diff --git a/geo-benches/Cargo.toml b/geo-benches/Cargo.toml
index 52836609c..0dccda51f 100644
--- a/geo-benches/Cargo.toml
+++ b/geo-benches/Cargo.toml
@@ -25,7 +25,7 @@ num-traits = "0.2"
 pretty_env_logger = "0.4"
 rand = "0.10.0"
 rand_distr = "0.6.0"
-rstar = "0.12.0"
+rstar = "0.13.0"
 serde = "1.0.137"
 serde_derive = "1.0.137"
 serde_json = "1.0.81"
diff --git a/geo-types/CHANGES.md b/geo-types/CHANGES.md
index 55bfdd88a..4ada893a9 100644
--- a/geo-types/CHANGES.md
+++ b/geo-types/CHANGES.md
@@ -1,5 +1,9 @@
 # Changes
 
+## Unreleased
+
+- Add support for `rstar` 0.13 via the `rstar_0_13` feature, alongside the existing `rstar` versions.
+
 ## 0.7.19 - 2026-04-15
 
 - POSSIBLY BREAKING: `Triangle::from([a, b, c])` now enforces CCW winding (same as `Triangle::new`).
diff --git a/geo-types/Cargo.toml b/geo-types/Cargo.toml
index b6809e0b6..9e9ea8c75 100644
--- a/geo-types/Cargo.toml
+++ b/geo-types/Cargo.toml
@@ -14,7 +14,7 @@ edition = "2021"
 default = ["std"]
 std = ["approx?/std", "num-traits/std", "serde?/std"]
 multithreading = ["rayon"]
-serde = [ "dep:serde", "rstar_0_8?/serde", "rstar_0_9?/serde", "rstar_0_10?/serde", "rstar_0_11?/serde", "rstar_0_12?/serde"]
+serde = [ "dep:serde", "rstar_0_8?/serde", "rstar_0_9?/serde", "rstar_0_10?/serde", "rstar_0_11?/serde", "rstar_0_12?/serde", "rstar_0_13?/serde"]
 
 rstar = ["rstar_0_8"]
 rstar_0_8 = ["dep:rstar_0_8", "approx"]
@@ -22,6 +22,7 @@ rstar_0_9 = ["dep:rstar_0_9", "approx"]
 rstar_0_10 = ["dep:rstar_0_10", "approx"]
 rstar_0_11 = ["dep:rstar_0_11", "approx"]
 rstar_0_12 = ["dep:rstar_0_12", "approx"]
+rstar_0_13 = ["dep:rstar_0_13", "approx"]
 
 # Deprecated feature flags with "use-" prefix from the days before `dep:`
 use-rstar = ["rstar"]
@@ -43,6 +44,7 @@ rstar_0_9 = { package = "rstar", version = "0.9", optional = true }
 rstar_0_10 = { package = "rstar", version = "0.10", optional = true }
 rstar_0_11 = { package = "rstar", version = "0.11", optional = true }
 rstar_0_12 = { package = "rstar", version = "0.12", optional = true }
+rstar_0_13 = { package = "rstar", version = "0.13", optional = true }
 serde = { version = "1", optional = true, default-features = false, features = ["alloc", "derive"] }
 spade_2 = { package = "spade", version = "2", optional = true }
 
diff --git a/geo-types/src/geometry/coord.rs b/geo-types/src/geometry/coord.rs
index 2709387ee..4196781df 100644
--- a/geo-types/src/geometry/coord.rs
+++ b/geo-types/src/geometry/coord.rs
@@ -503,6 +503,42 @@ where
     }
 }
 
