Subsequent Events	9 Months Ended	12 Months Ended
Sep. 30, 2013	Dec. 31, 2012
Subsequent Events [Abstract]
Subsequent Events	The Company evaluated all events or transactions after September 30, 2013 through the date the condensed consolidated financial statements were issued. On October 7, 2013, the Company received notice of a complaint filed in the Circuit Court of Montgomery County, Maryland in the matter of LegalLink Inc. vs. Spherix Incorporated. LegalLink, Inc., a Merrill Communications Company alleges that the Company failed to honor their contract regarding services provided by LegalLink, Inc. LegalLink, Inc. alleges that the Company owes them $47,309 for services rendered to the Company, that have gone unpaid. The Company’s legal counsel is reviewing this lawsuit and is assessing the likelihood of an unfavorable outcome at this time. As of September 30, 2013, the past due balance of $47,409 has been included in accounts payable and accrued expenses on the condensed consolidated financial statements. On October 11, 2013, the Company appointed Michael Pollack as its interim Chief Financial Officer. In connection with his appointment, the Company and Mr. Pollack entered into an Indemnification Agreement. On October 15, 2013, the Board approved the Company’s Amended and Restated Bylaws in order to update the Company’s bylaws in various respects. On October 15, 2013, the Board approved the amendment and restatement of the Company’s Certificate of Incorporation, as amended, to, among other things, increase the number of authorized shares from 50,000,000 shares of Common Stock and 5,000,000 shares of Preferred Stock to 200,000,000 shares and 50,000,000 shares respectively. The amendment and restatement of the Company’s Certificate of Incorporation is being submitted for stockholder approval at the Company’s 2013 Annual Stockholder meeting. On October 28, 2013, the Board appointed Alexander Poltorak to the Company’s Board of Directors. In connection with his appointment, the Company and Mr. Poltorak entered into an Indemnification Agreement. On November 6, 2013, the Company sold an aggregate of 304,250 shares of its newly designated Series F Preferred Stock and 48,438 shares of common stock to five accredited investors for gross proceeds to the Company of $2,235,000 pursuant to subscription agreements. The purchase price per share of Common Stock was $6.40 for $1,310,000 of such investment and $6.25 for $925,000 of such investment. No broker was utilized in connection with the sale. In accordance with the requirement of NASDAQ, each share of Series F Preferred Stock shall be entitled to .91 times the vote attributable to the shares of common stock. The Company anticipates correcting the Certificate of Designation; Rights and Preferences of the Series F Preferred Stock shall be entitled to 91% of one vote, subject to the beneficial ownership limitation covering the shares. In connection with the foregoing private placement, the Company agreed to file a “resale” registration statement with the SEC covering all shares of Common Stock and shares of Common Stock underlying the Series F Preferred Stock within 91 days of the final closing date and to maintain the effectiveness of the registration statement until all securities have been sold or are otherwise able to be sold pursuant to Rule 144. The Company has agreed to use its reasonable best efforts to have the registration statement declared effective within 180 days of the final closing. The Company is obligated to pay to investors a fee of one (1%) per month in cash for every thirty day period up to a maximum of six (6%) percent, (i) that the registration statement has not been filed after the required filing date, and (ii) following the required date of effectiveness that the registration statement has not been declared effective; provided, however, that the Company shall not be obligated to pay any such liquidated damages if the Company is unable to fulfill its registration obligations as a result of rules, regulations, positions or releases issued or actions taken by the SEC pursuant to its authority with respect to “Rule 415”, provided the Company registers at such time the maximum number of shares of Common Stock permissible upon consultation with the staff of the SEC. The Company also entered into a Lockup Agreement with certain investors which provides for restrictions on the resale of shares for a period of 180 days from the closing of the Private Placement held by certain investors through December 31, 2014, which in certain circumstances is subject to extension. The Lockup Agreement provides that additional 180 day restrictions shall commence without further action of the Company upon the sale of $15 million or greater gross proceeds of securities and upon a material acquisition.	The Company evaluated all events or transactions after December 31, 2012 through the date the financial statements were issued. Appointment of Interim Chief Executive Officer On February 27, 2013, Harvey J. Kesner, age 55, was appointed interim Chief Executive Officer of Spherix Incorporated (the “Company”). Mr. Kesner currently serves as a member of the Board of Directors of the Company. Nuta Technology Corp. In early 2013 the Company created a new wholly-owned subsidiary, Nuta Technology Corp. (“Nuta”), organized under the laws of the state of Virginia with its principal offices in Tysons Corner, Virginia. Office Lease Agreement In February 2013, the Company entered into a Lease Agreement to lease 837 square feet of office space in Tysons Corner, Virginia. The lease runs from March 1, 2013 through August 31, 2014. Letter of Intent On February 15, 2013, our wholly-owned