diff --git a/r/NAMESPACE b/r/NAMESPACE
index e98cdd51fb7..053c75742f2 100644
--- a/r/NAMESPACE
+++ b/r/NAMESPACE
@@ -388,6 +388,7 @@ importFrom(purrr,map)
 importFrom(purrr,map2)
 importFrom(purrr,map2_chr)
 importFrom(purrr,map_chr)
+importFrom(purrr,map_dbl)
 importFrom(purrr,map_dfr)
 importFrom(purrr,map_int)
 importFrom(purrr,map_lgl)
diff --git a/r/R/arrow-package.R b/r/R/arrow-package.R
index 7b59854f1e1..7e1e5451cc7 100644
--- a/r/R/arrow-package.R
+++ b/r/R/arrow-package.R
@@ -17,7 +17,7 @@
 
 #' @importFrom stats quantile median na.omit na.exclude na.pass na.fail
 #' @importFrom R6 R6Class
-#' @importFrom purrr as_mapper map map2 map_chr map2_chr map_dfr map_int map_lgl keep imap imap_chr flatten
+#' @importFrom purrr as_mapper map map2 map_chr map2_chr map_dbl map_dfr map_int map_lgl keep imap imap_chr flatten
 #' @importFrom assertthat assert_that is.string
 #' @importFrom rlang list2 %||% is_false abort dots_n warn enquo quo_is_null enquos is_integerish quos
 #' @importFrom rlang eval_tidy new_data_mask syms env new_environment env_bind set_names exec
diff --git a/r/R/record-batch.R b/r/R/record-batch.R
index 2a924afa56a..528ecef2f3d 100644
--- a/r/R/record-batch.R
+++ b/r/R/record-batch.R
@@ -196,8 +196,8 @@ rbind.RecordBatch <- function(...) {
 }
 
 cbind_check_length <- function(inputs, call = caller_env()) {
-  sizes <- map_int(inputs, NROW)
-  ok_lengths <- sizes %in% c(head(sizes, 1), 1L)
+  sizes <- map_dbl(inputs, NROW)
+  ok_lengths <- sizes %in% c(head(sizes, 1), 1)
   if (!all(ok_lengths)) {
     first_bad_one <- which.min(ok_lengths)
     abort(
diff --git a/r/R/util.R b/r/R/util.R
index 4aff69e471a..a51fde0c2d6 100644
--- a/r/R/util.R
+++ b/r/R/util.R
@@ -158,7 +158,7 @@ as_writable_table <- function(x) {
 #' @keywords internal
 recycle_scalars <- function(arrays) {
   # Get lengths of items in arrays
-  arr_lens <- map_int(arrays, NROW)
+  arr_lens <- map_dbl(arrays, NROW)
 
   is_scalar <- arr_lens == 1
 
diff --git a/r/src/array.cpp b/r/src/array.cpp
index 1503d3e76dd..8ba0c569ea4 100644
--- a/r/src/array.cpp
+++ b/r/src/array.cpp
@@ -244,15 +244,15 @@ int32_t ListArray__value_length(const std::shared_ptr<arrow::ListArray>& array,
 }
 
 // [[arrow::export]]
-int64_t LargeListArray__value_length(const std::shared_ptr<arrow::LargeListArray>& array,
-                                     int64_t i) {
-  return array->value_length(i);
+r_vec_size LargeListArray__value_length(
+    const std::shared_ptr<arrow::LargeListArray>& array, int64_t i) {
+  return r_vec_size(array->value_length(i));
 }
 
 // [[arrow::export]]
-int64_t FixedSizeListArray__value_length(
+r_vec_size FixedSizeListArray__value_length(
     const std::shared_ptr<arrow::FixedSizeListArray>& array, int64_t i) {
-  return array->value_length(i);
+  return r_vec_size(array->value_length(i));
 }
 
 // [[arrow::export]]
@@ -262,15 +262,15 @@ int32_t ListArray__value_offset(const std::shared_ptr<arrow::ListArray>& array,
 }
 
