diff --git a/api/pagination.py b/api/pagination.py
index 6029713..fa9c032 100644
--- a/api/pagination.py
+++ b/api/pagination.py
@@ -1,10 +1,20 @@
+import math
+
+
 def paginate(items, page, per_page=10):
-    """Return one page of `items` plus paging metadata for the JSON response."""
-    start = page * per_page
+    """Return one page of `items` plus paging metadata for the JSON response.
+
+    Pages are 1-indexed.
+    """
+    if page < 1:
+        raise ValueError(f"page must be >= 1, got {page}")
+    if per_page < 1:
+        raise ValueError(f"per_page must be >= 1, got {per_page}")
+    start = (page - 1) * per_page
     end = start + per_page
     return {
         "items": items[start:end],
         "page": page,
         "per_page": per_page,
-        "total_pages": len(items) // per_page,
+        "total_pages": math.ceil(len(items) / per_page),
     }
diff --git a/tests/test_pagination.py b/tests/test_pagination.py
index 897ad1d..6e37778 100644
--- a/tests/test_pagination.py
+++ b/tests/test_pagination.py
@@ -1,6 +1,29 @@
+import pytest
+
 from api.pagination import paginate
 
 
 def test_metadata_shape():
     result = paginate(list(range(30)), 1, per_page=10)
     assert set(result) == {"items", "page", "per_page", "total_pages"}
+
+
+def test_first_page_is_page_one():
+    assert paginate(list(range(23)), 1)["items"] == list(range(10))
+
+
+def test_last_partial_page():
+    result = paginate(list(range(23)), 3)
+    assert result["items"] == [20, 21, 22]
+    assert result["total_pages"] == 3
+
+
+def test_exact_multiple_and_empty():
+    assert paginate(list(range(20)), 1)["total_pages"] == 2
+    assert paginate([], 1)["total_pages"] == 0
+
+
+@pytest.mark.parametrize("page,per_page", [(0, 10), (-1, 10), (1, 0)])
+def test_rejects_out_of_range(page, per_page):
+    with pytest.raises(ValueError):
+        paginate(list(range(5)), page, per_page=per_page)