diff --git a/include/sway/tree/container.h b/include/sway/tree/container.h
index 751612e2c..fe3ee8a8b 100644
--- a/include/sway/tree/container.h
+++ b/include/sway/tree/container.h
@@ -113,6 +113,11 @@ struct sway_container {
 	// Hidden scratchpad containers have a NULL parent.
 	bool scratchpad;
 
+	// Stores last output size and position for adjusting coordinates of
+	// scratchpad windows.
+	// Unused for non-scratchpad windows.
+	struct wlr_box transform;
+
 	float alpha;
 
 	struct wlr_texture *title_focused;
@@ -196,6 +201,9 @@ size_t container_titlebar_height(void);
 void floating_calculate_constraints(int *min_width, int *max_width,
 		int *min_height, int *max_height);
 
+void floating_fix_coordinates(struct sway_container *con,
+		struct wlr_box *old, struct wlr_box *new);
+
 void container_floating_resize_and_center(struct sway_container *con);
 
 void container_floating_set_default_size(struct sway_container *con);
diff --git a/sway/commands/move.c b/sway/commands/move.c
index 7bd1fe3e1..9e40a3b47 100644
--- a/sway/commands/move.c
+++ b/sway/commands/move.c
@@ -206,9 +206,17 @@ static void container_move_to_workspace(struct sway_container *container,
 		container_detach(container);
 		workspace_add_floating(workspace, container);
 		container_handle_fullscreen_reparent(container);
-		// If changing output, center it within the workspace
+		// If changing output, adjust the coordinates of the window.
 		if (old_output != workspace->output && !container->pending.fullscreen_mode) {
-			container_floating_move_to_center(container);
+			struct wlr_box workspace_box, old_workspace_box;
+			workspace_get_box(workspace, &workspace_box);
+			workspace_get_box(old_workspace, &old_workspace_box);
+			floating_fix_coordinates(container, &old_workspace_box, &workspace_box);
+			if (container->scratchpad && workspace->output) {
+				struct wlr_box output_box;
+				output_get_box(workspace->output, &output_box);
+				container->transform = workspace_box;
+			}
 		}
 	} else {
 		container_detach(container);
diff --git a/sway/tree/arrange.c b/sway/tree/arrange.c
index 9c1a11e55..af925d054 100644
--- a/sway/tree/arrange.c
+++ b/sway/tree/arrange.c
@@ -264,6 +264,9 @@ void arrange_workspace(struct sway_workspace *workspace) {
 			area->width, area->height, area->x, area->y);
 
 	bool first_arrange = workspace->width == 0 && workspace->height == 0;
+	struct wlr_box prev_box;
+	workspace_get_box(workspace, &prev_box);
+
 	double prev_x = workspace->x - workspace->current_gaps.left;
 	double prev_y = workspace->y - workspace->current_gaps.top;
 	workspace->width = area->width;
@@ -277,13 +280,14 @@ void arrange_workspace(struct sway_workspace *workspace) {
 	if (!first_arrange && (diff_x != 0 || diff_y != 0)) {
 		for (int i = 0; i < workspace->floating->length; ++i) {
 			struct sway_container *floater = workspace->floating->items[i];
-			container_floating_translate(floater, diff_x, diff_y);
-			double center_x = floater->pending.x + floater->pending.width / 2;
-			double center_y = floater->pending.y + floater->pending.height / 2;
 			struct wlr_box workspace_box;
 			workspace_get_box(workspace, &workspace_box);
-			if (!wlr_box_contains_point(&workspace_box, center_x, center_y)) {
-				container_floating_move_to_center(floater);
+			floating_fix_coordinates(floater, &prev_box, &workspace_box);
+			// Set transformation for scratchpad windows.
+			if (floater->scratchpad) {
+				struct wlr_box output_box;
+				output_get_box(output, &output_box);
+				floater->transform = output_box;
 			}
 		}
 	}
diff --git a/sway/tree/container.c b/sway/tree/container.c
index 8222a5069..d2c4ffc44 100644
--- a/sway/tree/container.c
+++ b/sway/tree/container.c
@@ -712,6 +712,21 @@ void floating_calculate_constraints(int *min_width, int *max_width,
 
