diff --git a/crates/engine/src/cmd/format.rs b/crates/engine/src/cmd/format.rs
index c7e970fa5..585f68dc0 100644
--- a/crates/engine/src/cmd/format.rs
+++ b/crates/engine/src/cmd/format.rs
@@ -1025,6 +1025,10 @@ pub fn approx_text_width(text: &str, size: f32, bold: bool) -> f32 {
     w * size * if bold { 1.07 } else { 1.0 } * 96.0 / 72.0
 }
 
+/// Distinct texts AutoFit measures exactly; past this many, `Session::text_width` is asked for a
+/// quick measure so a huge column doesn't lay out every value.
+const EXACT_TEXT_WIDTHS: usize = 2_000;
+
 fn autofit_cols(s: &mut Session, p: &Json) -> Result<Json> {
     let lines = line_targets(s, p, false)?;
     let measure = s.text_width.clone();
@@ -1032,6 +1036,8 @@ fn autofit_cols(s: &mut Session, p: &Json) -> Result<Json> {
         let si = cx.sheet_index();
         let Some(sh) = cx.wb.sheet(si) else { return Ok(Json::Null) };
         let mut widths = Vec::new();
+        let mut measured: std::collections::HashMap<StyleId, std::collections::HashMap<String, f32>> = Default::default();
+        let mut distinct = 0usize;
         let used = sh.used_range();
         for (a, b) in lines {
             for c in a..=b.min(a + 16383) {
@@ -1042,11 +1048,23 @@ fn autofit_cols(s: &mut Session, p: &Json) -> Result<Json> {
                     if sh.merge_at(cell).is_some_and(|m| !m.is_single()) {
                         continue;
                     }
-                    let st = cx.wb.styles.get(sh.style_id(cell));
+                    let id = sh.style_id(cell);
+                    let st = cx.wb.styles.get(id);
                     let text = crate::display::cell_text(&cx.wb, sh, cell);
                     for line in text.lines() {
                         let w = match &measure {
-                            Some(m) => m(line, &st.font),
+                            Some(m) => {
+                                let known = measured.entry(id).or_default();
+                                match known.get(line) {
+                                    Some(w) => *w,
+                                    None => {
+                                        let w = m(line, &st.font, distinct < EXACT_TEXT_WIDTHS);
+                                        known.insert(line.to_owned(), w);
+                                        distinct += 1;
+                                        w
+                                    }
+                                }
+                            }
                             None => approx_text_width(line, st.font.size, st.font.bold),
                         };
                         max = max.max(w + 6.0 + st.align.indent as f32 * 9.0 + sh.filter_button_space(cell));
diff --git a/crates/engine/src/lib.rs b/crates/engine/src/lib.rs
index daa9875e5..f52984c4c 100644
--- a/crates/engine/src/lib.rs
+++ b/crates/engine/src/lib.rs
@@ -228,8 +228,11 @@ pub enum UiRequest {
 }
 
 /// Width in points of one line of text drawn in a cell font, measured by a front end that has
-/// the font the grid draws with.
-pub type TextWidth = Arc<dyn Fn(&str, &model::Font) -> f32 + Send + Sync>;
+/// the font the grid draws with. With `exact` false the front end may answer with a cheaper
+/// measure that is never narrower (AutoFit asks for it on columns with many distinct values).
+/// Commands call it while they run, so a front end must not run commands while holding a lock
+/// the measure takes (egui's: see `theme::cell_text_width` in the UI crate).
+pub type TextWidth = Arc<dyn Fn(&str, &model::Font, bool) -> f32 + Send + Sync>;
 
