the day number, which could be positive or negative.
     pub(crate) fn from_minute_with_remainder_days(minute: i32) -> (Time, i32) {
-        let minutes_a_hour = 60;
-        let hours_a_day = 24;
-        let minutes_a_day = minutes_a_hour * hours_a_day;
-        let extra_days = if minute.is_negative() {
-            // TODO: migrate to div_floor
-            (minute + 1) / minutes_a_day - 1
-        } else {
-            minute / minutes_a_day
-        };
-
-        let minutes = (minutes_a_hour + minute % minutes_a_hour) % minutes_a_hour;
-        let hours = if minute.is_negative() {
-            ((minutes_a_day - minutes - (minute % minutes_a_day).abs()) / minutes_a_hour)
-                % hours_a_day
-        } else {
-            (minute / minutes_a_hour) % hours_a_day
-        };
+        let (extra_days, minute_in_day) = helpers::div_rem_euclid(minute, 1440);
+        let (hours, minutes) = (minute_in_day / 60, minute_in_day % 60);
         #[allow(clippy::unwrap_used)] // values are moduloed to be in range
         (
             Self {