subsidiary Nuta, entered into a Letter of Intent (the “LOI”) with North South Holdings, Inc. (“North South”), the owner of patents and licenses covering various aspects of wireless communications. Pursuant to the LOI, at closing, Nuta would acquire 100% of the issued and outstanding capital stock of North South in consideration for the issuance of capital stock of the Company equal to 12,000,000 shares of the Company’s common stock. Pursuant to the LOI, Nuta will be capitalized with a minimum of $2,000,000 cash at closing and will have engaged management familiar with commercialization of intellectual property assets. The LOI has certain binding and non-binding obligations, including the acquisition consideration which is not subject to adjustment. However, the transaction is subject to various conditions to closing, including satisfactory completion of due diligence, approval of the Company’s shareholders and definitive documentation. Upon completion Nuta may seek to engage in commercialization activities related to the inventions that are the subject of the patents acquired, although there can be no assurance that such efforts would be successful. There can be no assurance that the transactions contemplated by the LOI will be consummated. Warrant Exchange Agreement On March 6, 2013, the Company, and certain investors that participated in the November 2012 private placement transaction (“Investors”), entered into separate Warrant Exchange Agreements pursuant to which the Investors exchanged common stock purchase warrants acquired in the private placement transaction for shares of the Company’s Series C Convertible Preferred Stock. Each share of Series C Convertible Preferred Stock is convertible into one (1) share of Common Stock at the option of the holder, subject to certain limitations on conversions that would result in the Investors acquiring more than 4.99%/9.99% of the outstanding voting stock of the Company. The Series C Convertible Preferred Stock was established on March 5, 2013 by the filing in the State of Delaware of a Certificate of Designation of Preferences, Rights and Limitations of Series C Convertible Preferred Stock (“Certificate of Designation”). Warrants were issued in November 2012 and were convertible for an aggregate of 483,657 shares of Common Stock. The Warrants were exercisable through November 7, 2017 at an exercise price of $6.53 per share. Pursuant to the Warrant Exchange Agreements, the Investors received in exchange for their warrants an aggregate of 229,337 shares of the Series C Convertible Preferred Stock, convertible into one share of Common Stock for each share of Series C Convertible Preferred Stock. The number of shares of common stock underlying the Series C Convertible Preferred stock is the same number as would have been-issued upon a “cashless exercise” of the exchanged Warrants under the terms of the Warrants based on the one-day volume weighted average price of the Company’s Common Stock on February 28, 2013, which was $12.6439 per share, as reported by Bloomberg. The Company has agreed to register the shares of Common Stock issuable upon conversion of the Series C Convertible Preferred Stock on the same basis as the shares of Common Stock issued in the November 2012 private placement transaction. Currently the Company is not obligated to file any registration statement for the Common Stock, or shares of Common Stock underlying the Warrants, until requested by a majority of the Investors. Rights Agreement Effective January 1, 2013, the Company and Equity Stock Transfer, LLC, as Rights Agent, entered into a Rights Agreement which continues through December 31, 2017. The Rights Agreement provides each Stockholder of record a dividend distribution of one “right” for each outstanding share of Common Stock. Rights become exercisable at the earlier of ten days following: (1) a public announcement that an acquirer has purchased or has the right to acquire 10% or more of our Common Stock, or (2) the commencement of a tender offer which would result in an offeror beneficially owning 10% or more of our outstanding Common Stock. All rights held by an acquirer or offeror expire on the announced acquisition date, and all rights expire at the close of business on December 31, 2017, subject to further extension. Each right entitles a Stockholder to acquire, at a stated purchase price, 1/100 of a share of our preferred stock, which carries voting and dividend rights similar to one share of our Common Stock. Alternatively, a right holder may elect to purchase for the stated price an equivalent number of shares of our Common Stock at a price per share equal to one-half of the average market price for a specified period. In lieu of the stated purchase price, a right holder may elect to acquire one-half of the Common Stock available under the second option. The purchase price of the preferred stock fractional amount is subject to adjustment for certain events as described in the Agreement. At the discretion of a majority of the Board and within a specified time period, we may redeem all of the rights at a price of $0.001 per right. The Board may also amend any provisions of the Agreement prior to exercise. Retention Agreement In January 2013, the Company entered into a Retention Agreement with Mr. Lodder which provides that (i) Mr. Lodder will remain with the Company as an executive officer through June 30, 2013 and receive compensation at the rate previously provided to him and (ii) the Company will pay Mr. Lodder a severance of $233,398 as had been provided under the terms of his Employment Agreement, which was terminated under the terms of his Retention Agreement.

