diff --git a/src/runtime/mbitmap.go b/src/runtime/mbitmap.go
index 55c0282403..2045789fa4 100644
--- a/src/runtime/mbitmap.go
+++ b/src/runtime/mbitmap.go
@@ -1921,7 +1921,11 @@ Run:
 // The bitmask starts at s.startAddr.
 // The result must be deallocated with dematerializeGCProg.
 func materializeGCProg(ptrdata uintptr, prog *byte) *mspan {
-	s := mheap_.allocManual((ptrdata/(8*sys.PtrSize)+pageSize-1)/pageSize, &memstats.gc_sys)
+	// Each word of ptrdata needs one bit in the bitmap.
+	bitmapBytes := divRoundUp(ptrdata, 8*sys.PtrSize)
+	// Compute the number of pages needed for bitmapBytes.
+	pages := divRoundUp(bitmapBytes, pageSize)
+	s := mheap_.allocManual(pages, &memstats.gc_sys)
 	runGCProg(addb(prog, 4), nil, (*byte)(unsafe.Pointer(s.startAddr)), 1)
 	return s
 }
diff --git a/src/runtime/stubs.go b/src/runtime/stubs.go
index b8d4d6b30a..2c6f027c2c 100644
--- a/src/runtime/stubs.go
+++ b/src/runtime/stubs.go
@@ -310,6 +310,13 @@ func alignDown(n, a uintptr) uintptr {
 	return n &^ (a - 1)
 }
 
+// divRoundUp returns ceil(n / a).
+func divRoundUp(n, a uintptr) uintptr {
+	// a is generally a power of two. This will get inlined and
+	// the compiler will optimize the division.
+	return (n + a - 1) / a
+}
+
 // checkASM reports whether assembly runtime checks have passed.
 func checkASM() bool