diff --git a/crates/engine/src/cmd/analysis.rs b/crates/engine/src/cmd/analysis.rs
index 9cd10e50f..92699b75f 100644
--- a/crates/engine/src/cmd/analysis.rs
+++ b/crates/engine/src/cmd/analysis.rs
@@ -152,26 +152,32 @@ fn input_range(s: &Session, p: &Json, keys: &[&str]) -> Result<(usize, RangeRef)
 /// Splits a range into variables (columns, or rows when `by_rows`); with `labels` the first
 /// cell of each names it, else `default(i)` does.
 fn variables(s: &Session, si: usize, r: RangeRef, by_rows: bool, labels: bool, default: &dyn Fn(usize) -> String) -> Result<Vec<Var>> {
-    let d = s.doc()?;
-    let sh = d.wb.sheet(si).ok_or(EngineError::NoDocument)?;
-    let (outer, inner) = if by_rows { (r.height(), r.width()) } else { (r.width(), r.height()) };
+    let outer = if by_rows { r.height() } else { r.width() };
     let mut out = Vec::with_capacity(outer as usize);
     for i in 0..outer {
-        let cell = |j: u32| if by_rows { CellRef::new(r.start.row + i, r.start.col + j) } else { CellRef::new(r.start.row + j, r.start.col + i) };
-        let mut vals: Vec<Value> = (0..inner).map(|j| sh.value(cell(j))).collect();
-        let mut name = default(i as usize);
-        if labels && !vals.is_empty() {
-            let first = vals.remove(0);
-            let t = first.display();
-            if !t.trim().is_empty() {
-                name = t;
-            }
-        }
-        out.push(Var { name, vals });
+        out.push(variable(s, si, r, by_rows, labels, default, i)?);
     }
     Ok(out)
 }
 
+/// Variable `i` of [`variables`], read alone so a caller that may stop early needn't build them all.
+fn variable(s: &Session, si: usize, r: RangeRef, by_rows: bool, labels: bool, default: &dyn Fn(usize) -> String, i: u32) -> Result<Var> {
+    let d = s.doc()?;
+    let sh = d.wb.sheet(si).ok_or(EngineError::NoDocument)?;
+    let inner = if by_rows { r.width() } else { r.height() };
+    let cell = |j: u32| if by_rows { CellRef::new(r.start.row + i, r.start.col + j) } else { CellRef::new(r.start.row + j, r.start.col + i) };
+    let mut vals: Vec<Value> = (0..inner).map(|j| sh.value(cell(j))).collect();
+    let mut name = default(i as usize);
+    if labels && !vals.is_empty() {
+        let first = vals.remove(0);
+        let t = first.display();
+        if !t.trim().is_empty() {
+            name = t;
+        }
+    }
+    Ok(Var { name, vals })
+}
+
 /// The numbers of a variable; blanks are skipped when `skip_blank`, anything else that isn't a
 /// number is an error.
 fn numbers(v: &[Value], skip_blank: bool) -> Result<Vec<f64>> {
@@ -272,11 +278,25 @@ struct Grid {
     cells: BTreeMap<(u32, u32), Value>,
     /// Cells shown as percentages.
     pct: Vec<(u32, u32)>,
+    /// Rows and columns spanned by `cells`.
+    rows: u32,
+    cols: u32,
+    /// A cell was dropped because the report outgrew [`MAX_OUTPUT_CELLS`]: the report is refused.
+    too_large: bool,
 }
 
 impl Grid {
+    /// Stores a value. Past [`MAX_OUTPUT_CELLS`] (the most a report writes) nothing more is kept,
+    /// so a builder that would produce millions of entries stops allocating them, and
+    /// [`write_report`] refuses the report.
     fn put(&mut self, r: u32, c: u32, v: Value) {
         if !v.is_empty() {
+            let (rows, cols) = (self.rows.max(r.saturating_add(1)), self.cols.max(c.saturating_add(1)));
+            if self.too_large || u64::from(rows) * u64::from(cols) > MAX_OUTPUT_CELLS {
+                self.too_large = true;
+                return;
+            }
+            (self.rows, self.cols) = (rows, cols);
             self.cells.insert((r, c), v);
         }
     }
@@ -296,9 +316,7 @@ impl Grid {
     }
     /// (rows, cols) spanned.
     fn extent(&self) -> (u32, u32) {
-        let rows = self.cells.keys().map(|(r, _)| r + 1).max().unwrap_or(0);
-        let cols = self.cells.keys().map(|(_, c)| c + 1).max().unwrap_or(0);
-        (rows, cols)
+        (self.rows, self.cols)
     }
 }
 
