Exhibit 5.1

Client: 67293-00257

February 16, 2018

Capital One Financial Corporation

1680 Capital One Drive

McLean, Virginia 22102

Re: Capital One Financial Corporation

Public Offering of Notes

Ladies and Gentlemen:

We have acted as counsel to Capital One Financial Corporation, a Delaware corporation (the “Company”) in connection with: (i) the preparation and filing with the Securities and Exchange Commission (the “Commission”) of a Registration Statement on Form S-3, file no. 333-203125 (the “Registration Statement”), under the Securities Act of 1933, as amended (the “Securities Act”); (ii) the prospectus included therein; (iii) the prospectus supplement, dated February 13, 2018, filed with the Commission on February 13, 2018 pursuant to Rule 424(b) of the Securities Act (“the Prospectus Supplement”); and (iv) the offering by the Company pursuant to the Prospectus Supplement of $250,000,000 aggregate principal amount of the Company’s Floating Rate Senior Notes due 2021 (the “Notes”).

The Notes have been issued pursuant to the Indenture dated as of November 1, 1996 between the Company and The Bank of New York Mellon Trust Company, N.A., formerly known as The Bank of New York Trust Company, N.A. (as successor to Harris Trust and Savings Bank), as trustee.

In arriving at the opinions expressed below, we have examined originals, or copies certified or otherwise identified to our satisfaction as being true and complete copies of the originals, of the Indenture, the Notes, the Officer’s Certificate dated February 16, 2018 setting forth the terms of the Notes, and such other documents, corporate records, certificates of officers of the Company and of public officials and other instruments as we have deemed necessary or advisable to enable us to render these opinions. In our examination, we have assumed, without independent investigation, the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies. As to any facts material to these opinions, we have relied to the extent we deemed appropriate and without independent investigation upon statements and representations of officers and other representatives of the Company and others.

Based upon the foregoing, and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that the Notes are legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms.

Capital One Financial Corporation

February 16, 2018

Page 2

The opinion expressed above is subject to the following additional exceptions, qualifications, limitations and assumptions:

A. We render no opinion herein as to matters involving the laws of any jurisdiction other than the State of New York and to the extent relevant for our opinions herein, the Delaware General Corporation Law. This opinion is limited to the effect of the current state of the laws of the State of New York and the Delaware General Corporation Law and New York Business Corporation Law and the facts as they currently exist. We assume no obligation to revise or supplement this opinion in the event of future changes in such laws or the interpretations thereof or such facts.

B. The opinion above is subject to (i) the effect of any bankruptcy, insolvency, reorganization, moratorium, arrangement or similar laws affecting the rights and remedies of creditors’ generally, including without limitation the effect of statutory or other laws regarding fraudulent transfers or preferential transfers, and (ii) general principles of equity, including without limitation concepts of materiality, reasonableness, good faith and fair dealing and the possible unavailability of specific performance, injunctive relief or other equitable remedies regardless of whether enforceability is considered in a proceeding in equity or at law.

C. We express no opinion regarding the effectiveness of (i) any waiver of stay, extension or usury laws or of unknown future rights, (ii) provisions relating to indemnification, exculpation or contribution, to the extent such provisions may be held unenforceable as contrary to public policy or federal or state securities laws, (iii) any purported fraudulent transfer “savings” clause (iv) any provision waiving the right to object to venue in any court; or (v) any agreement to submit to the jurisdiction of any Federal court; (vi) any waiver of the right to jury trial.

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Validity of the Securities” in the Registration Statement, and under the caption “Validity of the Notes” in the Prospectus Supplement. In giving these consents, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Gibson, Dunn & Crutcher LLP