diff --git a/doc/whats_new/v1.1.rst b/doc/whats_new/v1.1.rst
index b0d36364ec333..bd6a9445a9dce 100644
--- a/doc/whats_new/v1.1.rst
+++ b/doc/whats_new/v1.1.rst
@@ -289,6 +289,10 @@ Changelog
   :pr:`22300` by :user:`Meekail Zain <micky774>` and :pr:`15948` by
   :user:`sysuresh`.
 
+- |Fix| Greatly reduced peak memory usage in :class:`decomposition.PCA` when
+  calling `fit` or `fit_transform`.
+  :pr:`22553` by :user:`Meekail Zain <micky774>`.
+
 :mod:`sklearn.discriminant_analysis`
 ....................................
 
diff --git a/sklearn/decomposition/_pca.py b/sklearn/decomposition/_pca.py
index 53afa48bc9343..01cdf5f8ad279 100644
--- a/sklearn/decomposition/_pca.py
+++ b/sklearn/decomposition/_pca.py
@@ -619,12 +619,19 @@ def _fit_truncated(self, X, n_components, svd_solver):
 
         # Get variance explained by singular values
         self.explained_variance_ = (S**2) / (n_samples - 1)
-        total_var = np.var(X, ddof=1, axis=0)
-        self.explained_variance_ratio_ = self.explained_variance_ / total_var.sum()
+
+        # Workaround in-place variance calculation since at the time numpy
+        # did not have a way to calculate variance in-place.
+        N = X.shape[0] - 1
+        np.square(X, out=X)
+        np.sum(X, axis=0, out=X[0])
+        total_var = (X[0] / N).sum()
+
+        self.explained_variance_ratio_ = self.explained_variance_ / total_var
         self.singular_values_ = S.copy()  # Store the singular values.
 
         if self.n_components_ < min(n_features, n_samples):
-            self.noise_variance_ = total_var.sum() - self.explained_variance_.sum()
+            self.noise_variance_ = total_var - self.explained_variance_.sum()
             self.noise_variance_ /= min(n_features, n_samples) - n_components
         else:
             self.noise_variance_ = 0.0
diff --git a/sklearn/decomposition/tests/test_pca.py b/sklearn/decomposition/tests/test_pca.py
index b8c95deaee5a5..44b97a5fc1ce7 100644
--- a/sklearn/decomposition/tests/test_pca.py
+++ b/sklearn/decomposition/tests/test_pca.py
@@ -95,7 +95,7 @@ def test_whitening(solver, copy):
     X_ = X.copy()
     pca = PCA(
         n_components=n_components, whiten=False, copy=copy, svd_solver=solver
-    ).fit(X_)
+    ).fit(X_.copy())
     X_unwhitened = pca.transform(X_)
     assert X_unwhitened.shape == (n_samples, n_components)
 
@@ -720,3 +720,14 @@ def test_feature_names_out():
 
     names = pca.get_feature_names_out()
     assert_array_equal([f"pca{i}" for i in range(2)], names)
+
+
+@pytest.mark.parametrize("copy", [True, False])
+def test_variance_correctness(copy):
+    """Check the accuracy of PCA's internal variance calculation"""
+    rng = np.random.RandomState(0)
+    X = rng.randn(1000, 200)
+    pca = PCA().fit(X)
+    pca_var = pca.explained_variance_ / pca.explained_variance_ratio_
+    true_var = np.var(X, ddof=1, axis=0).sum()
+    np.testing.assert_allclose(pca_var, true_var)