 // [[arrow::export]]
-int64_t LargeListArray__value_offset(const std::shared_ptr<arrow::LargeListArray>& array,
-                                     int64_t i) {
-  return array->value_offset(i);
+r_vec_size LargeListArray__value_offset(
+    const std::shared_ptr<arrow::LargeListArray>& array, int64_t i) {
+  return r_vec_size(array->value_offset(i));
 }
 
 // [[arrow::export]]
-int64_t FixedSizeListArray__value_offset(
+r_vec_size FixedSizeListArray__value_offset(
     const std::shared_ptr<arrow::FixedSizeListArray>& array, int64_t i) {
-  return array->value_offset(i);
+  return r_vec_size(array->value_offset(i));
 }
 
 // [[arrow::export]]
@@ -319,8 +319,8 @@ bool Array__Same(const std::shared_ptr<arrow::Array>& x,
 }
 
 // [[arrow::export]]
-int64_t Array__ReferencedBufferSize(const std::shared_ptr<arrow::Array>& x) {
-  return ValueOrStop(arrow::util::ReferencedBufferSize(*x));
+r_vec_size Array__ReferencedBufferSize(const std::shared_ptr<arrow::Array>& x) {
+  return r_vec_size(ValueOrStop(arrow::util::ReferencedBufferSize(*x)));
 }
 
