Exhibit 5.1

November 4, 2014

Capnia, Inc.

3 Twin Dolphin Drive, Suite 160

Redwood City, CA 94065

Ladies and Gentlemen:

This opinion is furnished to you in connection with the Registration Statement on Form S-1 (Registration No. 333-196635), as amended (the “Registration Statement”), filed by Capnia, Inc. (the “Company”) with the Securities and Exchange Commission in connection with the registration under the Securities Act of 1933, as amended, of an aggregate of 1,550,000 units (the “Firm Units”) of the Company’s securities, and, at the election of the Representative, the equivalent of up to 232,500 additional units (the “Option Units”) of the Company’s securities (the Firm Units and the Option Units that the Underwriters elect to purchase pursuant to Section 2 hereof are herein collectively called the “Units”). Each Unit consists of one share of the Company’s common stock, par value $0.001 per share (the “Common Stock”), one series A warrant (each, a “Series A Warrant” and, collectively, the “Series A Warrants”) and one series B warrant (each, a “Series B Warrant” and, collectively, the “Series B Warrants” and collectively with the Series A Warrants, each a “Warrant” and collectively the “Warrants”). Each Option Unit shall not be sold to the underwriters as a unit, but shall instead be sold in its separate components, in whole or in part, which are one share of Common Stock (each, an “Option Share” and, collectively, the “Option Shares”), one Series A Warrant, and one Series B Warrant (collectively, and together with the Series A Warrants subject to the underwriters’ over-allotment option, the “Option Warrants”). Each Series A Warrant entitles the holder to purchase one share of Common Stock (as more fully described in Section 2 hereof) and each Series B Warrant entitles the holder to purchase one share of Common Stock (as more fully described in Section 2 hereof). The Units, the shares of Common Stock underlying the Units (the “Shares”), the Series A Warrants, the Series B Warrants, and the shares of Common Stock issuable upon exercise of the Series A Warrants and the Series B Warrants (the “Warrant Shares”) are hereinafter referred to collectively as the “Securities.” We understand that the Units are to be sold to the underwriters for resale to the public as described in the Registration Statement and pursuant to an underwriting agreement, substantially in the form to be filed as an exhibit to the Registration Statement, to be entered into by and among the Company and the several underwriters (the “Underwriting Agreement”).

We are acting as counsel for the Company in connection with the sale of the Units and the registration of Common Stock and Warrants by the Company. In such capacity, we have examined originals or copies, certified or otherwise identified to our satisfaction, of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary for the purposes of rendering this opinion. In our examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity with the originals of all documents submitted to us as copies, the authenticity of the originals of such documents and the legal competence of all signatories to such documents.

Based on the foregoing and in reliance thereon and subject to the assumptions, qualifications and limitations set forth herein, we are of the opinion that:

(i)    the Securities have been duly authorized for issuance by all necessary corporate action by the Company;

(ii)    the Units, including the Option Units, and the shares of Common Stock underlying such Units, when issued and sold by the Company in accordance with and in the manner described in the Registration Statement, will be validly issued, fully paid and non-assessable;

(iii)    each Warrant, including the Option Warrants, when issued and sold by the Company in accordance with the Underwriting Agreement, will be validly issued and will constitute a valid and binding agreement of the Company enforceable against the Company in accordance with its terms, subject to applicable bankruptcy, insolvency and similar laws affecting creditors’ rights generally and equitable principles of general applicability;

(iv)    the Warrant Shares (including the Warrant Shares underlying the Option Warrants), when issued and sold by the Company in accordance with the Warrants, will be validly issued, fully paid and non-assessable;

(v)    the Representative’s Warrant, when issued and sold by the Company in accordance with the Underwriting Agreement, will be validly issued and will constitute a valid and binding agreement of the Company enforceable against the Company in accordance with its terms, subject to applicable bankruptcy, insolvency and similar laws affecting creditors’ rights generally and equitable principles of general applicability; and

(vi)    the Representative’s Warrant Shares, when issued and sold by the Company in accordance with the Representative’s Warrant, will be validly issued, fully paid, and non-assessable.

We are members of the Bar of the State of New York and this opinion is limited solely to the federal laws of the United States of America, the General Corporation Law of the State of Delaware (including the statutory provisions and all applicable judicial decisions interpreting those laws), and, as to the Warrants constituting valid and legally binding obligations of the Company, solely to the laws of the State of New York.

November 4, 2014

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We consent to the use of this opinion as an exhibit to the Registration Statement, and we consent to the reference of our name under the caption “Legal Matters” in the prospectus forming part of the Registration Statement.