Exhibit 5.1

July 13, 2017

KalVista Pharmaceuticals, Inc.

One Kendall Square

Bld 200, Ste 2203

Cambridge, MA 02139

Gentlemen/Ladies:

We deliver this opinion with respect to certain matters in connection with the offering by KalVista Pharmaceuticals, Inc., a Delaware corporation (the “Company”), of the Company’s common stock, par value $0.001 per share (the “Common Stock”), with an aggregate maximum offering price of up to $6 million (the “Placement Shares”), to be issued from time to time pursuant to that certain At-the-Market Sales Agreement (the “Sales Agreement”), dated as of even date herewith, between the Company and BTIG, LLC (“BTIG”). The Placement Shares were registered pursuant to the Registration Statement on Form S-3 (File No. 333-217009) filed by the Company with the Securities and Exchange Commission (the “Commission”) on March 29, 2017 and declared effective on April 28, 2017 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”), the base prospectus dated April 27, 2017 included therein (the “Base Prospectus”), and the related prospectus supplement dated July 13, 2017, filed with the Commission pursuant to Rule 424(b) under the Securities Act (the “Prospectus Supplement” and together with the Base Prospectus, the “Prospectus”). The offering of the Placement Shares is referred to herein as the “Offering.” The Placement Shares are to be sold by the Company as described in the Registration Statement, the Prospectus and the Sales Agreement.

In connection with our opinion expressed below we have examined originals or copies of the Company’s Amended and Restated Certificate of Incorporation, as amended (the “Restated Certificate”) and Bylaws (the “Bylaws” and, together with the Restated Certificate, as each may be amended, modified or restated, the “Charter Documents”), certain corporate proceedings of the Company’s board of directors (the “Board”) and stockholders relating to the Registration Statement, the Charter Documents, and such other agreements, documents, certificates and statements of the Company, its transfer agent and public or government officials, as we have deemed advisable, and have examined such questions of law as we have considered necessary. We have assumed, and express no opinion as to, the genuineness of all signatures on documents submitted to us, the authenticity and completeness of all documents submitted to us as originals, the conformity to originals and completeness of all documents submitted to us as copies, the legal capacity of all persons or entities executing the same, the absence of any undisclosed termination, modification, waiver or amendment to any document reviewed by us, the absence of any other extrinsic agreements or documents that might change or affect the interpretation or terms of documents we have reviewed, and the due authorization, execution and delivery of all such documents where due authorization, execution and delivery are prerequisites to the effectiveness thereof. In giving our opinion, we have also relied upon a good standing certificate regarding the Company issued by the Delaware Secretary of State dated July 13, 2017 and a management certificate addressed to us and dated of even date herewith executed by the Company containing certain factual representations (the “Management Certificate”).

We also have assumed that any certificates or instruments representing the Placement Shares, will be, when issued, properly signed by authorized officers of the Company and delivered to the intended recipients with the intent that the Company be bound thereby. Furthermore, with respect to the Company’s uncertificated capital stock, we assume that issued Common Stock, including any Placement Shares, will not be reissued by the Company in uncertificated form until any previously issued stock certificate representing such issued Common Stock has been surrendered to the Company in accordance with Section 158 of the Delaware General Corporation Law, and that the Company will properly register the transfer of the Common Stock to the purchasers of such Common Stock on the Company’s record of uncertificated securities.

As to matters of fact relevant to this opinion, we have relied solely upon our examination of the documents referred to above and the Management Certificate and have assumed the current accuracy and completeness of the information obtained from the documents referred to above and the representations and warranties made by representatives of the Company to us, including but not limited to those set forth in the Management Certificate. We have made no independent investigation or other attempt to verify the accuracy of any of such information or to determine the existence or non-existence of any other factual matters.

We render this opinion only with respect to, and express no opinion herein concerning the application or effect of the laws of any jurisdiction other than the existing laws of the Delaware General Corporation Law (the “Applicable Laws”). Without limitation, we express no opinion with respect to the federal laws of the United States of America or the securities or “blue sky” laws of any state or any local or regional laws.

In connection with our opinions expressed below, we have assumed that, (i) at or prior to the time of the delivery of any of the Placement Shares, there will not have occurred any change in the law or the facts affecting the validity of the Placement Shares, (ii) at the time of the offer, issuance and sale of any Placement Shares, no stop order suspending the Registration Statement’s effectiveness will have been issued and remain in effect, (iii) no future amendments will be made to the Charter Documents that would be in conflict with or inconsistent with the Company’s right and ability to issue the Placement Shares, (iv) at the time of each offer, issuance and sale of any Placement Shares, the Company will have a sufficient number of authorized and unissued and unreserved shares of the applicable class or series of its capital stock included in (or purchasable upon exercise or conversion of) the Placement Shares so issued and sold (after taking into account all other outstanding securities of the Company which may require the Company to issue shares of such applicable class or series) to be able to issue all such shares, and (v) all purchasers of the Placement Shares will timely pay in full to the Company all amounts they have agreed to pay to purchase such Placement Shares, as approved by the Board or a duly authorized committee thereof, and that the purchase price of any Placement Shares will not be less than the par value thereof. We also have assumed that the issuance and delivery of the Placement Shares subsequent to the date hereof and the compliance by the Company with the terms of such Placement Shares will not violate any applicable law (including, without limitation, any law relating to usury or similar laws) or result in a violation of any provision of any of the Charter Documents or of any instrument or agreement then binding upon the Company or any restriction imposed by any court or governmental body having jurisdiction over the Company.

We express no opinion regarding the effectiveness of any waiver or stay, extension or of unknown future rights. Further, we express no opinion regarding the effect of provisions relating to indemnification, exculpation or contribution to the extent such provisions may be held unenforceable as contrary to federal or state securities laws or public policy.

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The Company has informed us that the Company intends to issue the Placement Shares, from time to time on a delayed or continuous basis. This opinion is limited to the Applicable Laws, including the rules and regulations thereunder, as in effect on the date hereof.

With respect to our opinion expressed below, we have assumed that, upon the issuance of any of the Placement Shares, the total number of shares of Common Stock issued and outstanding and reserved for future issuance will not exceed the total number of shares of Common Stock that the Company is then authorized to issue under its Certificate of Incorporation, as then in effect.

Based upon the foregoing, we are of the opinion that the Placement Shares to be issued and sold by the Company, when issued, sold and delivered in the manner and for the consideration stated in the Registration Statement and the Prospectus and in accordance with the resolutions adopted and to be adopted by the Board or a committee thereof, will be validly issued, fully paid and nonassessable.

We consent to the use of this opinion as an exhibit to the Form 8-K and further consent to all references to us, if any, in the Registration Statement, the Prospectus constituting a part thereof and any amendments or supplements thereto. 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 thereunder.

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This opinion is intended solely for use in connection with the issuance and sale of the Placement Shares subject to the Sales Agreement and is not to be relied upon for any other purpose. In providing this letter, we are opining only as to the specific legal issues expressly set forth above, and no opinion shall be inferred as to any other matter or matters. This opinion is rendered on, and speaks only as of, the date of this letter first written above, is based solely on our understanding of facts in existence as of such date after the aforementioned examination and does not address any potential changes in facts, circumstance or law that may occur after the date of this opinion letter. We assume no obligation to advise you of any fact, circumstance, event or change in the law or the facts that may hereafter be brought to our attention whether or not such occurrence would affect or modify any of the opinions expressed herein.

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