diff --git a/promql/durations.go b/promql/durations.go
index c660dbf464..3dc44fbbc6 100644
--- a/promql/durations.go
+++ b/promql/durations.go
@@ -87,10 +87,21 @@ func (v *durationVisitor) calculateDuration(expr parser.Expr, allowedNegative bo
 	if err != nil {
 		return 0, err
 	}
+	// Reject NaN and infinities up front. NaN compares false against everything,
+	// so without this guard a NaN duration would slip past the bounds check
+	// below and produce an implementation-defined int64 in the time.Duration
+	// conversion at the end of this function.
+	if math.IsNaN(duration) || math.IsInf(duration, 0) {
+		return 0, fmt.Errorf("%d:%d: duration is NaN or infinite", expr.PositionRange().Start, expr.PositionRange().End)
+	}
 	if duration <= 0 && !allowedNegative {
 		return 0, fmt.Errorf("%d:%d: duration must be greater than 0", expr.PositionRange().Start, expr.PositionRange().End)
 	}
-	if duration > 1<<63-1 || duration < -1<<63 {
+	// duration is in seconds; the conversion below produces nanoseconds in an
+	// int64, so the safe input range is +/- math.MaxInt64 / 1e9 seconds. Match
+	// the bound used by the parser for duration literals (see
+	// offset_duration_expr in generated_parser.y).
+	if duration > 1<<63/1e9 || duration < -(1<<63)/1e9 {
 		return 0, fmt.Errorf("%d:%d: duration is out of range", expr.PositionRange().Start, expr.PositionRange().End)
 	}
 	return time.Duration(duration*1000) * time.Millisecond, nil
diff --git a/promql/durations_test.go b/promql/durations_test.go
index 2ade9077c8..3b31e92dd6 100644
--- a/promql/durations_test.go
+++ b/promql/durations_test.go
@@ -266,6 +266,37 @@ func TestCalculateDuration(t *testing.T) {
 			},
 			errorMessage: "modulo by zero",
 		},
+		{
+			name: "NaN from negative base raised to fractional power",
+			expr: &parser.DurationExpr{
+				LHS: &parser.NumberLiteral{Val: -1},
+				RHS: &parser.NumberLiteral{Val: 0.5},
+				Op:  parser.POW,
+			},
+			errorMessage:    "duration is NaN or infinite",
+			allowedNegative: true,
+		},
+		{
+			name: "infinity from huge power",
+			expr: &parser.DurationExpr{
+				LHS: &parser.NumberLiteral{Val: 2},
+				RHS: &parser.NumberLiteral{Val: 1e10},
+				Op:  parser.POW,
+			},
+			errorMessage: "duration is NaN or infinite",
+		},
+		{
+			name:         "duration exceeds time.Duration range",
+			expr:         &parser.NumberLiteral{Val: 1e10},
+			errorMessage: "duration is out of range",
+		},
+		{
+			name: "duration just below the upper bound is accepted",
+			expr: &parser.NumberLiteral{Val: 1e9},
+			// 1e9 seconds is below 1<<63/1e9 seconds (~9.22e9), so it is
+			// representable as a time.Duration. The exact value is preserved.
+			expected: time.Duration(1e9) * time.Second,
+		},
 	}
 
 	for _, tt := range tests {