diff --git a/Lib/test/test_array.py b/Lib/test/test_array.py
index eb6d77fc29d..544c2cefa23 100755
--- a/Lib/test/test_array.py
+++ b/Lib/test/test_array.py
@@ -1015,6 +1015,19 @@ def test_create_from_bytes(self):
         a = array.array('H', b"1234")
         self.assertEqual(len(a) * a.itemsize, 4)
 
+    @support.cpython_only
+    def test_sizeof_with_buffer(self):
+        a = array.array(self.typecode, self.example)
+        basesize = support.calcvobjsize('Pn2Pi')
+        buffer_size = a.buffer_info()[1] * a.itemsize
+        support.check_sizeof(self, a, basesize + buffer_size)
+
+    @support.cpython_only
+    def test_sizeof_without_buffer(self):
+        a = array.array(self.typecode)
+        basesize = support.calcvobjsize('Pn2Pi')
+        support.check_sizeof(self, a, basesize)
+
 
 class StringTest(BaseTest):
 
diff --git a/Misc/ACKS b/Misc/ACKS
index 4dce609a046..037089679be 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -479,6 +479,7 @@ Greg Humphreys
 Eric Huss
 Taihyun Hwang
 Jeremy Hylton
+Ludwig Hähne
 Gerhard Häring
 Fredrik Håård
 Catalin Iacob
diff --git a/Misc/NEWS b/Misc/NEWS
index 972e769c05a..3de680549c4 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -80,6 +80,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #15424: Add a __sizeof__ implementation for array objects.
+  Patch by Ludwig Hähne.
+
 - Issue #15576: Allow extension modules to act as a package's __init__ module.
 
 - Issue #15502: Have importlib.invalidate_caches() work on sys.meta_path
diff --git a/Modules/arraymodule.c b/Modules/arraymodule.c
index f0615c995c5..04eb67c7906 100644
--- a/Modules/arraymodule.c
+++ b/Modules/arraymodule.c
@@ -1567,6 +1567,19 @@ array.tobytes().decode() to obtain a unicode string from\n\
 an array of some other type.");
 
 
+static PyObject *
+array_sizeof(arrayobject *self, PyObject *unused)
+{
+    Py_ssize_t res;
+    res = sizeof(arrayobject) + self->allocated * self->ob_descr->itemsize;
+    return PyLong_FromSsize_t(res);
+}
+
+PyDoc_STRVAR(sizeof_doc,
+"__sizeof__() -> int\n\
+\n\
+Size of the array in memory, in bytes.");
+
 
 /*********************** Pickling support ************************/
 
@@ -2143,6 +2156,8 @@ static PyMethodDef array_methods[] = {
      tobytes_doc},
     {"tounicode",   (PyCFunction)array_tounicode,       METH_NOARGS,
      tounicode_doc},
+    {"__sizeof__",      (PyCFunction)array_sizeof,      METH_NOARGS,
+     sizeof_doc},
     {NULL,              NULL}           /* sentinel */
 };