Subsequent Events

9 Months Ended

12 Months Ended

Sep. 30, 2013

Dec. 31, 2012

The Company evaluated all events or transactions after September 30, 2013 through the date the condensed consolidated financial statements were issued.

On October 7, 2013, the Company received notice of a complaint filed in the Circuit Court of Montgomery County, Maryland in the matter of LegalLink Inc. vs. Spherix Incorporated. LegalLink, Inc., a Merrill Communications Company alleges that the Company failed to honor their contract regarding services provided by LegalLink, Inc. LegalLink, Inc. alleges that the Company owes them $47,309 for services rendered to the Company, that have gone unpaid. The Company’s legal counsel is reviewing this lawsuit and is assessing the likelihood of an unfavorable outcome at this time. As of September 30, 2013, the past due balance of $47,409 has been included in accounts payable and accrued expenses on the condensed consolidated financial statements.

On October 11, 2013, the Company appointed Michael Pollack as its interim Chief Financial Officer. In connection with his appointment, the Company and Mr. Pollack entered into an Indemnification Agreement.

On October 15, 2013, the Board approved the Company’s Amended and Restated Bylaws in order to update the Company’s bylaws in various respects.

On October 15, 2013, the Board approved the amendment and restatement of the Company’s Certificate of Incorporation, as amended, to, among other things, increase the number of authorized shares from 50,000,000 shares of Common Stock and 5,000,000 shares of Preferred Stock to 200,000,000 shares and 50,000,000 shares respectively. The amendment and restatement of the Company’s Certificate of Incorporation is being submitted for stockholder approval at the Company’s 2013 Annual Stockholder meeting.

On October 28, 2013, the Board appointed Alexander Poltorak to the Company’s Board of Directors. In connection with his appointment, the Company and Mr. Poltorak entered into an Indemnification Agreement.

On November 6, 2013, the Company sold an aggregate of 304,250 shares of its newly designated Series F Preferred Stock and 48,438 shares of common stock to five accredited investors for gross proceeds to the Company of $2,235,000 pursuant to subscription agreements. The purchase price per share of Common Stock was $6.40 for $1,310,000 of such investment and $6.25 for $925,000 of such investment. No broker was utilized in connection with the sale. In accordance with the requirement of NASDAQ, each share of Series F Preferred Stock shall be entitled to .91 times the vote attributable to the shares of common stock. The Company anticipates correcting the Certificate of Designation; Rights and Preferences of the Series F Preferred Stock shall be entitled to 91% of one vote, subject to the beneficial ownership limitation covering the shares. In connection with the foregoing private placement, the Company agreed to file a “resale” registration statement with the SEC covering all shares of Common Stock and shares of Common Stock underlying the Series F Preferred Stock within 91 days of the final closing date and to maintain the effectiveness of the registration statement until all securities have been sold or are otherwise able to be sold pursuant to Rule 144. The Company has agreed to use its reasonable best efforts to have the registration statement declared effective within 180 days of the final closing.

The Company is obligated to pay to investors a fee of one (1%) per month in cash for every thirty day period up to a maximum of six (6%) percent, (i) that the registration statement has not been filed after the required filing date, and (ii) following the required date of effectiveness that the registration statement has not been declared effective; provided, however, that the Company shall not be obligated to pay any such liquidated damages if the Company is unable to fulfill its registration obligations as a result of rules, regulations, positions or releases issued or actions taken by the SEC pursuant to its authority with respect to “Rule 415”, provided the Company registers at such time the maximum number of shares of Common Stock permissible upon consultation with the staff of the SEC.

The Company also entered into a Lockup Agreement with certain investors which provides for restrictions on the resale of shares for a period of 180 days from the closing of the Private Placement held by certain investors through December 31, 2014, which in certain circumstances is subject to extension. The Lockup Agreement provides that additional 180 day restrictions shall commence without further action of the Company upon the sale of $15 million or greater gross proceeds of securities and upon a material acquisition.

The Company evaluated all events or transactions after December 31, 2012 through the date the financial statements were issued.

Appointment of Interim Chief Executive Officer

On February 27, 2013, Harvey J. Kesner, age 55, was appointed interim Chief Executive Officer of Spherix Incorporated (the “Company”). Mr. Kesner currently serves as a member of the Board of Directors of the Company.

Nuta Technology Corp.

In early 2013 the Company created a new wholly-owned subsidiary, Nuta Technology Corp. (“Nuta”), organized under the laws of the state of Virginia with its principal offices in Tysons Corner, Virginia.

Office Lease Agreement

In February 2013, the Company entered into a Lease Agreement to lease 837 square feet of office space in Tysons Corner, Virginia. The lease runs from March 1, 2013 through August 31, 2014.

