diff --git a/pkg/sql/logictest/testdata/logic_test/datetime b/pkg/sql/logictest/testdata/logic_test/datetime
index 5faa5ed51482..55955e782a79 100644
--- a/pkg/sql/logictest/testdata/logic_test/datetime
+++ b/pkg/sql/logictest/testdata/logic_test/datetime
@@ -2064,6 +2064,18 @@ SELECT make_timestamp(2013, 7, 15, 8, 15, 23.5231231244234)::string
 make_timestamp
 2013-07-15 08:15:23.523123
 
+# Test with seconds < 1.
+
+query T
+select make_timestamp(1, 1, 1, 0, 0, 0);
+----
+0001-01-01 00:00:00 +0000 +0000
+
+query T
+select make_timestamp(1, 1, 1, 0, 0, 0.1234);
+----
+0001-01-01 00:00:00.1234 +0000 +0000
+
 statement error pgcode 22008 pq: make_timestamp\(\): year value of 0 is not valid
 SELECT make_timestamp(0, 7, 15, 8, 15, 23.5);
 
@@ -2098,6 +2110,18 @@ SELECT make_timestamptz(2013, 7, 15, 8, 15, 23.5, 'America/New_York')
 make_timestamptz
 2013-07-15 07:15:23.5 -0500 EST
 
+# Test with seconds < 1.
+
+query T
+select make_timestamptz(2020, 1, 1, 0, 0, 0, 'America/New_York');
+----
+2020-01-01 00:00:00 -0500 EST
+
+query T
+select make_timestamptz(2020, 1, 1, 0, 0, 0.1234, 'America/New_York');
+----
+2020-01-01 00:00:00.1234 -0500 EST
+
 statement error pgcode 22008 pq: make_timestamptz\(\): year value of 0 is not valid
 SELECT make_timestamptz(0, 7, 15, 8, 15, 23.5);
 
diff --git a/pkg/sql/sem/builtins/builtins.go b/pkg/sql/sem/builtins/builtins.go
index d57524e2e996..db3ece9e7e7b 100644
--- a/pkg/sql/sem/builtins/builtins.go
+++ b/pkg/sql/sem/builtins/builtins.go
@@ -11998,8 +11998,8 @@ func makeTimestampStatementBuiltinOverload(withOutputTZ bool, withInputTZ bool)
 			hour := int(tree.MustBeDInt(args[3]))
 			min := int(tree.MustBeDInt(args[4]))
 			sec := float64(tree.MustBeDFloat(args[5]))
-			truncatedSec := math.Floor(sec)
-			nsec := math.Mod(sec, truncatedSec) * float64(time.Second)
+			truncatedSec, remainderSec := math.Modf(sec)
+			nsec := remainderSec * float64(time.Second)
 			t := time.Date(year, month, day, hour, min, int(truncatedSec), int(nsec), location)
 			if withOutputTZ {
 				return tree.MakeDTimestampTZ(t, time.Microsecond)