diff --git a/crates/calc/src/eval.rs b/crates/calc/src/eval.rs
--- a/crates/calc/src/eval.rs
+++ b/crates/calc/src/eval.rs
@@ -103,6 +103,12 @@ pub trait Host {
     fn visit_range(&mut self, _sheet: usize, _range: RangeRef, _f: &mut dyn FnMut(&Value) -> bool) -> bool {
         false
     }
+    /// `(sum, count)` of the numbers in a block that holds nothing but constants (no formula,
+    /// error or spilled value), added row-major from `0.0` exactly as `visit_range` would hand
+    /// them over. `None`: the block isn't like that, or this host can't tell.
+    fn range_sum(&mut self, _sheet: usize, _range: RangeRef) -> Option<(f64, u64)> {
+        None
+    }
     /// While a formula is calculated on demand inside another one: `stack_position()` where the
     /// outermost one started, which the stack budget is counted from.
     fn stack_top(&self) -> Option<usize> {
@@ -984,6 +990,14 @@ impl<'h> Evaluator<'h> {
     /// Adds one area to `acc`; `Err` is the result the function ends with.
     fn aggregate_area(&mut self, kind: Agg, a: &Area, acc: &mut Acc) -> Result<(), Ev> {
         if !a.range.is_single() {
+            // Adding the block's remembered sum to anything but +0.0 would add in another order.
+            if acc.sum.to_bits() == 0
+                && let Some((sum, count)) = self.host.range_sum(a.sheet, a.range)
+            {
+                acc.sum = sum;
+                acc.count = acc.count.saturating_add(count);
+                return Ok(());
+            }
             let mut error = None;
             let walked = self.host.visit_range(a.sheet, a.range, &mut |v| match acc.add_cell(kind, v) {
                 Ok(()) => true,
diff --git a/crates/calc/src/recalc.rs b/crates/calc/src/recalc.rs
--- a/crates/calc/src/recalc.rs
+++ b/crates/calc/src/recalc.rs
@@ -436,6 +436,10 @@ struct PassHost<'a> {
     stack_top: usize,
     /// Whether an evaluation ran past the stack budget since the innermost formula started.
     out_of_stack: bool,
+    /// Sum and count of blocks that hold only constants, for `range_sum`. Keyed by sheet, first
+    /// cell and last column; each value maps a last row to the block's result (`None`: the block
+    /// has a formula, an error value or a spilled value, so every longer one has too).
+    sums: HashMap<(usize, CellRef, u32), std::collections::BTreeMap<u32, Option<(f64, u64)>>>,
 }
 
 impl<'a> PassHost<'a> {
@@ -468,6 +472,7 @@ impl<'a> PassHost<'a> {
             taint: false,
             stack_top: 0,
             out_of_stack: false,
+            sums: HashMap::default(),
         }
     }
 }
@@ -909,6 +914,50 @@ impl Host for PassHost<'_> {
         }
         true
     }
+    fn range_sum(&mut self, sheet: usize, range: RangeRef) -> Option<(f64, u64)> {
+        // Constants can't change during a pass, so a block's result stays valid for it. Spills
+        // found in this pass (and iteration, which tracks what a read depends on) go the long way.
+        if self.iterate || self.spills.keys().any(|a| a.0 == sheet) {
+            return None;
+        }
+        let sh = self.wb.sheet(sheet)?;
+        let (key, last) = ((sheet, range.start, range.end.col), range.end.row);
+        let known = self.sums.entry(key).or_default();
+        if let Some(r) = known.get(&last) {
+            return *r;
+        }
+        // Start from the longest shorter block of the same rows from the top: summing row-major
+        // from there on is the same additions in the same order as one walk from the start.
+        let (from, mut sum, mut count) = match known.range(..last).next_back() {
+            Some((_, None)) => {
+                known.insert(last, None);
+                return None;
+            }
+            Some((&row, &Some((sum, count)))) => (row + 1, sum, count),
+            None => (range.start.row, 0.0, 0),
+        };
+        let rest = RangeRef::new(CellRef::new(from, range.start.col), range.end);
+        let mut plain = sh.spill.range(rest.start..=rest.end).all(|(c, _)| !rest.contains(*c));
+        if plain {
+            for (_, cell) in sh.cells.iter_range(rest) {
+                match &cell.value {
+                    _ if cell.formula.is_some() => plain = false,
+                    Value::Error(_) => plain = false,
+                    Value::Number(n) => {
+                        sum += n;
+                        count = u64::saturating_add(count, 1);
+                    }
+                    _ => {}
+                }
+                if !plain {
+                    break;
+                }
+            }
+        }
+        let result = plain.then_some((sum, count));
+        known.insert(last, result);
+        result
+    }
     fn used_range(&mut self, sheet: usize) -> Option<RangeRef> {
         let wb = self.wb;
         *self.used.entry(sheet).or_insert_with(|| wb.sheet(sheet).and_then(|s| s.used_range()))
diff --git a/crates/calc/src/tests.rs b/crates/calc/src/tests.rs
--- a/crates/calc/src/tests.rs
+++ b/crates/calc/src/tests.rs
@@ -2274,3 +2274,116 @@ fn loan_schedule_residue_keeps_excels_sign() {
     }
     assert_eq!(t.get("P7"), Value::Text("".into()));
 }
+
+/// `SUM`, `COUNT` and `AVERAGE` over blocks of constants share one pass-wide answer per block, and a
+/// running total extends the shorter block's. Every result must equal the left-to-right sum of the
+/// cells, bit for bit, with text, blanks, errors, formulas and a nonzero start in the mix.