@@ -310,7 +328,7 @@ fn idx(i: usize) -> u32 {
 
 fn descriptive(s: &Session, p: &Json) -> Result<Grid> {
     let (si, r) = input_range(s, p, &["range", "input"])?;
-    let vars = variables(s, si, r, by_rows(p), flag(p, "labels"), &|i| format!("Column{}", i + 1))?;
+    let (by_rows, labels) = (by_rows(p), flag(p, "labels"));
     let summary = p.get("summary").map(|_| flag(p, "summary")).unwrap_or(true);
     let conf = confidence(p, "confidence")?;
     let kl = num(p, "kthLargest").filter(|k| *k >= 1.0).map(|k| k as usize);
@@ -319,7 +337,14 @@ fn descriptive(s: &Session, p: &Json) -> Result<Grid> {
         return Err(bad(CMD, "choose at least one of summary, confidence, kthLargest or kthSmallest"));
     }
     let mut g = Grid::default();
-    for (i, v) in vars.iter().enumerate() {
+    // Variables are read one at a time: a million-row range grouped by rows is a million variables.
+    for i in 0..(if by_rows { r.height() } else { r.width() }) {
+        // The report is refused once the grid is too large: the rest would only build discarded labels.
+        if g.too_large {
+            break;
+        }
+        let v = variable(s, si, r, by_rows, labels, &|i| format!("Column{}", i + 1), i)?;
+        let i = i as usize;
         let x = numbers(&v.vals, true)?;
         let c = idx(i).saturating_mul(2);
         g.txt(0, c, &v.name);
@@ -1749,7 +1774,7 @@ fn sampling(s: &Session, p: &Json, seed: Option<u64>) -> Result<Grid> {
 fn write_report(s: &mut Session, p: &Json, tool: &str, g: Grid) -> Result<Json> {
     let (rows, cols) = g.extent();
     let (rows, cols) = (rows.max(1), cols.max(1));
-    if u64::from(rows) * u64::from(cols) > MAX_OUTPUT_CELLS {
+    if g.too_large || u64::from(rows) * u64::from(cols) > MAX_OUTPUT_CELLS {
         return Err(bad(CMD, "the report is too large"));
     }
     let d = s.doc()?;
@@ -1914,6 +1939,28 @@ mod tests {
         x
     }
 
+    #[test]
+    fn a_report_stops_growing_past_the_output_limit() {
+        // Entries past the limit are not kept, and the report is refused.
+        let mut g = super::Grid::default();
+        g.num(1999, 1999, 1.0);
+        assert!(!g.too_large);
+        g.num(0, 2000, 1.0);
+        assert!(g.too_large);
+        assert_eq!(g.cells.len(), 1);
+        assert_eq!(g.extent(), (2000, 2000));
+        // Row-grouped statistics of a tall, almost empty column: one variable per row would make
+        // millions of report entries; the report is refused instead of built.
+        let mut s = s();
+        s.execute("range.setValues", json!({"range": "A1", "values": [[1]]})).unwrap();
+        s.execute("range.setValues", json!({"range": "A1000000", "values": [[2]]})).unwrap();
+        let err = s
+            .execute("data.analysisToolPak", json!({"tool": "descriptive", "range": "A1:A1000000", "groupedBy": "rows", "output": "C1"}))
+            .expect_err("report too large");
+        assert!(err.to_string().contains("too large"), "{err}");
+        assert_eq!(v(&s, "C1"), Value::Empty);
+    }
+
     #[test]
     fn forecast_standard_errors_match_the_full_window_rescan() {
         // #1043: the running sum must give what re-adding every window gave, gaps included.