diff --git a/src/NeuralNet/Layers/BatchNorm.php b/src/NeuralNet/Layers/BatchNorm.php
index 421ec9607..7e7d0e15b 100644
--- a/src/NeuralNet/Layers/BatchNorm.php
+++ b/src/NeuralNet/Layers/BatchNorm.php
@@ -181,7 +181,7 @@ public function forward(Matrix $input) : Matrix
         }
 
         $mean = $input->mean();
-        $variance = $input->variance($mean)->clipLower(EPSILON);
+        $variance = $input->subtractColumnVector($mean)->square()->mean()->clipLower(EPSILON);
         $stdInv = $variance->sqrt()->reciprocal();
 
         $xHat = $stdInv->multiply($input->subtract($mean));
@@ -287,10 +287,10 @@ public function gradient(Matrix $dOut, ColumnVector $gamma, ColumnVector $stdInv
 
         $dXHatSigma = $dXHat->sum();
 
-        return $dXHat->multiply($dOut->m())
+        return $dXHat->multiply($dOut->n())
             ->subtract($dXHatSigma)
             ->subtract($xHat->multiply($xHatSigma))
-            ->multiply($stdInv->divide($dOut->m()));
+            ->multiply($stdInv->divide($dOut->n()));
     }
 
     /**
diff --git a/tests/NeuralNet/Layers/BatchNormTest.php b/tests/NeuralNet/Layers/BatchNormTest.php
index 211b0bdd6..fef6b7524 100644
--- a/tests/NeuralNet/Layers/BatchNormTest.php
+++ b/tests/NeuralNet/Layers/BatchNormTest.php
@@ -122,4 +122,65 @@ public function initializeForwardBackInfer() : void
         $this->assertInstanceOf(Matrix::class, $infer);
         $this->assertEqualsWithDelta($expected, $infer->asArray(), 1e-8);
     }
+
+    /**
+     * @test
+     */
+    public function normalizesOverBatchSize() : void
+    {
+        $fanIn = 3;
+
+        $input = Matrix::quick([
+            [1.0, 2.5, -0.1, 0.5],
+            [0.1, 0.0, 3.0, -1.0],
+            [0.002, -6.0, -0.5, 2.0],
+        ]);
+
+        $prevGrad = new Deferred(function () {
+            return Matrix::quick([
+                [0.25, 0.7, 0.1, 0.3],
+                [0.50, 0.2, 0.01, -0.4],
+                [0.25, 0.1, 0.89, 0.6],
+            ]);
+        });
+
+        $optimizer = new Stochastic(0.001);
+
+        $layer = new BatchNorm(0.9, new Constant(0.), new Constant(1.));
+
+        $layer->initialize($fanIn);
+
+        $expected = [
+            [0.025967457200229, 1.584014889214, -1.1166006596098, -0.49338168680435],
+            [-0.28480067232747, -0.35181259522806, 1.6585450917894, -1.0219318242339],
+            [0.3797862163235, -1.643717441354, 0.21054282476168, 1.0533884002688],
+        ];
+
+        $forward = $layer->forward($input);
+
+        $this->assertInstanceOf(Matrix::class, $forward);
+        $this->assertEqualsWithDelta($expected, $forward->asArray(), 1e-8);
+
+        $expected = [
+            [-0.096655673462753, 0.024584160424222, 0.0014008068617791, 0.070670706176752],
+            [0.29326885034768, 0.094619781903042, -0.10430387932137, -0.28358475292935],
+            [-0.094806324008858, -0.017466016738221, 0.13166046771019, -0.019388126963108],
+        ];
+
+        $gradient = $layer->back($prevGrad, $optimizer)->compute();
+
+        $this->assertInstanceOf(Matrix::class, $gradient);
+        $this->assertEqualsWithDelta($expected, $gradient->asArray(), 1e-8);
+
+        $expected = [
+            [0.024595238724167, 1.5813095621742, -1.1169952651392, -0.49430953575917],
+            [-0.28505012503587, -0.35204780151489, 1.6578824928559, -1.0220245663052],
+            [0.37766138009295, -1.6443246681253, 0.20854491954554, 1.0507583684868],
+        ];
+
+        $infer = $layer->infer($input);
+
+        $this->assertInstanceOf(Matrix::class, $infer);
+        $this->assertEqualsWithDelta($expected, $infer->asArray(), 1e-8);
+    }
 }