 }
 
+void floating_fix_coordinates(struct sway_container *con, struct wlr_box *old, struct wlr_box *new) {
+	if (!old->width || !old->height) {
+		// Fall back to centering on the workspace.
+		container_floating_move_to_center(con);
+	} else {
+		int rel_x = con->pending.x - old->x + (con->pending.width / 2);
+		int rel_y = con->pending.y - old->y + (con->pending.height / 2);
+
+		con->pending.x = new->x + (double)(rel_x * new->width) / old->width - (con->pending.width / 2);
+		con->pending.y = new->y + (double)(rel_y * new->height) / old->height - (con->pending.height / 2);
+
+		sway_log(SWAY_DEBUG, "Transformed container %p to coords (%f, %f)", con, con->pending.x, con->pending.y);
+	}
+}
+
 static void floating_natural_resize(struct sway_container *con) {
 	int min_width, max_width, min_height, max_height;
 	floating_calculate_constraints(&min_width, &max_width,
@@ -1025,6 +1040,13 @@ void container_floating_move_to(struct sway_container *con,
 		workspace_add_floating(new_workspace, con);
 		arrange_workspace(old_workspace);
 		arrange_workspace(new_workspace);
+		// If the moved container was a visible scratchpad container, then
+		// update its transform.
+		if (con->scratchpad) {
+			struct wlr_box output_box;
+			output_get_box(new_output, &output_box);
+			con->transform = output_box;
+		}
 		workspace_detect_urgent(old_workspace);
 		workspace_detect_urgent(new_workspace);
 	}
diff --git a/sway/tree/root.c b/sway/tree/root.c
index 95129a88f..233358d25 100644
--- a/sway/tree/root.c
+++ b/sway/tree/root.c
@@ -56,6 +56,16 @@ void root_destroy(struct sway_root *root) {
 	free(root);
 }
 
+static void set_container_transform(struct sway_workspace *ws,
+			struct sway_container *con) {
+	struct sway_output *output = ws->output;
+	struct wlr_box box = {0};
+	if (output) {
+		output_get_box(output, &box);
+	}
+	con->transform = box;
+}
+
 void root_scratchpad_add_container(struct sway_container *con, struct sway_workspace *ws) {
 	if (!sway_assert(!con->scratchpad, "Container is already in scratchpad")) {
 		return;
@@ -64,6 +74,8 @@ void root_scratchpad_add_container(struct sway_container *con, struct sway_works
 	struct sway_container *parent = con->pending.parent;
 	struct sway_workspace *workspace = con->pending.workspace;
 
+	set_container_transform(workspace, con);
+
 	// Clear the fullscreen mode when sending to the scratchpad
 	if (con->pending.fullscreen_mode != FULLSCREEN_NONE) {
 		container_fullscreen_disable(con);
@@ -142,15 +154,12 @@ void root_scratchpad_show(struct sway_container *con) {
 	}
 	workspace_add_floating(new_ws, con);
 
-	// Make sure the container's center point overlaps this workspace
-	double center_lx = con->pending.x + con->pending.width / 2;
-	double center_ly = con->pending.y + con->pending.height / 2;
-
-	struct wlr_box workspace_box;
-	workspace_get_box(new_ws, &workspace_box);
-	if (!wlr_box_contains_point(&workspace_box, center_lx, center_ly)) {
-		container_floating_resize_and_center(con);
+	if (new_ws->output) {
+		struct wlr_box output_box;
+		output_get_box(new_ws->output, &output_box);
+		floating_fix_coordinates(con, &con->transform, &output_box);
 	}
+	set_container_transform(new_ws, con);
 
 	arrange_workspace(new_ws);
 	seat_set_focus(seat, seat_get_focus_inactive(seat, &con->node));
@@ -173,6 +182,8 @@ void root_scratchpad_hide(struct sway_container *con) {
 		return;
 	}
 
+	set_container_transform(con->pending.workspace, con);
+
 	disable_fullscreen(con, NULL);
 	container_for_each_child(con, disable_fullscreen, NULL);
 	container_detach(con);