There's plenty of number floating around various source, one at random claims US$263,000[1] in the US and AU$812,000 in Australia[also 1]. Of course, it depends how much you spend (private school or public, $400 shoes or $40). A single parent on welfare in Australia will spend substantially less than a couple who have a combined income of one million. Also the single parent on welfare gets benefits like discounted healthcare (free primary care) and discounted public transport.
1. http://www.news.com.au/finance/money/costs/cost-of-raising-c...