diff --git a/cylc/flow/task_pool.py b/cylc/flow/task_pool.py
index 6ddc62d39f2..e964d2bfedb 100644
--- a/cylc/flow/task_pool.py
+++ b/cylc/flow/task_pool.py
@@ -51,13 +51,13 @@
 from cylc.flow.task_state import (
     TASK_STATUSES_ACTIVE,
     TASK_STATUSES_FINAL,
-    TASK_STATUS_WAITING,
     TASK_STATUS_EXPIRED,
+    TASK_STATUS_FAILED,
     TASK_STATUS_PREPARING,
-    TASK_STATUS_SUBMITTED,
     TASK_STATUS_RUNNING,
+    TASK_STATUS_SUBMITTED,
     TASK_STATUS_SUCCEEDED,
-    TASK_STATUS_FAILED,
+    TASK_STATUS_WAITING,
     TASK_OUTPUT_EXPIRED,
     TASK_OUTPUT_FAILED,
     TASK_OUTPUT_SUCCEEDED,
@@ -362,20 +362,35 @@ def compute_runahead(self, force=False) -> bool:
             # Find the earliest point with unfinished tasks.
             for point, itasks in sorted(self.get_tasks_by_point().items()):
                 if (
-                    points  # got the limit already so this point too
-                    or any(
-                        not itask.state(
-                            TASK_STATUS_FAILED,
-                            TASK_STATUS_SUCCEEDED,
-                            TASK_STATUS_EXPIRED
-                        )
-                        or (
-                            # For Cylc 7 back-compat, ignore incomplete tasks.
-                            # (Success is required in back-compat mode, so
-                            # failedtasks end up as incomplete; and Cylc 7
-                            # ignores failed tasks in computing the limit).
-                            itask.state.outputs.is_incomplete()
-                            and not cylc.flow.flags.cylc7_back_compat
+                    any(
+                        # filter out runahead tasks
+                        itask.state(is_runahead=False)
+                        and (
+                            # waiting tasks
+                            # * tasks with partially satisfied prereqs
+                            # * tasks with incomplete xtriggers
+                            # * held tasks
+                            itask.state(TASK_STATUS_WAITING)
+
+                            # unfinished tasks (back-compat mode)
+                            # * Cylc 7 runahead logic considered a cycle to be
+                            #   active if it had "unfinished" tasks
+                            or (
+                                cylc.flow.flags.cylc7_back_compat
+                                and not itask.state(
+                                    TASK_STATUS_FAILED,
+                                    TASK_STATUS_SUCCEEDED,
+                                    TASK_STATUS_EXPIRED,
+                                )
+                            )
+
+                            # incomplete tasks (optional outputs)
+                            # * tasks with one or more required outputs
+                            #   incomplete
+                            or (
+                                not cylc.flow.flags.cylc7_back_compat
+                                and itask.state.outputs.is_incomplete()
+                            )
                         )
                         for itask in itasks
                     )
diff --git a/tests/integration/test_task_pool.py b/tests/integration/test_task_pool.py
index 97526088660..1efc151a9b2 100644
--- a/tests/integration/test_task_pool.py
+++ b/tests/integration/test_task_pool.py
@@ -1246,3 +1246,91 @@ async def test_detect_incomplete_tasks(
             assert log_filter(log, contains=f"[{itask}] did not complete required outputs:")
             # the task should not have been removed
             assert itask in schd.pool.get_tasks()
+
+
+@pytest.mark.parametrize('back_compat', [True, False])
+@pytest.mark.parametrize('integer', [True, False])
+async def test_compute_runahead(
+    integer,
+    back_compat,
+    flow,
+    scheduler,
+    start,
+    monkeypatch,
+):
+    """Test the calculation of the runahead limit.
+
+    This test ensures that:
+    * Runahead tasks are excluded from computations
+      see https://github.com/cylc/cylc-flow/issues/5825
+    * Tasks are initiated with the correct is_runahead status on statup.
+    * Behaviour is the same in compat/regular modes.
+    * Behaviour is the same for integer/datetime cycling modes.
+
+    """
+    if integer:
+        # cycling mode = integer
+        config = {
+            'scheduler': {
+                'allow implicit tasks': 'True',
+            },
+            'scheduling': {
+                'initial cycle point': '1',
+                'cycling mode': 'integer',
+                'runahead limit': 'P3',
+                'graph': {
+                    'P1': 'a'
+                },
+            }
+        }
+        point = lambda point: IntegerPoint(str(int(point)))
+    else:
+        # cycling mode = gregorian
+        config = {
+            'scheduler': {
+                'allow implicit tasks': 'True',
+                'cycle point format': 'CCYY',
+            },
+            'scheduling': {
+                'initial cycle point': '0001',
+                'runahead limit': 'P3Y',
+                'graph': {
+                    'P1Y': 'a'
+                },
+            }
+        }
+        point = ISO8601Point
+
+    monkeypatch.setattr('cylc.flow.flags.cylc7_back_compat', back_compat)
+
+    id_ = flow(config)
+    schd = scheduler(id_)
+    async with start(schd):
+        schd.pool.compute_runahead(force=True)
+        assert int(str(schd.pool.runahead_limit_point)) == 4
+
+        # ensure task states are initiated with is_runahead status
+        assert schd.pool.get_task(point('0001'), 'a').state(is_runahead=False)
+        assert schd.pool.get_task(point('0005'), 'a').state(is_runahead=True)
+
+        # mark the first three cycles as running
+        for cycle in range(1, 4):
+            schd.pool.get_task(point(f'{cycle:04}'), 'a').state.reset(
+                TASK_STATUS_RUNNING
+            )
+        schd.pool.compute_runahead(force=True)
+        assert int(str(schd.pool.runahead_limit_point)) == 4  # no change
+
+        # mark cycle 1 as incomplete (but finished)
+        schd.pool.get_task(point('0001'), 'a').state.reset(
+            TASK_STATUS_SUBMIT_FAILED
+        )
+        schd.pool.compute_runahead(force=True)
+        assert int(str(schd.pool.runahead_limit_point)) == 4  # no change
+
+        # mark cycle 1 as complete
+        schd.pool.get_task(point('0001'), 'a').state.reset(
+            TASK_STATUS_SUCCEEDED
+        )
+        schd.pool.compute_runahead(force=True)
+        assert int(str(schd.pool.runahead_limit_point)) == 5  # +1