+#[cfg(feature = "rstar_0_13")]
+impl<T> ::rstar_0_13::Point for Coord<T>
+where
+    T: ::num_traits::Float + ::rstar_0_13::RTreeNum,
+{
+    type Scalar = T;
+
+    const DIMENSIONS: usize = 2;
+
+    #[inline]
+    fn generate(mut generator: impl FnMut(usize) -> Self::Scalar) -> Self {
+        coord! {
+            x: generator(0),
+            y: generator(1),
+        }
+    }
+
+    #[inline]
+    fn nth(&self, index: usize) -> Self::Scalar {
+        match index {
+            0 => self.x,
+            1 => self.y,
+            _ => unreachable!(),
+        }
+    }
+
+    #[inline]
+    fn nth_mut(&mut self, index: usize) -> &mut Self::Scalar {
+        match index {
+            0 => &mut self.x,
+            1 => &mut self.y,
+            _ => unreachable!(),
+        }
+    }
+}
+
 #[cfg(feature = "spade_2")]
 impl<T> ::spade_2::HasPosition for Coord<T>
 where
diff --git a/geo-types/src/geometry/line.rs b/geo-types/src/geometry/line.rs
index f74d5aeb5..1668fbc27 100644
--- a/geo-types/src/geometry/line.rs
+++ b/geo-types/src/geometry/line.rs
@@ -247,7 +247,8 @@ mod approx_integration {
     feature = "rstar_0_9",
     feature = "rstar_0_10",
     feature = "rstar_0_11",
-    feature = "rstar_0_12"
+    feature = "rstar_0_12",
+    feature = "rstar_0_13"
 ))]
 macro_rules! impl_rstar_line {
     ($rstar:ident) => {
@@ -289,6 +290,9 @@ impl_rstar_line!(rstar_0_11);
 #[cfg(feature = "rstar_0_12")]
 impl_rstar_line!(rstar_0_12);
 
+#[cfg(feature = "rstar_0_13")]
+impl_rstar_line!(rstar_0_13);
+
 #[cfg(test)]
 mod test {
     use super::*;
diff --git a/geo-types/src/geometry/line_string.rs b/geo-types/src/geometry/line_string.rs
index ed4fdd18b..938698d28 100644
--- a/geo-types/src/geometry/line_string.rs
+++ b/geo-types/src/geometry/line_string.rs
@@ -542,7 +542,8 @@ mod approx_integration {
     feature = "rstar_0_9",
     feature = "rstar_0_10",
     feature = "rstar_0_11",
-    feature = "rstar_0_12"
+    feature = "rstar_0_12",
+    feature = "rstar_0_13"
 ))]
 macro_rules! impl_rstar_line_string {
     ($rstar:ident) => {
@@ -599,6 +600,9 @@ impl_rstar_line_string!(rstar_0_11);
 #[cfg(feature = "rstar_0_12")]
 impl_rstar_line_string!(rstar_0_12);
 
+#[cfg(feature = "rstar_0_13")]
+impl_rstar_line_string!(rstar_0_13);
+
 #[cfg(test)]
 mod test {
     use super::*;
diff --git a/geo-types/src/geometry/multi_polygon.rs b/geo-types/src/geometry/multi_polygon.rs
index e9fe5eaf1..cd2a95f42 100644
--- a/geo-types/src/geometry/multi_polygon.rs
+++ b/geo-types/src/geometry/multi_polygon.rs
@@ -247,7 +247,8 @@ mod approx_integration {
     feature = "rstar_0_9",
     feature = "rstar_0_10",
     feature = "rstar_0_11",
-    feature = "rstar_0_12"
+    feature = "rstar_0_12",
+    feature = "rstar_0_13"
 ))]
 macro_rules! impl_rstar_multi_polygon {
     ($rstar:ident) => {
@@ -275,6 +276,8 @@ impl_rstar_multi_polygon!(rstar_0_10);
 impl_rstar_multi_polygon!(rstar_0_11);
 #[cfg(feature = "rstar_0_12")]
 impl_rstar_multi_polygon!(rstar_0_12);
+#[cfg(feature = "rstar_0_13")]
+impl_rstar_multi_polygon!(rstar_0_13);
 
 #[cfg(test)]
 mod test {
diff --git a/geo-types/src/geometry/point.rs b/geo-types/src/geometry/point.rs
index b5dbada10..b3389f94c 100644
--- a/geo-types/src/geometry/point.rs
+++ b/geo-types/src/geometry/point.rs
@@ -784,6 +784,35 @@ where
     }
 }
 
