diff --git a/backend/webdav/webdav.go b/backend/webdav/webdav.go
index 29ad1cdcf..1c2259db5 100644
--- a/backend/webdav/webdav.go
+++ b/backend/webdav/webdav.go
@@ -233,6 +233,7 @@ type Fs struct {
 	ntlmAuthMu         sync.Mutex    // mutex to serialize NTLM auth roundtrips
 	chunksUploadURL    string        // upload URL for nextcloud chunked
 	canChunk           bool          // set if nextcloud and nextcloud_chunk_size is set
+	canRecalcHash      bool          // set if the server can recalculate checksums with PATCH (nextcloud)
 	authSingleflight   *singleflight.Group
 }
 
@@ -664,6 +665,7 @@ func (f *Fs) setQuirks(ctx context.Context, vendor string) error {
 		f.propsetMtime = true
 		f.hasOCSHA1 = true
 		f.canChunk = true
+		f.canRecalcHash = true
 
 		if f.opt.ChunkSize == 0 {
 			fs.Logf(nil, "Chunked uploads are disabled because nextcloud_chunk_size is set to 0")
@@ -1471,11 +1473,16 @@ var owncloudPropsetWithChecksum = `<?xml version="1.0" encoding="utf-8" ?>
 // SetModTime sets the modification time of the local fs object
 func (o *Object) SetModTime(ctx context.Context, modTime time.Time) error {
 	if o.fs.propsetMtime {
+		// Setting the modification time discards the stored
+		// checksums so they are set again in the same request.
+		// Servers which can't do that recalculate them afterwards.
 		checksums := ""
-		if o.fs.hasOCSHA1 && o.sha1 != "" {
-			checksums = "SHA1:" + o.sha1
-		} else if o.fs.hasOCMD5 && o.md5 != "" {
-			checksums = "MD5:" + o.md5
+		if !o.fs.canRecalcHash {
+			if o.fs.hasOCSHA1 && o.sha1 != "" {
+				checksums = "SHA1:" + o.sha1
+			} else if o.fs.hasOCMD5 && o.md5 != "" {
+				checksums = "MD5:" + o.md5
+			}
 		}
 
 		opts := rest.Opts{
@@ -1510,6 +1517,12 @@ func (o *Object) SetModTime(ctx context.Context, modTime time.Time) error {
 			// in-memory modtime identical to the one a fresh
 			// listing returns
 			o.modTime = modTime.Truncate(time.Second)
+			if o.fs.canRecalcHash && (o.sha1 != "" || o.md5 != "") {
+				err = o.recalculateHash(ctx)
+				if err != nil {
+					return fmt.Errorf("couldn't restore checksum after setting modified time: %w", err)
+				}
+			}
 			return nil
 		}
 		// got an error, but it's possible it actually worked, so double-check
@@ -1608,7 +1621,54 @@ func (o *Object) Update(ctx context.Context, in io.Reader, src fs.ObjectInfo, op
 	}
 	// read metadata from remote
 	o.hasMetaData = false
-	return o.readMetaData(ctx)
+	err = o.readMetaData(ctx)
+	if err != nil {
+		return err
+	}
+	// The server only stores a checksum supplied with the upload,
+	// so ask the server to calculate one if it is missing.
+	if o.fs.canRecalcHash && o.sha1 == "" && o.md5 == "" {
+		err = o.recalculateHash(ctx)
+		if err != nil {
+			return fmt.Errorf("couldn't calculate checksum after upload: %w", err)
+		}
+	}
+	return nil
+}
+
+// recalculateHash asks the server to calculate and store the checksum
+// of the object's contents, updating the cached hash from the result.
+//
+// This uses the nextcloud PATCH extension with the X-Recalculate-Hash
+// header which returns the checksum in the OC-Checksum header.
+func (o *Object) recalculateHash(ctx context.Context) error {
+	hashName := ""
+	if o.fs.hasOCSHA1 {
+		hashName = "sha1"
+	} else if o.fs.hasOCMD5 {
+		hashName = "md5"
+	} else {
+		return nil
+	}
+	opts := rest.Opts{
+		Method:       "PATCH",
+		Path:         o.filePath(),
+		NoResponse:   true,
+		ExtraHeaders: map[string]string{"X-Recalculate-Hash": hashName},
+	}
+	var resp *http.Response
+	err := o.fs.pacer.Call(func() (bool, error) {
+		var err error
+		resp, err = o.fs.srv.Call(ctx, &opts)
+		return o.fs.shouldRetry(ctx, resp, err)
+	})
+	if err != nil {
+		return err
+	}
+	hashes := (&api.Prop{Checksums: []string{resp.Header.Get("OC-Checksum")}}).Hashes()
+	o.sha1 = hashes[hash.SHA1]
+	o.md5 = hashes[hash.MD5]
+	return nil
 }
 
 func (o *Object) extraHeaders(ctx context.Context, src fs.ObjectInfo) map[string]string {
diff --git a/docs/content/webdav.md b/docs/content/webdav.md
index 6faacafcf..823549fe6 100644
--- a/docs/content/webdav.md
+++ b/docs/content/webdav.md
@@ -119,7 +119,9 @@ Likewise plain WebDAV does not support hashes, however when used with
 Fastmail Files, ownCloud or Nextcloud rclone will support SHA1 and MD5 hashes.
 Depending on the exact version of ownCloud or Nextcloud hashes may
 appear on all objects, or only on objects which had a hash uploaded
-with them.
+with them. With Nextcloud, rclone asks the server to calculate the SHA1
+of uploads which had no hash to send, such as streamed uploads, and
+after setting the modification time, which discards the stored hash.
 
 <!-- autogenerated options start - DO NOT EDIT - instead edit fs.RegInfo in backend/webdav/webdav.go and run make backenddocs to verify --> <!-- markdownlint-disable-line line-length -->
 ### Standard options