Exhibit 32.1

Certification of Chief Executive Officer and Chief Financial Officer

Pursuant to

18 U.S.C. Section 1350,

as adopted pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

The undersigned, the Chief Executive Officer of Extra Space Storage Inc. (the “Company”), hereby certifies to his knowledge on the date hereof, pursuant to 18 U.S.C. 1350(a), as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that the Quarterly Report on Form 10-Q for the quarter ended March 31, 2015 (the “Form 10-Q”), filed concurrently herewith by the Company, fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended, and that the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.

The undersigned, the Chief Financial Officer of Extra Space Storage Inc. (the “Company”), hereby certifies to his knowledge on the date hereof, pursuant to 18 U.S.C. 1350(a), as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that the Quarterly Report on Form 10-Q for the quarter ended March 31, 2015 (the “Form 10-Q”), filed concurrently herewith by the Company, fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended, and that the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.