+#[cfg(feature = "rstar_0_13")]
+impl<T> ::rstar_0_13::Point for Point<T>
+where
+    T: ::num_traits::Float + ::rstar_0_13::RTreeNum,
+{
+    type Scalar = T;
+
+    const DIMENSIONS: usize = 2;
+
+    fn generate(mut generator: impl FnMut(usize) -> Self::Scalar) -> Self {
+        Point::new(generator(0), generator(1))
+    }
+
+    fn nth(&self, index: usize) -> Self::Scalar {
+        match index {
+            0 => self.0.x,
+            1 => self.0.y,
+            _ => unreachable!(),
+        }
+    }
+    fn nth_mut(&mut self, index: usize) -> &mut Self::Scalar {
+        match index {
+            0 => &mut self.0.x,
+            1 => &mut self.0.y,
+            _ => unreachable!(),
+        }
+    }
+}
+
 impl<T: CoordNum> AsRef<Coord<T>> for Point<T> {
     fn as_ref(&self) -> &Coord<T> {
         &self.0
diff --git a/geo-types/src/geometry/polygon.rs b/geo-types/src/geometry/polygon.rs
index 4de38d31f..88136ef45 100644
--- a/geo-types/src/geometry/polygon.rs
+++ b/geo-types/src/geometry/polygon.rs
@@ -651,7 +651,8 @@ mod approx_integration {
     feature = "rstar_0_9",
     feature = "rstar_0_10",
     feature = "rstar_0_11",
-    feature = "rstar_0_12"
+    feature = "rstar_0_12",
+    feature = "rstar_0_13"
 ))]
 macro_rules! impl_rstar_polygon {
     ($rstar:ident) => {
@@ -683,6 +684,9 @@ impl_rstar_polygon!(rstar_0_11);
 #[cfg(feature = "rstar_0_12")]
 impl_rstar_polygon!(rstar_0_12);
 
+#[cfg(feature = "rstar_0_13")]
+impl_rstar_polygon!(rstar_0_13);
+
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/geo-types/src/geometry/triangle.rs b/geo-types/src/geometry/triangle.rs
index c2bc6e7df..29d4e2de2 100644
--- a/geo-types/src/geometry/triangle.rs
+++ b/geo-types/src/geometry/triangle.rs
@@ -235,7 +235,8 @@ mod approx_integration {
     feature = "rstar_0_9",
     feature = "rstar_0_10",
     feature = "rstar_0_11",
-    feature = "rstar_0_12"
+    feature = "rstar_0_12",
+    feature = "rstar_0_13"
 ))]
 macro_rules! impl_rstar_triangle {
     ($rstar:ident) => {
@@ -268,3 +269,6 @@ impl_rstar_triangle!(rstar_0_11);
 
 #[cfg(feature = "rstar_0_12")]
 impl_rstar_triangle!(rstar_0_12);
+
+#[cfg(feature = "rstar_0_13")]
+impl_rstar_triangle!(rstar_0_13);
diff --git a/geo-types/src/lib.rs b/geo-types/src/lib.rs
index ea6905c3a..31a0c8bb2 100644
--- a/geo-types/src/lib.rs
+++ b/geo-types/src/lib.rs
@@ -72,6 +72,7 @@
 //! - `use-rstar_0_10`: Allows geometry types to be inserted into [rstar] R*-trees (`rstar v0.10`)
 //! - `use-rstar_0_11`: Allows geometry types to be inserted into [rstar] R*-trees (`rstar v0.11`)
 //! - `use-rstar_0_12`: Allows geometry types to be inserted into [rstar] R*-trees (`rstar v0.12`)
+//! - `rstar_0_13`: Allows geometry types to be inserted into [rstar] R*-trees (`rstar v0.13`)
 //!
 //! This library can be used in `#![no_std]` environments if the default `std` feature is disabled. At
 //! the moment, the `arbitrary` and `use-rstar_0_8` features require `std`. This may change in a
@@ -144,7 +145,8 @@ mod arbitrary;
     feature = "rstar_0_9",
     feature = "rstar_0_10",
     feature = "rstar_0_11",
-    feature = "rstar_0_12"
+    feature = "rstar_0_12",
+    feature = "rstar_0_13"
 ))]
 #[doc(hidden)]
 pub mod private_utils;
@@ -388,6 +390,21 @@ mod tests {
         assert_relative_eq!(25.999999999999996, l.distance_2(&Point::new(4.0, 10.0)));
     }
 
+    #[cfg(feature = "rstar_0_13")]
+    #[test]
+    /// ensure Line's SpatialObject impl is correct
+    fn line_test_0_13() {
+        use rstar_0_13::primitives::Line as RStarLine;
+        use rstar_0_13::{PointDistance, RTreeObject};
+
+        let rl = RStarLine::new(Point::new(0.0, 0.0), Point::new(5.0, 5.0));
+        let l = Line::new(coord! { x: 0.0, y: 0.0 }, coord! { x: 5., y: 5. });
+        assert_eq!(rl.envelope(), l.envelope());
+        // difference in 15th decimal place
+        assert_relative_eq!(26.0, rl.distance_2(&Point::new(4.0, 10.0)));
+        assert_relative_eq!(25.999999999999996, l.distance_2(&Point::new(4.0, 10.0)));
+    }
+
     #[test]
     fn test_rects() {
         let r = Rect::new(coord! { x: -1., y: -1. }, coord! { x: 1., y: 1. });
diff --git a/geo/CHANGES.md b/geo/CHANGES.md
index 47aa6118b..d1284975a 100644
--- a/geo/CHANGES.md
+++ b/geo/CHANGES.md
@@ -2,6 +2,7 @@
 