 // [[arrow::export]]
diff --git a/r/src/arrowExports.cpp b/r/src/arrowExports.cpp
index 62c8b6695c8..e89718144ab 100644
--- a/r/src/arrowExports.cpp
+++ b/r/src/arrowExports.cpp
@@ -255,7 +255,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // array.cpp
-int64_t LargeListArray__value_length(const std::shared_ptr<arrow::LargeListArray>& array, int64_t i);
+r_vec_size LargeListArray__value_length(const std::shared_ptr<arrow::LargeListArray>& array, int64_t i);
 extern "C" SEXP _arrow_LargeListArray__value_length(SEXP array_sexp, SEXP i_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::LargeListArray>&>::type array(array_sexp);
@@ -264,7 +264,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // array.cpp
-int64_t FixedSizeListArray__value_length(const std::shared_ptr<arrow::FixedSizeListArray>& array, int64_t i);
+r_vec_size FixedSizeListArray__value_length(const std::shared_ptr<arrow::FixedSizeListArray>& array, int64_t i);
 extern "C" SEXP _arrow_FixedSizeListArray__value_length(SEXP array_sexp, SEXP i_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::FixedSizeListArray>&>::type array(array_sexp);
@@ -282,7 +282,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // array.cpp
-int64_t LargeListArray__value_offset(const std::shared_ptr<arrow::LargeListArray>& array, int64_t i);
+r_vec_size LargeListArray__value_offset(const std::shared_ptr<arrow::LargeListArray>& array, int64_t i);
 extern "C" SEXP _arrow_LargeListArray__value_offset(SEXP array_sexp, SEXP i_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::LargeListArray>&>::type array(array_sexp);
@@ -291,7 +291,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // array.cpp
-int64_t FixedSizeListArray__value_offset(const std::shared_ptr<arrow::FixedSizeListArray>& array, int64_t i);
+r_vec_size FixedSizeListArray__value_offset(const std::shared_ptr<arrow::FixedSizeListArray>& array, int64_t i);
 extern "C" SEXP _arrow_FixedSizeListArray__value_offset(SEXP array_sexp, SEXP i_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::FixedSizeListArray>&>::type array(array_sexp);
@@ -357,7 +357,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // array.cpp
-int64_t Array__ReferencedBufferSize(const std::shared_ptr<arrow::Array>& x);
+r_vec_size Array__ReferencedBufferSize(const std::shared_ptr<arrow::Array>& x);
 extern "C" SEXP _arrow_Array__ReferencedBufferSize(SEXP x_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::Array>&>::type x(x_sexp);
@@ -657,7 +657,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // buffer.cpp
-int64_t Buffer__capacity(const std::shared_ptr<arrow::Buffer>& buffer);
+r_vec_size Buffer__capacity(const std::shared_ptr<arrow::Buffer>& buffer);
 extern "C" SEXP _arrow_Buffer__capacity(SEXP buffer_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::Buffer>&>::type buffer(buffer_sexp);
@@ -665,7 +665,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // buffer.cpp
-int64_t Buffer__size(const std::shared_ptr<arrow::Buffer>& buffer);
+r_vec_size Buffer__size(const std::shared_ptr<arrow::Buffer>& buffer);
 extern "C" SEXP _arrow_Buffer__size(SEXP buffer_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::Buffer>&>::type buffer(buffer_sexp);
@@ -698,7 +698,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // chunkedarray.cpp
-int ChunkedArray__length(const std::shared_ptr<arrow::ChunkedArray>& chunked_array);
+r_vec_size ChunkedArray__length(const std::shared_ptr<arrow::ChunkedArray>& chunked_array);
 extern "C" SEXP _arrow_ChunkedArray__length(SEXP chunked_array_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::ChunkedArray>&>::type chunked_array(chunked_array_sexp);
@@ -706,7 +706,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // chunkedarray.cpp
-int ChunkedArray__null_count(const std::shared_ptr<arrow::ChunkedArray>& chunked_array);
+r_vec_size ChunkedArray__null_count(const std::shared_ptr<arrow::ChunkedArray>& chunked_array);
 extern "C" SEXP _arrow_ChunkedArray__null_count(SEXP chunked_array_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::ChunkedArray>&>::type chunked_array(chunked_array_sexp);
@@ -714,7 +714,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // chunkedarray.cpp
-int ChunkedArray__num_chunks(const std::shared_ptr<arrow::ChunkedArray>& chunked_array);
+r_vec_size ChunkedArray__num_chunks(const std::shared_ptr<arrow::ChunkedArray>& chunked_array);
 extern "C" SEXP _arrow_ChunkedArray__num_chunks(SEXP chunked_array_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::ChunkedArray>&>::type chunked_array(chunked_array_sexp);
@@ -810,7 +810,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // chunkedarray.cpp
-int64_t ChunkedArray__ReferencedBufferSize(const std::shared_ptr<arrow::ChunkedArray>& chunked_array);
+r_vec_size ChunkedArray__ReferencedBufferSize(const std::shared_ptr<arrow::ChunkedArray>& chunked_array);
 extern "C" SEXP _arrow_ChunkedArray__ReferencedBufferSize(SEXP chunked_array_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::ChunkedArray>&>::type chunked_array(chunked_array_sexp);
@@ -2062,7 +2062,7 @@ extern "C" SEXP _arrow_dataset___Scanner__TakeRows(SEXP scanner_sexp, SEXP indic
 