 #[derive(Default)]
 pub struct Session {
diff --git a/crates/engine/tests/autofit_filter_buttons.rs b/crates/engine/tests/autofit_filter_buttons.rs
index 307bb998d..dbf25eced 100644
--- a/crates/engine/tests/autofit_filter_buttons.rs
+++ b/crates/engine/tests/autofit_filter_buttons.rs
@@ -100,3 +100,26 @@ fn autofit_filter_width_is_undoable_without_changing_selection() {
     s.execute("edit.undo", json!({})).unwrap();
     assert_eq!(s.doc().unwrap().wb.active().unwrap().col_width(0), 80.0);
 }
+
+#[test]
+fn autofit_measures_each_distinct_text_once_and_quickly_past_the_limit() {
+    use std::sync::{Arc, Mutex};
+    let mut s = Session::new();
+    s.new_workbook();
+    // 2,500 distinct texts, each in two cells.
+    let values: Vec<_> = (0..5000).map(|i| json!([format!("v{}", i % 2500)])).collect();
+    s.execute("range.setValues", json!({"range":"A1", "values": values})).unwrap();
+    let calls = Arc::new(Mutex::new(Vec::new()));
+    let seen = calls.clone();
+    s.text_width = Some(Arc::new(move |text: &str, _: &gridcraft_engine::model::Font, exact: bool| {
+        seen.lock().unwrap().push((text.to_owned(), exact));
+        if text == "v2499" { 300.0 } else { 10.0 }
+    }));
+    s.execute("home.autofitColumnWidth", json!({"cols":"A:A"})).unwrap();
+    let calls = calls.lock().unwrap();
+    assert_eq!(calls.len(), 2500, "one measure per distinct text");
+    assert_eq!(calls.iter().filter(|(_, exact)| *exact).count(), 2000);
+    assert!(calls.iter().skip(2000).all(|(_, exact)| !exact));
+    // The quick measures still size the column.
+    assert_eq!(s.doc().unwrap().wb.active().unwrap().col_width(0), 306.0);
+}
diff --git a/crates/ui-egui/src/lib.rs b/crates/ui-egui/src/lib.rs
index c9616bc0e..3bb674dce 100644
--- a/crates/ui-egui/src/lib.rs
+++ b/crates/ui-egui/src/lib.rs
@@ -992,7 +992,7 @@ impl SheetApp {
     pub fn logic(&mut self, ctx: &egui::Context) {
         if self.session.text_width.is_none() {
             let ctx = ctx.clone();
-            self.session.text_width = Some(std::sync::Arc::new(move |text, font| theme::cell_text_width(&ctx, text, font)));
+            self.session.text_width = Some(std::sync::Arc::new(move |text, font, exact| theme::cell_text_width(&ctx, text, font, exact)));
         }
         // A keytip control request lives one frame: the ribbon consumes it during `ui`, and
         // anything that never reached a control (collapsed ribbon, tab switch) is dropped.
diff --git a/crates/ui-egui/src/theme.rs b/crates/ui-egui/src/theme.rs
index 23c7fd35e..46ac1ea4a 100644
--- a/crates/ui-egui/src/theme.rs
+++ b/crates/ui-egui/src/theme.rs
@@ -196,11 +196,24 @@ pub fn cell_family(name: &str, bold: bool, italic: bool) -> FontFamily {
 /// face [`cell_family`] picks, which on a machine without the named font is a wider or narrower
 /// substitute (#1316). A family the active font set doesn't have yet (bound fonts apply from the
 /// next frame) falls back to the engine's estimate rather than letting egui panic on it.
-pub fn cell_text_width(ctx: &egui::Context, text: &str, font: &gridcraft_engine::model::Font) -> f32 {
+///
+/// `exact` lays the text out (a galley kept until the end of the frame); otherwise the glyph
+/// advances are summed without kerning, which is cheap and never narrower. This takes the
+/// Context lock (`fonts_mut`): never call it, or run a command, while an egui lock is held.
+pub fn cell_text_width(ctx: &egui::Context, text: &str, font: &gridcraft_engine::model::Font, exact: bool) -> f32 {
     let family = cell_family(&font.name, font.bold, font.italic);
     let id = FontId::new(font.size * 96.0 / 72.0, family);
-    ctx.fonts_mut(|f| f.families().contains(&id.family).then(|| f.layout_no_wrap(text.to_owned(), id, Color32::PLACEHOLDER).size().x))
-        .unwrap_or_else(|| gridcraft_engine::cmd::format::approx_text_width(text, font.size, font.bold))
+    ctx.fonts_mut(|f| {
+        f.families().contains(&id.family).then(|| {
+            if exact {
+                f.layout_no_wrap(text.to_owned(), id, Color32::PLACEHOLDER).size().x
+            } else {
+                // Half a point covers the galley's rounding of its width up to the pixel grid.
+                text.chars().map(|c| f.glyph_width(&id, c)).sum::<f32>() + 0.5
+            }
+        })
+    })
+    .unwrap_or_else(|| gridcraft_engine::cmd::format::approx_text_width(text, font.size, font.bold))
 }
 
 /// Whether epaint can open face `index` of this font file and it maps characters to glyphs.
diff --git a/crates/ui-egui/tests/header_autofit.rs b/crates/ui-egui/tests/header_autofit.rs
index b4f104f4b..e5cf0cc21 100644
--- a/crates/ui-egui/tests/header_autofit.rs
+++ b/crates/ui-egui/tests/header_autofit.rs
@@ -199,7 +199,10 @@ fn header_double_click_fits_the_text_as_the_grid_draws_it() {
     let text = "sarmstrong@example.com %%% @@@";
     let mut h = harness("A1");
     h.state_mut().session.execute("range.setValues", json!({"range":"A1", "values":[[text]]})).unwrap();
-    h.run_steps(3);
+    // Let the installed-font scan finish and bind its faces first, so the cell's font can't
+    // change between the AutoFit and the measurement below.
+    gridcraft_ui_egui::fonts::catalog();
+    h.run_steps(6);
     let (pos, _) = edge(&h, false, 0);
     button(&mut h, pos, true);
     button(&mut h, pos, false);
@@ -218,3 +221,21 @@ fn header_double_click_fits_the_text_as_the_grid_draws_it() {
     // Two 2.5 px paddings and the gridline, as the grid lays out the cell.
     assert!(sheet.col_width(0) >= drawn + 6.0, "column {} is narrower than the drawn text {drawn} + padding", sheet.col_width(0));
 }
+
+#[test]
+fn the_quick_measure_is_never_narrower_than_the_drawn_text() {
+    // Columns with many distinct values are measured by summing glyph advances; that must cover
+    // the laid-out text, or AutoFit would clip again on large columns.
+    let h = harness("A1");
+    let app = h.state();
+    let sheet = app.session.active().unwrap().wb.active().unwrap();
+    let mut font = app.session.active().unwrap().wb.styles.get(sheet.style_id(gridcraft_engine::core::CellRef::new(0, 0))).font.clone();
+    for bold in [false, true] {
+        font.bold = bold;
+        for text in ["sarmstrong@example.com", "Quarterly revenue summary", "WWW MMM Wide Headers", "AVATAR To Ty", "fi ffl 1,234.56"] {
+            let quick = gridcraft_ui_egui::theme::cell_text_width(&h.ctx, text, &font, false);
+            let exact = gridcraft_ui_egui::theme::cell_text_width(&h.ctx, text, &font, true);
+            assert!(exact > 0.0 && quick >= exact, "{text:?} bold={bold}: quick {quick} < drawn {exact}");
+        }
+    }
+}