diff --git a/log4j-core-test/src/test/java/org/apache/logging/log4j/core/appender/rolling/PatternProcessorTest.java b/log4j-core-test/src/test/java/org/apache/logging/log4j/core/appender/rolling/PatternProcessorTest.java
index 0c3e6dfabc1..ee333d6fe42 100644
--- a/log4j-core-test/src/test/java/org/apache/logging/log4j/core/appender/rolling/PatternProcessorTest.java
+++ b/log4j-core-test/src/test/java/org/apache/logging/log4j/core/appender/rolling/PatternProcessorTest.java
@@ -16,6 +16,7 @@
  */
 package org.apache.logging.log4j.core.appender.rolling;
 
+import static org.junit.jupiter.api.Assertions.assertDoesNotThrow;
 import static org.junit.jupiter.api.Assertions.assertEquals;
 
 import java.time.Instant;
@@ -29,6 +30,8 @@
 import org.junit.jupiter.api.parallel.ResourceAccessMode;
 import org.junit.jupiter.api.parallel.ResourceLock;
 import org.junit.jupiter.api.parallel.Resources;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.ValueSource;
 
 /**
  * Tests the PatternProcessor class.
@@ -394,4 +397,10 @@ public void testGetNextTimeDailyReturnsFirstHourOfNextDayInGmtIfZoneIsInvalid()
             TimeZone.setDefault(old);
         }
     }
+
+    @ParameterizedTest
+    @ValueSource(strings = {"%d{UNIX}", "%d{UNIX_MILLIS}"})
+    void does_not_throw_with_unix_pattern(final String pattern) {
+        assertDoesNotThrow(() -> new PatternProcessor(pattern));
+    }
 }
diff --git a/log4j-core/src/main/java/org/apache/logging/log4j/core/appender/rolling/PatternProcessor.java b/log4j-core/src/main/java/org/apache/logging/log4j/core/appender/rolling/PatternProcessor.java
index feb26cebc54..ea8998f0175 100644
--- a/log4j-core/src/main/java/org/apache/logging/log4j/core/appender/rolling/PatternProcessor.java
+++ b/log4j-core/src/main/java/org/apache/logging/log4j/core/appender/rolling/PatternProcessor.java
@@ -325,6 +325,10 @@ protected final void formatFileName(final StringBuilder buf, final Object... obj
     }
 
     private RolloverFrequency calculateFrequency(final String pattern) {
+        // The UNIX and UNIX_MILLIS converters do not have a pattern
+        if (pattern == null) {
+            return null;
+        }
         if (patternContains(pattern, MILLIS_CHAR)) {
             return RolloverFrequency.EVERY_MILLISECOND;
         }
diff --git a/log4j-core/src/main/java/org/apache/logging/log4j/core/pattern/DatePatternConverter.java b/log4j-core/src/main/java/org/apache/logging/log4j/core/pattern/DatePatternConverter.java
index 327593c9662..05157f812a3 100644
--- a/log4j-core/src/main/java/org/apache/logging/log4j/core/pattern/DatePatternConverter.java
+++ b/log4j-core/src/main/java/org/apache/logging/log4j/core/pattern/DatePatternConverter.java
@@ -359,7 +359,7 @@ public void format(final StringBuilder toAppendTo, final Object... objects) {
     /**
      * Gets the pattern string describing this date format.
      *
-     * @return the pattern string describing this date format.
+     * @return the pattern string describing this date format or {@code  null} if the format does not have a pattern.
      */
     public String getPattern() {
         return formatter.toPattern();
diff --git a/src/changelog/.2.x.x/2346_unix_millis_data_pattern.xml b/src/changelog/.2.x.x/2346_unix_millis_data_pattern.xml
new file mode 100644
index 00000000000..53a94729e19
--- /dev/null
+++ b/src/changelog/.2.x.x/2346_unix_millis_data_pattern.xml
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<entry xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+       xmlns="http://logging.apache.org/log4j/changelog"
+       xsi:schemaLocation="http://logging.apache.org/log4j/changelog https://logging.apache.org/log4j/changelog-0.1.3.xsd"
+       type="changed">
+  <issue id="2346" link="https://github.com/apache/logging-log4j2/pull/2346"/>
+  <description format="asciidoc">Fix `NullPointerException` in `PatternProcessor` for a `UNIX_MILLIS` pattern.</description>
+</entry>