 // dataset.cpp
 #if defined(ARROW_R_WITH_DATASET)
-int64_t dataset___Scanner__CountRows(const std::shared_ptr<ds::Scanner>& scanner);
+r_vec_size dataset___Scanner__CountRows(const std::shared_ptr<ds::Scanner>& scanner);
 extern "C" SEXP _arrow_dataset___Scanner__CountRows(SEXP scanner_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<ds::Scanner>&>::type scanner(scanner_sexp);
@@ -2902,7 +2902,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // filesystem.cpp
-int64_t fs___FileInfo__size(const std::shared_ptr<fs::FileInfo>& x);
+r_vec_size fs___FileInfo__size(const std::shared_ptr<fs::FileInfo>& x);
 extern "C" SEXP _arrow_fs___FileInfo__size(SEXP x_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<fs::FileInfo>&>::type x(x_sexp);
@@ -3264,7 +3264,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // io.cpp
-int64_t io___RandomAccessFile__GetSize(const std::shared_ptr<arrow::io::RandomAccessFile>& x);
+r_vec_size io___RandomAccessFile__GetSize(const std::shared_ptr<arrow::io::RandomAccessFile>& x);
 extern "C" SEXP _arrow_io___RandomAccessFile__GetSize(SEXP x_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::io::RandomAccessFile>&>::type x(x_sexp);
@@ -3290,7 +3290,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // io.cpp
-int64_t io___RandomAccessFile__Tell(const std::shared_ptr<arrow::io::RandomAccessFile>& x);
+r_vec_size io___RandomAccessFile__Tell(const std::shared_ptr<arrow::io::RandomAccessFile>& x);
 extern "C" SEXP _arrow_io___RandomAccessFile__Tell(SEXP x_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::io::RandomAccessFile>&>::type x(x_sexp);
@@ -3378,7 +3378,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // io.cpp
-int64_t io___OutputStream__Tell(const std::shared_ptr<arrow::io::OutputStream>& stream);
+r_vec_size io___OutputStream__Tell(const std::shared_ptr<arrow::io::OutputStream>& stream);
 extern "C" SEXP _arrow_io___OutputStream__Tell(SEXP stream_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::io::OutputStream>&>::type stream(stream_sexp);
@@ -3402,7 +3402,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // io.cpp
-int64_t io___BufferOutputStream__capacity(const std::shared_ptr<arrow::io::BufferOutputStream>& stream);
+r_vec_size io___BufferOutputStream__capacity(const std::shared_ptr<arrow::io::BufferOutputStream>& stream);
 extern "C" SEXP _arrow_io___BufferOutputStream__capacity(SEXP stream_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::io::BufferOutputStream>&>::type stream(stream_sexp);
@@ -3418,7 +3418,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // io.cpp
-int64_t io___BufferOutputStream__Tell(const std::shared_ptr<arrow::io::BufferOutputStream>& stream);
+r_vec_size io___BufferOutputStream__Tell(const std::shared_ptr<arrow::io::BufferOutputStream>& stream);
 extern "C" SEXP _arrow_io___BufferOutputStream__Tell(SEXP stream_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::io::BufferOutputStream>&>::type stream(stream_sexp);
@@ -3586,7 +3586,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // message.cpp
-int64_t ipc___Message__body_length(const std::unique_ptr<arrow::ipc::Message>& message);
+r_vec_size ipc___Message__body_length(const std::unique_ptr<arrow::ipc::Message>& message);
 extern "C" SEXP _arrow_ipc___Message__body_length(SEXP message_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::unique_ptr<arrow::ipc::Message>&>::type message(message_sexp);
@@ -3610,7 +3610,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // message.cpp
-int64_t ipc___Message__Verify(const std::unique_ptr<arrow::ipc::Message>& message);
+r_vec_size ipc___Message__Verify(const std::unique_ptr<arrow::ipc::Message>& message);
 extern "C" SEXP _arrow_ipc___Message__Verify(SEXP message_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::unique_ptr<arrow::ipc::Message>&>::type message(message_sexp);
@@ -3912,7 +3912,7 @@ extern "C" SEXP _arrow_parquet___arrow___FileReader__ReadRowGroups2(SEXP reader_
 