Letter of Intent

On February 15, 2013, our wholly-owned subsidiary Nuta, entered into a Letter of Intent (the “LOI”) with North South Holdings, Inc. (“North South”), the owner of patents and licenses covering various aspects of wireless communications. Pursuant to the LOI, at closing, Nuta would acquire 100% of the issued and outstanding capital stock of North South in consideration for the issuance of capital stock of the Company equal to 12,000,000 shares of the Company’s common stock. Pursuant to the LOI, Nuta will be capitalized with a minimum of $2,000,000 cash at closing and will have engaged management familiar with commercialization of intellectual property assets.

The LOI has certain binding and non-binding obligations, including the acquisition consideration which is not subject to adjustment. However, the transaction is subject to various conditions to closing, including satisfactory completion of due diligence, approval of the Company’s shareholders and definitive documentation. Upon completion Nuta may seek to engage in commercialization activities related to the inventions that are the subject of the patents acquired, although there can be no assurance that such efforts would be successful.

There can be no assurance that the transactions contemplated by the LOI will be consummated.

Warrant Exchange Agreement

On March 6, 2013, the Company, and certain investors that participated in the November 2012 private placement transaction (“Investors”), entered into separate Warrant Exchange Agreements pursuant to which the Investors exchanged common stock purchase warrants acquired in the private placement transaction for shares of the Company’s Series C Convertible Preferred Stock. Each share of Series C Convertible Preferred Stock is convertible into one (1) share of Common Stock at the option of the holder, subject to certain limitations on conversions that would result in the Investors acquiring more than 4.99%/9.99% of the outstanding voting stock of the Company. The Series C Convertible Preferred Stock was established on March 5, 2013 by the filing in the State of Delaware of a Certificate of Designation of Preferences, Rights and Limitations of Series C Convertible Preferred Stock (“Certificate of Designation”).

Warrants were issued in November 2012 and were convertible for an aggregate of 483,657 shares of Common Stock. The Warrants were exercisable through November 7, 2017 at an exercise price of $6.53 per share.

Pursuant to the Warrant Exchange Agreements, the Investors received in exchange for their warrants an aggregate of 229,337 shares of the Series C Convertible Preferred Stock, convertible into one share of Common Stock for each share of Series C Convertible Preferred Stock. The number of shares of common stock underlying the Series C Convertible Preferred stock is the same number as would have been-issued upon a “cashless exercise” of the exchanged Warrants under the terms of the Warrants based on the one-day volume weighted average price of the Company’s Common Stock on February 28, 2013, which was $12.6439 per share, as reported by Bloomberg. The Company has agreed to register the shares of Common Stock issuable upon conversion of the Series C Convertible Preferred Stock on the same basis as the shares of Common Stock issued in the November 2012 private placement transaction. Currently the Company is not obligated to file any registration statement for the Common Stock, or shares of Common Stock underlying the Warrants, until requested by a majority of the Investors.

Rights Agreement

Effective January 1, 2013, the Company and Equity Stock Transfer, LLC, as Rights Agent, entered into a Rights Agreement which continues through December 31, 2017. The Rights Agreement provides each Stockholder of record a dividend distribution of one “right” for each outstanding share of Common Stock. Rights become exercisable at the earlier of ten days following: (1) a public announcement that an acquirer has purchased or has the right to acquire 10% or more of our Common Stock, or (2) the commencement of a tender offer which would result in an offeror beneficially owning 10% or more of our outstanding Common Stock. All rights held by an acquirer or offeror expire on the announced acquisition date, and all rights expire at the close of business on December 31, 2017, subject to further extension. Each right entitles a Stockholder to acquire, at a stated purchase price, 1/100 of a share of our preferred stock, which carries voting and dividend rights similar to one share of our Common Stock. Alternatively, a right holder may elect to purchase for the stated price an equivalent number of shares of our Common Stock at a price per share equal to one-half of the average market price for a specified period. In lieu of the stated purchase price, a right holder may elect to acquire one-half of the Common Stock available under the second option. The purchase price of the preferred stock fractional amount is subject to adjustment for certain events as described in the Agreement. At the discretion of a majority of the Board and within a specified time period, we may redeem all of the rights at a price of $0.001 per right. The Board may also amend any provisions of the Agreement prior to exercise.

Retention Agreement

In January 2013, the Company entered into a Retention Agreement with Mr. Lodder which provides that (i) Mr. Lodder will remain with the Company as an executive officer through June 30, 2013 and receive compensation at the rate previously provided to him and (ii) the Company will pay Mr. Lodder a severance of $233,398 as had been provided under the terms of his Employment Agreement, which was terminated under the terms of his Retention Agreement.