WooCommerce add "Save x%" next to sale prices

functions.php

<?php
// Add save percent next to sale item prices.
add_filter( 'woocommerce_sale_price_html', 'woocommerce_custom_sales_price', 10, 2 );
function woocommerce_custom_sales_price( $price, $product ) {
	$percentage = round( ( ( $product->regular_price - $product->sale_price ) / $product->regular_price ) * 100 );
	return $price . sprintf( __(' Save %s', 'woocommerce' ), $percentage . '%' );
}
?>

Your snippet only works on simple products. For variable products, instead, give the following code a try:

// For Variable Products Discount
add_filter( 'woocommerce_available_variation', 'custom_variation_price_saving_percentage', 10, 3 );
function custom_variation_price_saving_percentage( $data, $product, $variation ) {
$active_price = $data['display_price'];
$regular_price = $data['display_regular_price'];

if( $active_price !== $regular_price ) {
$saving_percentage = round( 100 - ( $active_price / $regular_price * 100 ), 1 ) . '%';
$data['price_html'] .= sprintf( __('You Saved: %s', 'woocommerce' ), $saving_percentage );
}
return $data;
}