diff --git a/src/AggregateFunctions/AggregateFunctionStatisticsSimple.h b/src/AggregateFunctions/AggregateFunctionStatisticsSimple.h
index 72c2ce014e4..0d214d5677c 100644
--- a/src/AggregateFunctions/AggregateFunctionStatisticsSimple.h
+++ b/src/AggregateFunctions/AggregateFunctionStatisticsSimple.h
@@ -82,14 +82,17 @@ struct VarMoments
 
     T NO_SANITIZE_UNDEFINED getPopulation() const
     {
-        return (m[2] - m[1] * m[1] / m[0]) / m[0];
+        /// Due to numerical errors, the result can be slightly less than zero,
+        /// but it should be impossible. Trim to zero.
+
+        return std::max(T{}, (m[2] - m[1] * m[1] / m[0]) / m[0]);
     }
 
     T NO_SANITIZE_UNDEFINED getSample() const
     {
         if (m[0] == 0)
             return std::numeric_limits<T>::quiet_NaN();
-        return (m[2] - m[1] * m[1] / m[0]) / (m[0] - 1);
+        return std::max(T{}, (m[2] - m[1] * m[1] / m[0]) / (m[0] - 1));
     }
 
     T NO_SANITIZE_UNDEFINED getMoment3() const
@@ -180,7 +183,7 @@ struct VarMomentsDecimal
         if (common::mulOverflow(getM(1), getM(1), tmp) ||
             common::subOverflow(getM(2), NativeType(tmp / m0), tmp))
             throw Exception("Decimal math overflow", ErrorCodes::DECIMAL_OVERFLOW);
-        return convertFromDecimal<DataTypeDecimal<T>, DataTypeNumber<Float64>>(tmp / m0, scale);
+        return std::max(Float64{}, convertFromDecimal<DataTypeDecimal<T>, DataTypeNumber<Float64>>(tmp / m0, scale));
     }
 
     Float64 getSample(UInt32 scale) const
@@ -194,7 +197,7 @@ struct VarMomentsDecimal
         if (common::mulOverflow(getM(1), getM(1), tmp) ||
             common::subOverflow(getM(2), NativeType(tmp / m0), tmp))
             throw Exception("Decimal math overflow", ErrorCodes::DECIMAL_OVERFLOW);
-        return convertFromDecimal<DataTypeDecimal<T>, DataTypeNumber<Float64>>(tmp / (m0 - 1), scale);
+        return std::max(Float64{}, convertFromDecimal<DataTypeDecimal<T>, DataTypeNumber<Float64>>(tmp / (m0 - 1), scale));
     }
 
     Float64 getMoment3(UInt32 scale) const
diff --git a/tests/queries/0_stateless/01278_variance_nonnegative.reference b/tests/queries/0_stateless/01278_variance_nonnegative.reference
new file mode 100644
index 00000000000..405d3348775
--- /dev/null
+++ b/tests/queries/0_stateless/01278_variance_nonnegative.reference
@@ -0,0 +1,8 @@
+0
+0
+0
+0
+0
+0
+0
+0
diff --git a/tests/queries/0_stateless/01278_variance_nonnegative.sql b/tests/queries/0_stateless/01278_variance_nonnegative.sql
new file mode 100644
index 00000000000..aa676d8b269
--- /dev/null
+++ b/tests/queries/0_stateless/01278_variance_nonnegative.sql
@@ -0,0 +1,9 @@
+SELECT varSamp(0.1) FROM numbers(1000000);
+SELECT varPop(0.1) FROM numbers(1000000);
+SELECT stddevSamp(0.1) FROM numbers(1000000);
+SELECT stddevPop(0.1) FROM numbers(1000000);
+
+SELECT varSampStable(0.1) FROM numbers(1000000);
+SELECT varPopStable(0.1) FROM numbers(1000000);
+SELECT stddevSampStable(0.1) FROM numbers(1000000);
+SELECT stddevPopStable(0.1) FROM numbers(1000000);