 ## Unreleased
 
+- Update the `rstar` dependency to 0.13.
 - Unpin the `earcut` dependency now that the upstream semver violation has been reverted.
   - <https://github.com/georust/geo/pull/1533>
 - Added `Earcutter` and `TriangulateEarcut::earcut_triangulation_ref` to avoid per-call memory allocations across multiple triangulations.
diff --git a/geo/Cargo.toml b/geo/Cargo.toml
index ae4f5e90a..1325bd164 100644
--- a/geo/Cargo.toml
+++ b/geo/Cargo.toml
@@ -31,13 +31,13 @@ __allow_deprecated_features = []
 earcut = { version = "0.4.9", optional = true }
 spade = { version = "2.10.0", optional = true }
 float_next_after = "2.0.0"
-geo-types = { version = "0.7.19", features = ["approx", "rstar_0_12"] }
+geo-types = { version = "0.7.19", features = ["approx", "rstar_0_13"] }
 geographiclib-rs = { version = "0.2.3", default-features = false }
 log = "0.4.11"
 num-traits = "0.2"
 proj = { version = "0.31.0", optional = true }
 robust = "1.1.0"
-rstar = "0.12.0"
+rstar = "0.13.0"
 serde = { version = "1.0", optional = true, features = ["derive"] }
 i_overlay = { version = "4.5.1, < 4.6.0", default-features = false }
 sif-itree = "0.4.0"
diff --git a/geo/src/algorithm/concave_hull.rs b/geo/src/algorithm/concave_hull.rs
index 2a14e17bf..c83c08adc 100644
--- a/geo/src/algorithm/concave_hull.rs
+++ b/geo/src/algorithm/concave_hull.rs
@@ -366,7 +366,7 @@ where
     let bbox = AABB::from_corners(point!([min_x, min_y]), point!([max_x, max_y]));
 
     // Iterate over all lines in the hull which intersect with the bounding box
-    let hull_lines = current_hull_tree.locate_in_envelope_intersecting(&bbox);
+    let hull_lines = current_hull_tree.locate_in_envelope_intersecting(bbox);
     for hull_line in hull_lines {
         // Skip lines which share an endpoint
         if hull_line.start == line.start
@@ -633,7 +633,7 @@ where
 #[cfg(test)]
 mod tests {
     use super::*;
-    use crate::{coord, line_string, polygon};
+    use crate::{Relate, coord, line_string, polygon};
 
     #[test]
     fn test_concavity() {
@@ -723,6 +723,10 @@ mod tests {
         ]
         .into();
         let hull = mp.concave_hull();
+        // The bottom edge runs straight from (0, 0) to (4, 0). The intermediate
+        // points (2, 0) and (3, 0) are collinear, so whether they are retained as
+        // explicit vertices depends on R-tree iteration order, which changed in
+        // rstar 0.13. Compare topologically rather than by exact vertex list.
         let correct_hull = polygon![
             (x: 4.0, y: 0.0),
             (x: 4.0, y: 5.0),
@@ -734,7 +738,7 @@ mod tests {
             (x: 3.0, y: 0.0),
             (x: 4.0, y: 0.0),
         ];
-        assert_eq!(hull, correct_hull);
+        assert!(hull.relate(&correct_hull).is_equal_topo());
     }
 
