diff --git a/esphome/components/display/display_buffer.cpp b/esphome/components/display/display_buffer.cpp
index 420801f863..7cd85dabd4 100644
--- a/esphome/components/display/display_buffer.cpp
+++ b/esphome/components/display/display_buffer.cpp
@@ -32,9 +32,11 @@ void Rect::extend(Rect rect) {
     this->h = rect.h;
   } else {
     if (this->x > rect.x) {
+      this->w = this->w + (this->x - rect.x);
       this->x = rect.x;
     }
     if (this->y > rect.y) {
+      this->h = this->h + (this->y - rect.y);
       this->y = rect.y;
     }
     if (this->x2() < rect.x2()) {
@@ -49,29 +51,35 @@ void Rect::shrink(Rect rect) {
   if (!this->inside(rect)) {
     (*this) = Rect();
   } else {
-    if (this->x < rect.x) {
-      this->x = rect.x;
-    }
-    if (this->y < rect.y) {
-      this->y = rect.y;
-    }
     if (this->x2() > rect.x2()) {
       this->w = rect.x2() - this->x;
     }
+    if (this->x < rect.x) {
+      this->w = this->w + (this->x - rect.x);
+      this->x = rect.x;
+    }
     if (this->y2() > rect.y2()) {
       this->h = rect.y2() - this->y;
     }
+    if (this->y < rect.y) {
+      this->h = this->h + (this->y - rect.y);
+      this->y = rect.y;
+    }
   }
 }
 
-bool Rect::inside(int16_t x, int16_t y, bool absolute) {  // NOLINT
+bool Rect::equal(Rect rect) {
+  return (rect.x == this->x) && (rect.w == this->w) && (rect.y == this->y) && (rect.h == this->h);
+}
+
+bool Rect::inside(int16_t test_x, int16_t test_y, bool absolute) {  // NOLINT
   if (!this->is_set()) {
     return true;
   }
   if (absolute) {
-    return ((x >= 0) && (x <= this->w) && (y >= 0) && (y <= this->h));
+    return ((test_x >= this->x) && (test_x <= this->x2()) && (test_y >= this->y) && (test_y <= this->y2()));
   } else {
-    return ((x >= this->x) && (x <= this->x2()) && (y >= this->y) && (y <= this->y2()));
+    return ((test_x >= 0) && (test_x <= this->w) && (test_y >= 0) && (test_y <= this->h));
   }
 }
 
@@ -80,15 +88,16 @@ bool Rect::inside(Rect rect, bool absolute) {
     return true;
   }
   if (absolute) {
-    return ((rect.x <= this->w) && (rect.w >= 0) && (rect.y <= this->h) && (rect.h >= 0));
-  } else {
     return ((rect.x <= this->x2()) && (rect.x2() >= this->x) && (rect.y <= this->y2()) && (rect.y2() >= this->y));
+  } else {
+    return ((rect.x <= this->w) && (rect.w >= 0) && (rect.y <= this->h) && (rect.h >= 0));
   }
 }
 
 void Rect::info(const std::string &prefix) {
   if (this->is_set()) {
-    ESP_LOGI(TAG, "%s [%3d,%3d,%3d,%3d]", prefix.c_str(), this->x, this->y, this->w, this->h);
+    ESP_LOGI(TAG, "%s [%3d,%3d,%3d,%3d] (%3d,%3d)", prefix.c_str(), this->x, this->y, this->w, this->h, this->x2(),
+             this->y2());
   } else
     ESP_LOGI(TAG, "%s ** IS NOT SET **", prefix.c_str());
 }
diff --git a/esphome/components/display/display_buffer.h b/esphome/components/display/display_buffer.h
index 0402826594..4477685e1b 100644
--- a/esphome/components/display/display_buffer.h
+++ b/esphome/components/display/display_buffer.h
@@ -120,8 +120,9 @@ class Rect {
   void extend(Rect rect);
   void shrink(Rect rect);
 
-  bool inside(Rect rect, bool absolute = false);
-  bool inside(int16_t x, int16_t y, bool absolute = false);
+  bool inside(Rect rect, bool absolute = true);
+  bool inside(int16_t test_x, int16_t test_y, bool absolute = true);
+  bool equal(Rect rect);
   void info(const std::string &prefix = "rect info:");
 };