diff --git a/src/format/mod.rs b/src/format/mod.rs
index d5c4212a40..e3b9b51344 100644
--- a/src/format/mod.rs
+++ b/src/format/mod.rs
@@ -521,10 +521,10 @@ fn format_inner(
             use self::Numeric::*;
 
             let week_from_sun = |d: &NaiveDate| {
-                (d.ordinal() as i32 - d.weekday().num_days_from_sunday() as i32 + 7) / 7
+                (d.ordinal() as i32 - d.weekday().num_days_from_sunday() as i32 + 6) / 7
             };
             let week_from_mon = |d: &NaiveDate| {
-                (d.ordinal() as i32 - d.weekday().num_days_from_monday() as i32 + 7) / 7
+                (d.ordinal() as i32 - d.weekday().num_days_from_monday() as i32 + 6) / 7
             };
 
             let (width, v) = match *spec {
diff --git a/src/format/strftime.rs b/src/format/strftime.rs
index aafe01f736..dcaabe49f2 100644
--- a/src/format/strftime.rs
+++ b/src/format/strftime.rs
@@ -584,7 +584,7 @@ fn test_strftime_docs() {
     assert_eq!(dt.format("%A").to_string(), "Sunday");
     assert_eq!(dt.format("%w").to_string(), "0");
     assert_eq!(dt.format("%u").to_string(), "7");
-    assert_eq!(dt.format("%U").to_string(), "28");
+    assert_eq!(dt.format("%U").to_string(), "27");
     assert_eq!(dt.format("%W").to_string(), "27");
     assert_eq!(dt.format("%G").to_string(), "2001");
     assert_eq!(dt.format("%g").to_string(), "01");
diff --git a/src/naive/date.rs b/src/naive/date.rs
index 79d0a98baa..e3cc9b6c6a 100644
--- a/src/naive/date.rs
+++ b/src/naive/date.rs
@@ -2869,7 +2869,7 @@ mod tests {
         // corner cases
         assert_eq!(
             NaiveDate::from_ymd_opt(2007, 12, 31).unwrap().format("%G,%g,%U,%W,%V").to_string(),
-            "2008,08,53,53,01"
+            "2008,08,52,53,01"
         );
         assert_eq!(
             NaiveDate::from_ymd_opt(2010, 1, 3).unwrap().format("%G,%g,%U,%W,%V").to_string(),
diff --git a/tests/dateutils.rs b/tests/dateutils.rs
index 130649a71f..dec6bfe117 100644
--- a/tests/dateutils.rs
+++ b/tests/dateutils.rs
@@ -74,3 +74,58 @@ fn try_verify_against_date_command() {
         date += chrono::Duration::hours(1);
     }
 }
+
+#[cfg(target_os = "linux")]
+fn verify_against_date_command_format_local(path: &'static str, dt: NaiveDateTime) {
+    let required_format =
+        "d%d D%D F%F H%H I%I j%j k%k l%l m%m M%M S%S T%T u%u U%U w%w W%W X%X y%y Y%Y z%:z";
+    // a%a - depends from localization
+    // A%A - depends from localization
+    // b%b - depends from localization
+    // B%B - depends from localization
+    // h%h - depends from localization
+    // c%c - depends from localization
+    // p%p - depends from localization
+    // r%r - depends from localization
+    // x%x - fails, date is dd/mm/yyyy, chrono is dd/mm/yy, same as %D
+    // Z%Z - too many ways to represent it, will most likely fail
+
+    let output = process::Command::new(path)
+        .arg("-d")
+        .arg(format!(
+            "{}-{:02}-{:02} {:02}:{:02}:{:02}",
+            dt.year(),
+            dt.month(),
+            dt.day(),
+            dt.hour(),
+            dt.minute(),
+            dt.second()
+        ))
+        .arg(format!("+{}", required_format))
+        .output()
+        .unwrap();
+
+    let date_command_str = String::from_utf8(output.stdout).unwrap();
+    let date = NaiveDate::from_ymd_opt(dt.year(), dt.month(), dt.day()).unwrap();
+    let ldt = Local
+        .from_local_datetime(&date.and_hms_opt(dt.hour(), dt.minute(), dt.second()).unwrap())
+        .unwrap();
+    let formated_date = format!("{}\n", ldt.format(required_format));
+    assert_eq!(date_command_str, formated_date);
+}
+
+#[test]
+#[cfg(target_os = "linux")]
+fn try_verify_against_date_command_format() {
+    let date_path = "/usr/bin/date";
+
+    if !path::Path::new(date_path).exists() {
+        // date command not found, skipping
+        return;
+    }
+    let mut date = NaiveDate::from_ymd_opt(1970, 1, 1).unwrap().and_hms_opt(12, 11, 13).unwrap();
+    while date.year() < 2008 {
+        verify_against_date_command_format_local(date_path, date);
+        date += chrono::Duration::days(55);
+    }
+}