+#[test]
+fn aggregates_over_ranges_match_a_plain_fold_bit_for_bit() {
+    struct Rng(u64);
+    impl Rng {
+        fn next(&mut self, n: u64) -> u64 {
+            self.0 ^= self.0 << 13;
+            self.0 ^= self.0 >> 7;
+            self.0 ^= self.0 << 17;
+            self.0 % n
+        }
+    }
+    let nums = [0.1, 0.2, 0.3, 1e16, -1e16, 1.0, 3.7, -0.0, 12345.678, 1e-9, 7.0];
+    let rows = 40u32;
+    let mut rng = Rng(0x9E37_79B9_7F4A_7C15);
+    let mut wb = Workbook::new();
+    let fresh = |rng: &mut Rng, plain: bool| match rng.next(if plain { 8 } else { 14 }) {
+        0 => Cell::value(Value::text("t")),
+        1 => Cell::default(),
+        2 => Cell::value(Value::Bool(true)),
+        3 if !plain => Cell::value(Value::Error(CellError::NA)),
+        4 if !plain => Cell::formula(Formula::new("=A1*2")),
+        5 if !plain => Cell::formula(Formula::new("=\"x\"&B2")),
+        _ => Cell::value(Value::Number(nums[rng.next(nums.len() as u64) as usize])),
+    };
+    // Columns A:C mostly numbers; E holds a formula column and some errors only in a few rows.
+    for r in 0..rows {
+        for col in 0..3 {
+            let plain = !(r % 13 == 7 && col == 1);
+            wb.sheet_mut(0).unwrap().cells.set(CellRef::new(r, col), fresh(&mut rng, plain));
+        }
+    }
+    // Formulas in column H and up: (function, optional leading number, blocks).
+    let mut oracle: Vec<(CellRef, &str, Option<f64>, Vec<(u32, u32, u32, u32)>)> = vec![];
+    let funcs = ["SUM", "COUNT", "AVERAGE"];
+    let mut at = 0;
+    let mut add = |wb: &mut Workbook, f: &'static str, lead: Option<f64>, blocks: Vec<(u32, u32, u32, u32)>| {
+        let args: Vec<String> = blocks
+            .iter()
+            .map(|&(r0, c0, r1, c1)| format!("{}{}:{}{}", (b'A' + c0 as u8) as char, r0 + 1, (b'A' + c1 as u8) as char, r1 + 1))
+            .collect();
+        let lead_s = lead.map(|l| format!("{l:e},")).unwrap_or_default();
+        let cell = CellRef::new(at % rows, 7 + at / rows);
+        wb.sheet_mut(0).unwrap().cells.set(cell, Cell::formula(Formula::new(&format!("={f}({lead_s}{})", args.join(",")))));
+        oracle.push((cell, f, lead, blocks));
+        at += 1;
+    };
+    // Running totals over a clean column and over a column with an error further down.
+    for r in 0..rows {
+        add(&mut wb, "SUM", None, vec![(0, 0, r, 0)]);
+        add(&mut wb, "SUM", None, vec![(0, 1, r, 1)]);
+        add(&mut wb, "COUNT", None, vec![(0, 0, r, 2)]);
+    }
+    for _ in 0..120 {
+        let (r0, r1) = (rng.next(rows as u64) as u32, rng.next(rows as u64) as u32);
+        let (c0, c1) = (rng.next(3) as u32, rng.next(3) as u32);
+        let n = 1 + rng.next(2) as usize;
+        let blocks = (0..n).map(|_| (r0.min(r1), c0.min(c1), r0.max(r1), c0.max(c1))).collect();
+        let lead = [None, Some(1e16), Some(0.5), Some(2.0)][rng.next(4) as usize];
+        let f = funcs[rng.next(3) as usize];
+        add(&mut wb, f, lead, blocks);
+    }
+    let check = |wb: &Workbook, when: &str| {
+        let sh = wb.sheet(0).unwrap();
+        for (cell, f, lead, blocks) in &oracle {
+            let (mut sum, mut count, mut error) = (lead.unwrap_or(0.0), u64::from(lead.is_some()), None);
+            for &(r0, c0, r1, c1) in blocks {
+                for r in r0..=r1 {
+                    for col in c0..=c1 {
+                        match sh.value(CellRef::new(r, col)) {
+                            Value::Number(n) => {
+                                sum += n;
+                                count += 1;
+                            }
+                            Value::Error(e) if *f != "COUNT" => error = error.or(Some(e)),
+                            _ => {}
+                        }
+                    }
+                }
+            }
+            let want = match (error, *f) {
+                (Some(e), _) => Value::Error(e),
+                (_, "SUM") => Value::number(sum),
+                (_, "COUNT") => Value::number(count as f64),
+                (_, _) if count == 0 => Value::Error(CellError::Div0),
+                _ => Value::number(sum / count as f64),
+            };
+            let got = sh.value(*cell);
+            let same = match (&got, &want) {
+                (Value::Number(a), Value::Number(b)) => a.to_bits() == b.to_bits(),
+                (a, b) => a == b,
+            };
+            assert!(same, "{when}: {:?} = {:?}, plain fold {:?}", cell, got, want);
+        }
+    };
+    let mut calc = Calc::new();
+    calc.rebuild(&wb);
+    calc.recalc_all(&mut wb);
+    check(&wb, "full recalc");
+    for round in 0..30 {
+        let mut changed = vec![];
+        for _ in 0..1 + rng.next(4) {
+            let at = CellRef::new(rng.next(rows as u64) as u32, rng.next(3) as u32);
+            wb.sheet_mut(0).unwrap().cells.set(at, fresh(&mut rng, round % 2 == 0));
+            changed.push((0, at));
+        }
+        calc.cells_changed(&mut wb, &changed);
+        check(&wb, &format!("edit round {round}"));
+    }
+}