     #[test]
diff --git a/geo/src/algorithm/euclidean_distance.rs b/geo/src/algorithm/euclidean_distance.rs
index 80217a1ba..d1087dae7 100644
--- a/geo/src/algorithm/euclidean_distance.rs
+++ b/geo/src/algorithm/euclidean_distance.rs
@@ -500,12 +500,12 @@ where
     geom2
         .points()
         .fold(<T as Bounded>::max_value(), |acc, point| {
-            let nearest = tree_a.nearest_neighbor(&point).unwrap();
+            let nearest = tree_a.nearest_neighbor(point).unwrap();
             #[allow(deprecated)]
             acc.min(nearest.euclidean_distance(&point))
         })
         .min(geom1.points().fold(Bounded::max_value(), |acc, point| {
-            let nearest = tree_b.nearest_neighbor(&point).unwrap();
+            let nearest = tree_b.nearest_neighbor(point).unwrap();
             #[allow(deprecated)]
             acc.min(nearest.euclidean_distance(&point))
         }))
diff --git a/geo/src/algorithm/k_nearest_concave_hull.rs b/geo/src/algorithm/k_nearest_concave_hull.rs
index c96f2ecda..339f46148 100644
--- a/geo/src/algorithm/k_nearest_concave_hull.rs
+++ b/geo/src/algorithm/k_nearest_concave_hull.rs
@@ -105,7 +105,7 @@ where
 {
     let mut dataset: rstar::RTree<Coord<T>> = rstar::RTree::new();
     for coord in coords {
-        let closest = dataset.nearest_neighbor(coord);
+        let closest = dataset.nearest_neighbor(*coord);
         if let Some(closest) = closest
             && coords_are_equal(coord, closest)
         {
@@ -257,7 +257,7 @@ where
     T: GeoFloat + RTreeNum,
 {
     dataset
-        .nearest_neighbor_iter(base_coord)
+        .nearest_neighbor_iter(*base_coord)
         .take(candidate_no as usize)
 }
 
diff --git a/geo/src/algorithm/line_measures/metric_spaces/euclidean/distance.rs b/geo/src/algorithm/line_measures/metric_spaces/euclidean/distance.rs
index dc502664f..70f5d032e 100644
--- a/geo/src/algorithm/line_measures/metric_spaces/euclidean/distance.rs
+++ b/geo/src/algorithm/line_measures/metric_spaces/euclidean/distance.rs
@@ -448,11 +448,11 @@ fn nearest_neighbour_distance<F: GeoFloat>(geom1: &LineString<F>, geom2: &LineSt
     geom2
         .points()
         .fold(Bounded::max_value(), |acc: F, point| {
-            let nearest = tree_a.nearest_neighbor(&point).unwrap();
+            let nearest = tree_a.nearest_neighbor(point).unwrap();
             acc.min(Euclidean.distance(nearest as &Line<F>, &point))
         })
         .min(geom1.points().fold(Bounded::max_value(), |acc, point| {
-            let nearest = tree_b.nearest_neighbor(&point).unwrap();
+            let nearest = tree_b.nearest_neighbor(point).unwrap();
             acc.min(Euclidean.distance(nearest as &Line<F>, &point))
         }))
 }
diff --git a/geo/src/algorithm/outlier_detection.rs b/geo/src/algorithm/outlier_detection.rs
index 861efd92e..320744417 100644
--- a/geo/src/algorithm/outlier_detection.rs
+++ b/geo/src/algorithm/outlier_detection.rs
@@ -212,7 +212,7 @@ where
         .iter()
         .map(|point| {
             let neighbours = tree
-                .nearest_neighbor_iter_with_distance_2(point)
+                .nearest_neighbor_iter_with_distance_2(*point)
                 .take(k_neighbours)
                 .collect::<Vec<_>>();
             let kth_dist = neighbours.last().map(|(_, d)| *d).unwrap();
diff --git a/geo/src/algorithm/simplify_vw.rs b/geo/src/algorithm/simplify_vw.rs
index 1cb145d50..05dde15b2 100644
--- a/geo/src/algorithm/simplify_vw.rs
+++ b/geo/src/algorithm/simplify_vw.rs
@@ -415,7 +415,7 @@ where
         orig[triangle.right],
     )
     .bounding_rect();
-    tree.locate_in_envelope_intersecting(&rstar::AABB::from_corners(
+    tree.locate_in_envelope_intersecting(rstar::AABB::from_corners(
         bounding_rect.min().into(),
         bounding_rect.max().into(),
     ))
diff --git a/geo/src/algorithm/triangulate_delaunay.rs b/geo/src/algorithm/triangulate_delaunay.rs
index 17c849434..ebae1479b 100644
--- a/geo/src/algorithm/triangulate_delaunay.rs
+++ b/geo/src/algorithm/triangulate_delaunay.rs
@@ -629,7 +629,7 @@ pub(crate) fn snap_or_register_point<T: SpadeTriangulationFloat>(
     snap_radius: T,
 ) -> Coord<T> {
     known_points
-        .nearest_neighbor(&point)
+        .nearest_neighbor(point)
         // only snap if closest is within snap radius
         .filter(|nearest_point| Euclidean.distance(**nearest_point, point) < snap_radius)
         .cloned()