diff --git a/crates/io/src/pdf.rs b/crates/io/src/pdf.rs
index 90fdf15b9..b33e9ad5d 100644
--- a/crates/io/src/pdf.rs
+++ b/crates/io/src/pdf.rs
@@ -507,7 +507,7 @@ fn links(list: &cadcraft_render::DisplayList, map: &Map, clip_pt: &Bounds2, link
 }
 
 /// Paper units per drawing unit for a plot.
-fn plot_scale(b: &Bounds2, sheet: &Sheet, fit: bool, scale: Option<f64>) -> f64 {
+pub(crate) fn plot_scale(b: &Bounds2, sheet: &Sheet, fit: bool, scale: Option<f64>) -> f64 {
     if let Some(s) = scale.filter(|s| s.is_finite() && *s > 0.0)
         && !fit
     {
diff --git a/crates/io/src/plotter.rs b/crates/io/src/plotter.rs
index 03c26ace8..cc6a07784 100644
--- a/crates/io/src/plotter.rs
+++ b/crates/io/src/plotter.rs
@@ -56,18 +56,10 @@ fn sheet(d: &Drawing, space: &Space, o: &PdfOptions) -> Result<(Sheet, cadcraft_
     Ok((Sheet::from_page(&page, paper::paper_unit_mm(d)), page))
 }
 
-/// Paper units per drawing unit fitting `b` into the printable area (or the `scale` option).
+/// Paper units per drawing unit fitting `b` into the printable area; with `fit: false`, the
+/// `scale` option or 1:1, as PDF plots it.
 fn fit_scale(b: &Bounds2, sheet: &Sheet, o: &PdfOptions) -> f64 {
-    if let Some(s) = o.scale.filter(|s| s.is_finite() && *s > 0.0)
-        && o.fit == Some(false)
-    {
-        return s;
-    }
-    if b.is_empty() {
-        return 1.0;
-    }
-    let s = (sheet.printable.width() / b.width().max(1e-12)).min(sheet.printable.height() / b.height().max(1e-12));
-    if s.is_finite() && s > 0.0 { s } else { 1.0 }
+    pdf::plot_scale(b, sheet, o.fit != Some(false), o.scale)
 }
 
 fn png(d: &Drawing, space: &Space, opts: &Value) -> Result<Vec<u8>> {
diff --git a/crates/io/tests/plot_model_png_scale.rs b/crates/io/tests/plot_model_png_scale.rs
new file mode 100644
index 000000000..2f2e6d466
--- /dev/null
+++ b/crates/io/tests/plot_model_png_scale.rs
@@ -0,0 +1,87 @@
+//! A model-space PNG plot with `fit: false` and no `scale` plots at 1:1, as PDF does (issue #713).
+
+use cadcraft_doc::{Common, Drawing, EntityKind, Line, Space};
+use cadcraft_geom::Vec3;
+use serde_json::{Value, json};
+
+/// The RGBA rows of an 8-bit RGBA PNG (the only kind the plotter writes).
+fn decode_rgba(png: &[u8]) -> (usize, Vec<Vec<u8>>) {
+    let be = |i: usize| u32::from_be_bytes([png[i], png[i + 1], png[i + 2], png[i + 3]]) as usize;
+    let (w, h) = (be(16), be(20));
+    assert_eq!((png[24], png[25]), (8, 6), "8-bit RGBA");
+    let mut idat = Vec::new();
+    let mut at = 8;
+    while at + 8 <= png.len() {
+        let len = be(at);
+        if &png[at + 4..at + 8] == b"IDAT" {
+            idat.extend_from_slice(&png[at + 8..at + 8 + len]);
+        }
+        at += 12 + len;
+    }
+    let raw = miniz_oxide::inflate::decompress_to_vec_zlib(&idat).unwrap();
+    let stride = w * 4;
+    let mut rows: Vec<Vec<u8>> = Vec::with_capacity(h);
+    for y in 0..h {
+        let line = &raw[y * (stride + 1)..(y + 1) * (stride + 1)];
+        let prev = if y > 0 { rows[y - 1].clone() } else { vec![0; stride] };
+        let mut cur = line[1..].to_vec();
+        for i in 0..stride {
+            let a = if i >= 4 { i32::from(cur[i - 4]) } else { 0 };
+            let b = i32::from(prev[i]);
+            let c = if i >= 4 { i32::from(prev[i - 4]) } else { 0 };
+            let add = match line[0] {
+                0 => 0,
+                1 => a,
+                2 => b,
+                3 => (a + b) / 2,
+                4 => {
+                    let p = a + b - c;
+                    let (pa, pb, pc) = ((p - a).abs(), (p - b).abs(), (p - c).abs());
+                    if pa <= pb && pa <= pc {
+                        a
+                    } else if pb <= pc {
+                        b
+                    } else {
+                        c
+                    }
+                }
+                f => panic!("PNG filter {f}"),
+            };
+            cur[i] = cur[i].wrapping_add(add as u8);
+        }
+        rows.push(cur);
+    }
+    (w, rows)
+}
+
+/// Plotted length in millimetres of a 100-unit horizontal line in model space, on an A4
+/// landscape PNG at 100 dpi with 5 mm margins (printable area 287 × 200 mm).
+fn plotted_mm(opts: Value) -> f64 {
+    let mut d = Drawing::new_metric();
+    let line = EntityKind::Line(Line { a: Vec3::ZERO, b: Vec3::new(100.0, 0.0, 0.0) });
+    d.add(&Space::Model, Common::default(), line).unwrap();
+    let mut o =
+        json!({"output": "png", "width": 210, "height": 297, "landscape": true, "margins": [5, 5, 5, 5], "resolution": 100, "lineweights": false});
+    if let (Some(o), Some(e)) = (o.as_object_mut(), opts.as_object()) {
+        o.extend(e.clone());
+    }
+    let (w, rows) = decode_rgba(&cadcraft_io::plotter::plot(&d, &Space::Model, &o).unwrap());
+    let inked: Vec<usize> = (0..w).filter(|x| rows.iter().any(|r| r[x * 4] < 128)).collect();
+    let (first, last) = (inked.first().unwrap(), inked.last().unwrap());
+    (last - first) as f64 * 25.4 / 100.0
+}
+
+#[test]
+fn model_png_without_fit_or_scale_plots_one_to_one() {
+    // One pixel is 0.254 mm at 100 dpi.
+    for (opts, mm) in [
+        (json!({"fit": false}), 100.0),
+        (json!({"fit": false, "scale": 1}), 100.0),
+        (json!({"fit": false, "scale": 0.5}), 50.0),
+        (json!({"fit": true}), 287.0),
+        (json!({}), 287.0),
+    ] {
+        let got = plotted_mm(opts.clone());
+        assert!((got - mm).abs() < 0.6, "{opts}: {got} mm, want {mm}");
+    }
+}