diff --git a/backend/s3/s3.go b/backend/s3/s3.go
index f7c3f46f3..c49d9c9b7 100644
--- a/backend/s3/s3.go
+++ b/backend/s3/s3.go
@@ -26,6 +26,7 @@ import (
 	"regexp"
 	"strconv"
 	"strings"
+	"sync"
 	"time"
 
 	"github.com/aws/aws-sdk-go/aws"
@@ -693,14 +694,25 @@ The minimum is 0 and the maximum is 5GB.`,
 			Name: "chunk_size",
 			Help: `Chunk size to use for uploading.
 
-When uploading files larger than upload_cutoff they will be uploaded
-as multipart uploads using this chunk size.
+When uploading files larger than upload_cutoff or files with unknown
+size (eg from "rclone rcat" or uploaded with "rclone mount" or google
+photos or google docs) they will be uploaded as multipart uploads
+using this chunk size.
 
 Note that "--s3-upload-concurrency" chunks of this size are buffered
 in memory per transfer.
 
 If you are transferring large files over high speed links and you have
-enough memory, then increasing this will speed up the transfers.`,
+enough memory, then increasing this will speed up the transfers.
+
+Rclone will automatically increase the chunk size when uploading a
+large file of known size to stay below the 10,000 chunks limit.
+
+Files of unknown size are uploaded with the configured
+chunk_size. Since the default chunk size is 5MB and there can be at
+most 10,000 chunks, this means that by default the maximum size of
+file you can stream upload is 48GB.  If you wish to stream upload
+larger files then you will need to increase chunk_size.`,
 			Default:  minChunkSize,
 			Advanced: true,
 		}, {
@@ -771,12 +783,11 @@ WARNING: Storing parts of an incomplete multipart upload counts towards space us
 
 // Constants
 const (
-	metaMtime           = "Mtime"                       // the meta key to store mtime in - eg X-Amz-Meta-Mtime
-	metaMD5Hash         = "Md5chksum"                   // the meta key to store md5hash in
-	listChunkSize       = 1000                          // number of items to read at once
-	maxRetries          = 10                            // number of retries to make of operations
-	maxSizeForCopy      = 5 * 1024 * 1024 * 1024        // The maximum size of object we can COPY
-	maxFileSize         = 5 * 1024 * 1024 * 1024 * 1024 // largest possible upload file size
+	metaMtime           = "Mtime"                // the meta key to store mtime in - eg X-Amz-Meta-Mtime
+	metaMD5Hash         = "Md5chksum"            // the meta key to store md5hash in
+	listChunkSize       = 1000                   // number of items to read at once
+	maxRetries          = 10                     // number of retries to make of operations
+	maxSizeForCopy      = 5 * 1024 * 1024 * 1024 // The maximum size of object we can COPY
 	minChunkSize        = fs.SizeSuffix(s3manager.MinUploadPartSize)
 	defaultUploadCutoff = fs.SizeSuffix(200 * 1024 * 1024)
 	maxUploadCutoff     = fs.SizeSuffix(5 * 1024 * 1024 * 1024)
@@ -1982,6 +1993,8 @@ func (o *Object) Open(ctx context.Context, options ...fs.OpenOption) (in io.Read
 	return resp.Body, nil
 }
 
+var warnStreamUpload sync.Once
+
 // Update the Object from in with modTime and size
 func (o *Object) Update(ctx context.Context, in io.Reader, src fs.ObjectInfo, options ...fs.OpenOption) error {
 	bucket, bucketPath := o.split()
@@ -2001,10 +2014,14 @@ func (o *Object) Update(ctx context.Context, in io.Reader, src fs.ObjectInfo, op
 			u.S3 = o.fs.c
 			u.PartSize = int64(o.fs.opt.ChunkSize)
 
+			// size can be -1 here meaning we don't know the size of the incoming file.  We use ChunkSize
+			// buffers here (default 5MB). With a maximum number of parts (10,000) this will be a file of
+			// 48GB which seems like a not too unreasonable limit.
 			if size == -1 {
-				// Make parts as small as possible while still being able to upload to the
-				// S3 file size limit. Rounded up to nearest MB.
-				u.PartSize = (((maxFileSize / s3manager.MaxUploadParts) >> 20) + 1) << 20
+				warnStreamUpload.Do(func() {
+					fs.Logf(o.fs, "Streaming uploads using chunk size %v will have maximum file size of %v",
+						o.fs.opt.ChunkSize, fs.SizeSuffix(u.PartSize*s3manager.MaxUploadParts))
+				})
 				return
 			}
 			// Adjust PartSize until the number of parts is small enough.