diff --git a/scripts/mutation-registry.mjs b/scripts/mutation-registry.mjs
index 8d1945d8..235b74c1 100644
--- a/scripts/mutation-registry.mjs
+++ b/scripts/mutation-registry.mjs
@@ -96,6 +96,18 @@ const MUTANT_DEFINITIONS = [
       replace: '    return source; // mutant: footprints no longer affect clean area\n',
     }],
   },
+  {
+    id: 'stairs-summary-area-clips-all-footprints-in-one-task',
+    guard: 'npx tsc -p tsconfig.test.json && node scripts/fix-test-build.mjs '
+      + '&& node --test test/stairs.test.mjs',
+    because: '#663 AC13: the maximum 250 stair footprints must be clipped in bounded slices; '
+      + 'one polyclip sweep blocks the summary panel main thread on slower clients.',
+    patches: [{
+      file: 'src/stairs.ts',
+      find: '  batchSize = 24,\n',
+      replace: '  batchSize = MAX_STAIRS_PER_SPACE, // mutant: one long main-thread clip\n',
+    }],
+  },
   {
     id: 'stairs-view-pan-opens-target-floor',
     guard: 'node demo/smoke_stairs.mjs',
diff --git a/src/stairs.ts b/src/stairs.ts
index 1543f340..23ad5916 100644
--- a/src/stairs.ts
+++ b/src/stairs.ts
@@ -247,3 +247,33 @@ export function geometryMinusStairs(
     return geometry;
   }
 }
+
+/**
+ * The summary panel calculates floor area after the first paint. A maximum
+ * size space may contain 250 stairs; clipping all their footprints in one
+ * polyclip call is observably one long main-thread task on slower clients.
+ * Keep the synchronous helper above for ordinary room-sized callers, while
+ * this iterator bounds each background slice and lets the scheduler yield.
+ */
+export function* geometryMinusStairsSteps(
+  source: Geom,
+  stairs: readonly Stair[] | null | undefined,
+  scale = NORM_W,
+  batchSize = 24,
+): Generator<void, Geom, void> {
+  const footprints = stairList(stairs).map((stair) => stairFootprintGeometry(stair, scale));
+  const size = Math.max(1, Math.floor(batchSize));
+  let geometry = source;
+  for (let index = 0; index < footprints.length; index += size) {
+    const batch = footprints.slice(index, index + size);
+    try {
+      geometry = difference(geometry, ...batch);
+    } catch {
+      for (const footprint of batch) {
+        try { geometry = difference(geometry, footprint); } catch { /* skip only the bad record */ }
+      }
+    }
+    yield;
+  }
+  return geometry;
+}
diff --git a/src/summary-panel-metrics.ts b/src/summary-panel-metrics.ts
index 8c987951..320f1964 100644
--- a/src/summary-panel-metrics.ts
+++ b/src/summary-panel-metrics.ts
@@ -9,7 +9,7 @@ import { innerContourForRoom, multiWallNodesForGeometry, wallBodiesGeometry } fr
 import type { Marker, ServerConfig, SpaceModel, SummaryPanelSource } from './types';
 import type { HaRegistrySnapshot } from './ha-binding-status';
 import type { SummaryHass } from './summary-panel-host';
-import { geometryMinusStairs } from './stairs';
+import { geometryMinusStairsSteps } from './stairs';
 
 /** Count the unique real HA devices represented anywhere on the plan. */
 export function representedHaDeviceIds(input: {
@@ -119,9 +119,16 @@ export function* cleanFloorAreaSteps(
         spaceFloor = unionGeometry(spaceFloor, clean);
         yield;
       }
-      // Difference distributes over union. Subtracting the shared stair set once
-      // avoids rooms x stairs polygon clips on dense plans (#663).
-      spaceFloor = geometryMinusStairs(spaceFloor || [], space.stairs);
+      // Difference distributes over union. Subtract the shared stair set once,
+      // but in bounded batches: 250 footprints in one polyclip sweep becomes a
+      // visible long task on slower clients (#663).
+      const stairSteps = geometryMinusStairsSteps(spaceFloor || [], space.stairs);
+      let stairStep = stairSteps.next();
+      while (!stairStep.done) {
+        yield;
+        stairStep = stairSteps.next();
+      }
+      spaceFloor = stairStep.value;
       const cmPerUnit = prepared.cellCm / GRID_PITCH;
       total += geometryArea(spaceFloor) * cmPerUnit * cmPerUnit / 1e4;
     }
diff --git a/test/stairs.test.mjs b/test/stairs.test.mjs
index a962f576..388cd8c6 100644
--- a/test/stairs.test.mjs
+++ b/test/stairs.test.mjs
@@ -6,6 +6,7 @@ import {
   cachedStairRenderGeometry,
   floorAreaMinusStairs,
   geometryAreaMinusStairs,
+  geometryMinusStairsSteps,
   isStair,
   stairRenderGeometry,
 } from '../test-build/stairs.js';
@@ -128,6 +129,31 @@ test('#663 area removes only stair overlap and never becomes negative', () => {
   assert.equal(geometryAreaMinusStairs(source, [straight({ length: 2, width: 2 })]), 0);
 });
 
+test('#663 dense stair subtraction yields between bounded polygon batches', () => {
+  const source = [[[[0, 0], [1000, 0], [1000, 1000], [0, 1000], [0, 0]]]];
+  const stairs = Array.from({ length: 5 }, (_, index) => straight({
+    id: `stair-${index}`, x: 0.15 + index * 0.16, length: 0.1, width: 0.1,
+  }));
+  const steps = geometryMinusStairsSteps(source, stairs, 1000, 2);
+  assert.equal(steps.next().done, false);
+  assert.equal(steps.next().done, false);
+  assert.equal(steps.next().done, false);
+  const finished = steps.next();
+  assert.equal(finished.done, true);
+  assert.equal(geometryAreaMinusStairs(finished.value, []), 950_000);
+
+  const denseSteps = geometryMinusStairsSteps(source, Array.from({ length: 49 }, (_, index) => (
+    straight({ id: `dense-${index}` })
+  )));
+  let slices = 0;
+  let denseStep = denseSteps.next();
+  while (!denseStep.done) {
+    slices += 1;
+    denseStep = denseSteps.next();
+  }
+  assert.equal(slices, 3, 'the default keeps a 49-stair calculation out of one main-thread task');
+});
+
 test('#663 target states distinguish active, missing, self, deleted and fixed', () => {
   const spaces = new Set(['ground', 'upper']);
   assert.equal(stairTargetState(straight(), 'ground', spaces, false), 'active');