diff --git a/spec/manual/hash_large_spec.cr b/spec/manual/hash_large_spec.cr
new file mode 100644
index 000000000000..d4ca4af96a8f
--- /dev/null
+++ b/spec/manual/hash_large_spec.cr
@@ -0,0 +1,8 @@
+require "spec"
+
+it "creates Hash at maximum capacity" do
+  # we don't try to go as high as Int32::MAX because it would allocate 18GB of
+  # memory in total. This already tests for Int32 overflows while 'only' needing
+  # 4.5GB of memory.
+  Hash(Int32, Int32).new(initial_capacity: (Int32::MAX // 4) + 1)
+end
diff --git a/src/hash.cr b/src/hash.cr
index 9b2936ddd618..1be6543d730c 100644
--- a/src/hash.cr
+++ b/src/hash.cr
@@ -236,12 +236,14 @@ class Hash(K, V)
       # Translate initial capacity to the nearest power of 2, but keep it a minimum of 8.
       if initial_capacity < 8
         initial_entries_size = 8
+      elsif initial_capacity > 2**30
+        initial_entries_size = Int32::MAX
       else
         initial_entries_size = Math.pw2ceil(initial_capacity)
       end
 
       # Because we always keep indice_size >= entries_size * 2
-      initial_indices_size = initial_entries_size * 2
+      initial_indices_size = initial_entries_size.to_u64 * 2
 
       @entries = malloc_entries(initial_entries_size)
 
@@ -830,7 +832,7 @@ class Hash(K, V)
 
   # The actual number of bytes needed to allocate `@indices`.
   private def indices_malloc_size(size)
-    size * @indices_bytesize
+    size.to_u64 * @indices_bytesize
   end
 
   # Reallocates `size` number of indices for `@indices`.