diff --git a/server/src/main/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsAggregator.java b/server/src/main/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsAggregator.java
index 1d383a2ae19..4774bec573e 100644
--- a/server/src/main/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsAggregator.java
+++ b/server/src/main/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsAggregator.java
@@ -202,7 +202,8 @@ class ExtendedStatsAggregator extends NumericMetricsAggregator.MultiValue {
     private double variance(long owningBucketOrd) {
         double sum = sums.get(owningBucketOrd);
         long count = counts.get(owningBucketOrd);
-        return (sumOfSqrs.get(owningBucketOrd) - ((sum * sum) / count)) / count;
+        double variance = (sumOfSqrs.get(owningBucketOrd) - ((sum * sum) / count)) / count;
+        return variance < 0  ? 0 : variance;
     }
 
     @Override
diff --git a/server/src/main/java/org/elasticsearch/search/aggregations/metrics/InternalExtendedStats.java b/server/src/main/java/org/elasticsearch/search/aggregations/metrics/InternalExtendedStats.java
index 608fd1de435..26a244c8ddf 100644
--- a/server/src/main/java/org/elasticsearch/search/aggregations/metrics/InternalExtendedStats.java
+++ b/server/src/main/java/org/elasticsearch/search/aggregations/metrics/InternalExtendedStats.java
@@ -101,7 +101,8 @@ public class InternalExtendedStats extends InternalStats implements ExtendedStat
 
     @Override
     public double getVariance() {
-        return (sumOfSqrs - ((sum * sum) / count)) / count;
+        double variance =  (sumOfSqrs - ((sum * sum) / count)) / count;
+        return variance < 0  ? 0 : variance;
     }
 
     @Override
diff --git a/server/src/test/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsAggregatorTests.java b/server/src/test/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsAggregatorTests.java
index ca26ba1b206..83713ff52af 100644
--- a/server/src/test/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsAggregatorTests.java
+++ b/server/src/test/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsAggregatorTests.java
@@ -99,6 +99,34 @@ public class ExtendedStatsAggregatorTests extends AggregatorTestCase {
         );
     }
 
+    /**
+     * Testcase for https://github.com/elastic/elasticsearch/issues/37303
+     */
+    public void testVarianceNonNegative() throws IOException {
+        MappedFieldType ft =
+            new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.DOUBLE);
+        ft.setName("field");
+        final ExtendedSimpleStatsAggregator expected = new ExtendedSimpleStatsAggregator();
+        testCase(ft,
+            iw -> {
+                int numDocs = 3;
+                for (int i = 0; i < numDocs; i++) {
+                    Document doc = new Document();
+                    double value = 49.95d;
+                    long valueAsLong = NumericUtils.doubleToSortableLong(value);
+                    doc.add(new SortedNumericDocValuesField("field", valueAsLong));
+                    expected.add(value);
+                    iw.addDocument(doc);
+                }
+            },
+            stats -> {
+                //since the value(49.95) is a constant, variance should be 0
+                assertEquals(0.0d, stats.getVariance(), TOLERANCE);
+                assertEquals(0.0d, stats.getStdDeviation(), TOLERANCE);
+            }
+        );
+    }
+
     public void testRandomLongs() throws IOException {
         MappedFieldType ft =
             new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.LONG);
@@ -236,7 +264,8 @@ public class ExtendedStatsAggregatorTests extends AggregatorTestCase {
         }
 
         double variance() {
-            return (sumOfSqrs - ((sum * sum) / count)) / count;
+            double variance = (sumOfSqrs - ((sum * sum) / count)) / count;
+            return variance < 0  ? 0 : variance;
         }
     }
 }
diff --git a/server/src/test/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsIT.java b/server/src/test/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsIT.java
index 4aa16d6f1d5..bdf67817496 100644
--- a/server/src/test/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsIT.java
+++ b/server/src/test/java/org/elasticsearch/search/aggregations/metrics/ExtendedStatsIT.java
@@ -73,7 +73,8 @@ public class ExtendedStatsIT extends AbstractNumericTestCase {
             sum += val;
             sumOfSqrs += val * val;
         }
-        return (sumOfSqrs - ((sum * sum) / vals.length)) / vals.length;
+        double variance  = (sumOfSqrs - ((sum * sum) / vals.length)) / vals.length;
+        return variance < 0  ? 0 : variance;
     }
 
     @Override
diff --git a/server/src/test/java/org/elasticsearch/search/aggregations/pipeline/ExtendedStatsBucketIT.java b/server/src/test/java/org/elasticsearch/search/aggregations/pipeline/ExtendedStatsBucketIT.java
index a8ebf687ad6..9155947e3b6 100644
--- a/server/src/test/java/org/elasticsearch/search/aggregations/pipeline/ExtendedStatsBucketIT.java
+++ b/server/src/test/java/org/elasticsearch/search/aggregations/pipeline/ExtendedStatsBucketIT.java
@@ -137,6 +137,7 @@ public class ExtendedStatsBucketIT extends ESIntegTestCase {
         double sumOfSqrs = 1.0 + 1.0 + 1.0 + 4.0 + 0.0 + 1.0;
         double avg = sum / count;
         double var = (sumOfSqrs - ((sum * sum) / count)) / count;
+        var = var < 0  ? 0 : var;
         double stdDev = Math.sqrt(var);
         assertThat(extendedStatsBucketValue, notNullValue());
         assertThat(extendedStatsBucketValue.getName(), equalTo("extended_stats_bucket"));