 // parquet.cpp
 #if defined(ARROW_R_WITH_PARQUET)
-int64_t parquet___arrow___FileReader__num_rows(const std::shared_ptr<parquet::arrow::FileReader>& reader);
+r_vec_size parquet___arrow___FileReader__num_rows(const std::shared_ptr<parquet::arrow::FileReader>& reader);
 extern "C" SEXP _arrow_parquet___arrow___FileReader__num_rows(SEXP reader_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<parquet::arrow::FileReader>&>::type reader(reader_sexp);
@@ -4239,7 +4239,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // recordbatch.cpp
-int RecordBatch__num_columns(const std::shared_ptr<arrow::RecordBatch>& x);
+r_vec_size RecordBatch__num_columns(const std::shared_ptr<arrow::RecordBatch>& x);
 extern "C" SEXP _arrow_RecordBatch__num_columns(SEXP x_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::RecordBatch>&>::type x(x_sexp);
@@ -4247,7 +4247,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // recordbatch.cpp
-int RecordBatch__num_rows(const std::shared_ptr<arrow::RecordBatch>& x);
+r_vec_size RecordBatch__num_rows(const std::shared_ptr<arrow::RecordBatch>& x);
 extern "C" SEXP _arrow_RecordBatch__num_rows(SEXP x_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::RecordBatch>&>::type x(x_sexp);
@@ -4419,7 +4419,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // recordbatch.cpp
-int64_t RecordBatch__ReferencedBufferSize(const std::shared_ptr<arrow::RecordBatch>& batch);
+r_vec_size RecordBatch__ReferencedBufferSize(const std::shared_ptr<arrow::RecordBatch>& batch);
 extern "C" SEXP _arrow_RecordBatch__ReferencedBufferSize(SEXP batch_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::RecordBatch>&>::type batch(batch_sexp);
@@ -4834,7 +4834,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // table.cpp
-int Table__num_columns(const std::shared_ptr<arrow::Table>& x);
+r_vec_size Table__num_columns(const std::shared_ptr<arrow::Table>& x);
 extern "C" SEXP _arrow_Table__num_columns(SEXP x_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::Table>&>::type x(x_sexp);
@@ -4842,7 +4842,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // table.cpp
-int Table__num_rows(const std::shared_ptr<arrow::Table>& x);
+r_vec_size Table__num_rows(const std::shared_ptr<arrow::Table>& x);
 extern "C" SEXP _arrow_Table__num_rows(SEXP x_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::Table>&>::type x(x_sexp);
@@ -5021,7 +5021,7 @@ BEGIN_CPP11
 END_CPP11
 }
 // table.cpp
-int64_t Table__ReferencedBufferSize(const std::shared_ptr<arrow::Table>& table);
+r_vec_size Table__ReferencedBufferSize(const std::shared_ptr<arrow::Table>& table);
 extern "C" SEXP _arrow_Table__ReferencedBufferSize(SEXP table_sexp){
 BEGIN_CPP11
 	arrow::r::Input<const std::shared_ptr<arrow::Table>&>::type table(table_sexp);
diff --git a/r/src/buffer.cpp b/r/src/buffer.cpp
index 11a80a8d56d..97f6db5535a 100644
--- a/r/src/buffer.cpp
+++ b/r/src/buffer.cpp
@@ -28,13 +28,13 @@ void Buffer__ZeroPadding(const std::shared_ptr<arrow::Buffer>& buffer) {
 }
 
 // [[arrow::export]]
-int64_t Buffer__capacity(const std::shared_ptr<arrow::Buffer>& buffer) {
-  return buffer->capacity();
+r_vec_size Buffer__capacity(const std::shared_ptr<arrow::Buffer>& buffer) {
+  return r_vec_size(buffer->capacity());
 }
 
 // [[arrow::export]]
-int64_t Buffer__size(const std::shared_ptr<arrow::Buffer>& buffer) {
-  return buffer->size();
+r_vec_size Buffer__size(const std::shared_ptr<arrow::Buffer>& buffer) {
+  return r_vec_size(buffer->size());
 }
 
 // [[arrow::export]]
diff --git a/r/src/chunkedarray.cpp b/r/src/chunkedarray.cpp
index b495f3d1edf..36884bb531b 100644
--- a/r/src/chunkedarray.cpp
+++ b/r/src/chunkedarray.cpp
@@ -22,18 +22,21 @@
 #include <arrow/util/byte_size.h>
 
 // [[arrow::export]]
-int ChunkedArray__length(const std::shared_ptr<arrow::ChunkedArray>& chunked_array) {
-  return chunked_array->length();
+r_vec_size ChunkedArray__length(
+    const std::shared_ptr<arrow::ChunkedArray>& chunked_array) {
+  return r_vec_size(chunked_array->length());
 }
 
