Energy Consumers Relief Act of 2013

Energy Consumers Relief Act of 2013 - Requires the Administrator of the Environmental Protection Agency (EPA), before promulgating a final rule that regulates any aspect of the production, supply, distribution, or use of energy (or that provides for such regulation by state or local governments) and that is estimated by the Administrator or the Director of the Office of Management and Budget (OMB) to impose aggregate costs of more than $1 billion, to submit a report that contains: (1) an estimate of the total costs and benefits of the rule, (2) an estimate of the increases in energy prices that may result from implementation or enforcement of the rule, and (3) a detailed description of the employment effects that may result from implementation or enforcement of the rule.

Requires the Secretary of Energy (DOE): (1) to prepare an independent analysis to determine whether such rule will cause any increase in energy prices for consumers, any impact on fuel diversity of the nation's electricity generation portfolio or on electric reliability, or any adverse effect on energy supply, distribution, or use; and (2) upon making such a determination, to determine whether the rule will cause significant adverse effects to the economy and publish such determination in the Federal Register.

Prohibits the Administrator from promulgating any such final rule if the Secretary determines that such rule will cause significant adverse effects to the economy.

Prohibits the Administrator from using the social cost of carbon in any cost-benefit analysis relating to an energy-related rule estimated to cost more than $1 billion unless and until a federal law is enacted authorizing such use.