 // [[arrow::export]]
-int ChunkedArray__null_count(const std::shared_ptr<arrow::ChunkedArray>& chunked_array) {
-  return chunked_array->null_count();
+r_vec_size ChunkedArray__null_count(
+    const std::shared_ptr<arrow::ChunkedArray>& chunked_array) {
+  return r_vec_size(chunked_array->null_count());
 }
 
 // [[arrow::export]]
-int ChunkedArray__num_chunks(const std::shared_ptr<arrow::ChunkedArray>& chunked_array) {
-  return chunked_array->num_chunks();
+r_vec_size ChunkedArray__num_chunks(
+    const std::shared_ptr<arrow::ChunkedArray>& chunked_array) {
+  return r_vec_size(chunked_array->num_chunks());
 }
 
 // [[arrow::export]]
@@ -144,7 +147,7 @@ std::shared_ptr<arrow::ChunkedArray> ChunkedArray__from_list(cpp11::list chunks,
 }
 
 // [[arrow::export]]
-int64_t ChunkedArray__ReferencedBufferSize(
+r_vec_size ChunkedArray__ReferencedBufferSize(
     const std::shared_ptr<arrow::ChunkedArray>& chunked_array) {
-  return ValueOrStop(arrow::util::ReferencedBufferSize(*chunked_array));
+  return r_vec_size(ValueOrStop(arrow::util::ReferencedBufferSize(*chunked_array)));
 }
diff --git a/r/src/dataset.cpp b/r/src/dataset.cpp
index aa44a0721e3..713c0d3b237 100644
--- a/r/src/dataset.cpp
+++ b/r/src/dataset.cpp
@@ -511,8 +511,8 @@ std::shared_ptr<arrow::Table> dataset___Scanner__TakeRows(
 }
 
 // [[dataset::export]]
-int64_t dataset___Scanner__CountRows(const std::shared_ptr<ds::Scanner>& scanner) {
-  return ValueOrStop(scanner->CountRows());
+r_vec_size dataset___Scanner__CountRows(const std::shared_ptr<ds::Scanner>& scanner) {
+  return r_vec_size(ValueOrStop(scanner->CountRows()));
 }
 
 #endif
diff --git a/r/src/filesystem.cpp b/r/src/filesystem.cpp
index cdf536b3bc8..f6c5499bd3d 100644
--- a/r/src/filesystem.cpp
+++ b/r/src/filesystem.cpp
@@ -71,7 +71,9 @@ void fs___FileInfo__set_path(const std::shared_ptr<fs::FileInfo>& x,
 }
 
 // [[arrow::export]]
-int64_t fs___FileInfo__size(const std::shared_ptr<fs::FileInfo>& x) { return x->size(); }
+r_vec_size fs___FileInfo__size(const std::shared_ptr<fs::FileInfo>& x) {
+  return r_vec_size(x->size());
+}
 
 // [[arrow::export]]
 void fs___FileInfo__set_size(const std::shared_ptr<fs::FileInfo>& x, int64_t size) {
diff --git a/r/src/io.cpp b/r/src/io.cpp
index a0f53478a0d..42766ddd2f5 100644
--- a/r/src/io.cpp
+++ b/r/src/io.cpp
@@ -51,9 +51,9 @@ void io___OutputStream__Close(const std::shared_ptr<arrow::io::OutputStream>& x)
 // ------ arrow::io::RandomAccessFile
 
 // [[arrow::export]]
-int64_t io___RandomAccessFile__GetSize(
+r_vec_size io___RandomAccessFile__GetSize(
     const std::shared_ptr<arrow::io::RandomAccessFile>& x) {
-  return ValueOrStop(x->GetSize());
+  return r_vec_size(ValueOrStop(x->GetSize()));
 }
 
 // [[arrow::export]]
@@ -69,9 +69,9 @@ void io___RandomAccessFile__Seek(const std::shared_ptr<arrow::io::RandomAccessFi
 }
 
 // [[arrow::export]]
-int64_t io___RandomAccessFile__Tell(
+r_vec_size io___RandomAccessFile__Tell(
     const std::shared_ptr<arrow::io::RandomAccessFile>& x) {
-  return ValueOrStop(x->Tell());
+  return r_vec_size(ValueOrStop(x->Tell()));
 }
 
 // [[arrow::export]]
@@ -161,8 +161,9 @@ void io___Writable__write(const std::shared_ptr<arrow::io::Writable>& stream,
 // ------- arrow::io::OutputStream
 
 // [[arrow::export]]
-int64_t io___OutputStream__Tell(const std::shared_ptr<arrow::io::OutputStream>& stream) {
-  return ValueOrStop(stream->Tell());
+r_vec_size io___OutputStream__Tell(
+    const std::shared_ptr<arrow::io::OutputStream>& stream) {
+  return r_vec_size(ValueOrStop(stream->Tell()));
 }
 
 // ------ arrow::io::FileOutputStream
@@ -183,9 +184,9 @@ std::shared_ptr<arrow::io::BufferOutputStream> io___BufferOutputStream__Create(
 }
 
 // [[arrow::export]]
-int64_t io___BufferOutputStream__capacity(
+r_vec_size io___BufferOutputStream__capacity(
     const std::shared_ptr<arrow::io::BufferOutputStream>& stream) {
-  return stream->capacity();
+  return r_vec_size(stream->capacity());
 }
 
 // [[arrow::export]]
@@ -195,9 +196,9 @@ std::shared_ptr<arrow::Buffer> io___BufferOutputStream__Finish(
 }
 
 // [[arrow::export]]
-int64_t io___BufferOutputStream__Tell(
+r_vec_size io___BufferOutputStream__Tell(
     const std::shared_ptr<arrow::io::BufferOutputStream>& stream) {
-  return ValueOrStop(stream->Tell());
+  return r_vec_size(ValueOrStop(stream->Tell()));
 }
 
 // [[arrow::export]]
diff --git a/r/src/message.cpp b/r/src/message.cpp
index 16044d9a92d..d9832ddc22a 100644
--- a/r/src/message.cpp
+++ b/r/src/message.cpp
@@ -21,8 +21,9 @@
 #include <arrow/ipc/writer.h>
 
 // [[arrow::export]]
-int64_t ipc___Message__body_length(const std::unique_ptr<arrow::ipc::Message>& message) {
-  return message->body_length();
+r_vec_size ipc___Message__body_length(
+    const std::unique_ptr<arrow::ipc::Message>& message) {
+  return r_vec_size(message->body_length());
 }
 
 // [[arrow::export]]
@@ -38,8 +39,8 @@ std::shared_ptr<arrow::Buffer> ipc___Message__body(
 }
 
 // [[arrow::export]]
-int64_t ipc___Message__Verify(const std::unique_ptr<arrow::ipc::Message>& message) {
-  return message->Verify();
+r_vec_size ipc___Message__Verify(const std::unique_ptr<arrow::ipc::Message>& message) {
+  return r_vec_size(message->Verify());
 }
 
 // [[arrow::export]]
diff --git a/r/src/parquet.cpp b/r/src/parquet.cpp
index 5d5fd9b7f46..d92650252c8 100644
--- a/r/src/parquet.cpp
+++ b/r/src/parquet.cpp
@@ -148,9 +148,9 @@ std::shared_ptr<arrow::Table> parquet___arrow___FileReader__ReadRowGroups2(
 }
 
 // [[parquet::export]]
-int64_t parquet___arrow___FileReader__num_rows(
+r_vec_size parquet___arrow___FileReader__num_rows(
     const std::shared_ptr<parquet::arrow::FileReader>& reader) {
-  return reader->parquet_reader()->metadata()->num_rows();
+  return r_vec_size(reader->parquet_reader()->metadata()->num_rows());
 }
 
 // [[parquet::export]]
diff --git a/r/src/recordbatch.cpp b/r/src/recordbatch.cpp
index 01bd8a3f35b..aca3a74fd81 100644
--- a/r/src/recordbatch.cpp
+++ b/r/src/recordbatch.cpp
@@ -27,8 +27,8 @@
 #include <arrow/util/key_value_metadata.h>
 
 // [[arrow::export]]
-int RecordBatch__num_columns(const std::shared_ptr<arrow::RecordBatch>& x) {
-  return x->num_columns();
+r_vec_size RecordBatch__num_columns(const std::shared_ptr<arrow::RecordBatch>& x) {
+  return r_vec_size(x->num_columns());
 }
 
 // [[arrow::export]]
@@ -307,7 +307,7 @@ std::shared_ptr<arrow::RecordBatch> RecordBatch__from_arrays(SEXP schema_sxp, SE
 }
 
 // [[arrow::export]]
-int64_t RecordBatch__ReferencedBufferSize(
+r_vec_size RecordBatch__ReferencedBufferSize(
     const std::shared_ptr<arrow::RecordBatch>& batch) {
-  return ValueOrStop(arrow::util::ReferencedBufferSize(*batch));
+  return r_vec_size(ValueOrStop(arrow::util::ReferencedBufferSize(*batch)));
 }
diff --git a/r/src/table.cpp b/r/src/table.cpp
index 07bf44750a1..f31aac33eff 100644
--- a/r/src/table.cpp
+++ b/r/src/table.cpp
@@ -23,8 +23,8 @@
 #include <arrow/util/key_value_metadata.h>
 
 // [[arrow::export]]
-int Table__num_columns(const std::shared_ptr<arrow::Table>& x) {
-  return x->num_columns();
+r_vec_size Table__num_columns(const std::shared_ptr<arrow::Table>& x) {
+  return r_vec_size(x->num_columns());
 }
 
 // [[arrow::export]]
@@ -303,8 +303,8 @@ std::shared_ptr<arrow::Table> Table__from_record_batches(
 }
 
 // [[arrow::export]]
-int64_t Table__ReferencedBufferSize(const std::shared_ptr<arrow::Table>& table) {
-  return ValueOrStop(arrow::util::ReferencedBufferSize(*table));
+r_vec_size Table__ReferencedBufferSize(const std::shared_ptr<arrow::Table>& table) {
+  return r_vec_size(ValueOrStop(arrow::util::ReferencedBufferSize(*table)));
 }
 
 // [[arrow::export]]
diff --git a/r/tests/testthat/test-Table.R b/r/tests/testthat/test-Table.R
index 791e3ce2988..b9bbe5b559e 100644
--- a/r/tests/testthat/test-Table.R
+++ b/r/tests/testthat/test-Table.R
@@ -696,3 +696,28 @@ test_that("as_arrow_table() errors for invalid input", {
     class = "arrow_no_method_as_arrow_table"
   )
 })
+
+test_that("num_rows method not susceptible to integer overflow", {
+  skip_if_not_running_large_memory_tests()
+
+  small_array <- Array$create(raw(1))
+  big_array <- Array$create(raw(.Machine$integer.max))
+  big_chunked_array <- chunked_array(big_array, small_array)
+  # LargeString array with data buffer > MAX_INT32
+  big_string_array <- Array$create(make_big_string())
+
+  small_table <- Table$create(col = small_array)
+  big_table <- Table$create(col = big_chunked_array)
+
+  expect_type(big_array$nbytes(), "integer")
+  expect_type(big_chunked_array$nbytes(), "double")
+
+  expect_type(length(big_array), "integer")
+  expect_type(length(big_chunked_array), "double")
+
+  expect_type(small_table$num_rows, "integer")
+  expect_type(big_table$num_rows, "double")
+
+  expect_identical(big_string_array$data()$buffers[[3]]$size, 2148007936)
+
+})