Acurx Pharmaceuticals, Inc. General form of registration statement for all companies including face-amount certificate companies

General form of registration statement for all companies including face-amount certificate companies

ISSUANCE OF EQUITY INTERESTS (Details)

ISSUANCE OF EQUITY INTERESTS (Details)									1 Months Ended	3 Months Ended				9 Months Ended		12 Months Ended
ISSUANCE OF EQUITY INTERESTS (Details)	Oct. 01, 2024 shares	Jan. 02, 2024 shares	Nov. 15, 2023 USD ($) shares	May 18, 2023 USD ($) $ / shares shares	May 16, 2023 USD ($) $ / shares shares	Jul. 27, 2022 USD ($) $ / shares shares	Jul. 25, 2022 USD ($) shares	Jun. 29, 2021 USD ($) $ / shares shares	Jan. 31, 2024 USD ($) shares	Sep. 30, 2024 USD ($) $ / shares shares	Jun. 30, 2024 USD ($)	Mar. 31, 2024 USD ($)	Jun. 30, 2023 USD ($)	Sep. 30, 2024 USD ($) $ / shares shares	Sep. 30, 2023 USD ($)	Dec. 31, 2023 USD ($) $ / shares shares	Dec. 31, 2022 shares	Jun. 23, 2021 shares
Equity
Common stock, Authorized (in shares)										200,000,000				200,000,000		200,000,000	200,000,000	200,000,000
Common stock, Outstanding (in shares)										16,770,378				16,770,378		14,468,229	11,627,609
Shares issued (in shares)		17,869	698,121	601,851	601,851	1,159,211	1,159,211	2,875,000
Purchase price (in dollars per share) \| $ / shares				$ 3	$ 3			$ 6
Cash issuance cost \| $						$ 287,874				$ 51,455	$ 10,601	$ 135,741	$ 456,314		$ 1,990,153
Number of warrants				731,482	731,482	63,018
Warrant exercise price (in dollars per share) \| $ / shares				$ 2.9999	$ 2.9999	$ 3.6
Proceeds from warrant exercises \| $														$ 210,199		$ 2,218,999
Pre-funded Warrant Exercise (in shares)				731,482	731,482	130,769	130,769
Gross proceeds from stock issue \| $			$ 2,600,000	$ 4,000,000	$ 4,000,000	$ 4,200,000	$ 4,200,000	$ 17,300,000
Net proceeds stock issuance \| $				3,500,000	3,500,000	$ 3,700,000
Weighted average aggregate offering price (as a percent)						110.00%
Warrants fair value increase adjustment \| $				$ 2,000,000	$ 2,000,000
Series A warrants
Equity
Number of warrants						1,289,980	1,289,980
Series B warrants
Equity
Number of warrants						1,289,980	1,289,980
Number of warrants exercised																682,769
Proceeds from warrant exercises \| $																$ 2,200,000
Series C warrants
Equity
Number of warrants				1,333,333	1,333,333
Warrant exercise price (in dollars per share) \| $ / shares				$ 3.26	$ 3.26
Series D warrants
Equity
Number of warrants				1,333,333	1,333,333
Warrant exercise price (in dollars per share) \| $ / shares				$ 3.26	$ 3.26
Affiliate Investors
Equity
Shares issued (in shares)						59,211
Purchase price (in dollars per share) \| $ / shares						$ 3.8
Affiliate Investors \| Series A warrants
Equity
Number of warrants						59,211
Warrant exercise price (in dollars per share) \| $ / shares						$ 3.25
Affiliate Investors \| Series B warrants
Equity
Number of warrants						59,211
Warrant exercise price (in dollars per share) \| $ / shares						$ 3.55
Number of warrants exercised									59,211
Proceeds from warrant exercises \| $									$ 200,000
Investor
Equity
Shares issued (in shares)						1,100,000
Purchase price (in dollars per share) \| $ / shares						$ 3.25
Warrant exercise price (in dollars per share) \| $ / shares				$ 0.0001	$ 0.0001	$ 0.0001
Pre-funded Warrant Exercise (in shares)						130,769
Warrant exercise price, exercised (in dollars per share) \| $ / shares						$ 3.2499
Investor \| Series A warrants
Equity
Number of warrants					1,230,769	1,230,769
Investor \| Series B warrants
Equity
Number of warrants					1,230,769	1,230,769
IPO
Equity
Shares issued (in shares)								2,875,000
Purchase price (in dollars per share) \| $ / shares								$ 6
Proceeds from IPO, net of issuance costs \| $								$ 14,800,000
Cash issuance cost \| $								$ 2,400,000
Shares of common stock issued in conversion (in shares)								7,041,208
IPO \| Members' Equity, Class A and Class B
Equity
Convertible conversion ratio								0.5
Converted to common stock (in shares)								14,082,318
IPO \| Series A warrants
Equity
Number of shares called by Warrant								0.5
Number of warrants								1,437,577
Warrant exercise price (in dollars per share) \| $ / shares								$ 2.88
Underwriter option
Equity
Number of warrants								150,000
Warrant exercise price (in dollars per share) \| $ / shares								$ 7.5
Warrants term								4 years 6 months
At the Market Offering
Equity
Shares issued (in shares)	25,000													1,994,069		698,121
Cash issuance cost \| $																$ 222,161
Gross proceeds from stock issue \| $														$ 6,400,000		2,600,000
Net proceeds stock issuance \| $														6,211,210		2,400,638
Aggregate offering price \| $			$ 17,000,000											$ 8,000,000		$ 14,400,000
Percentage on gross offering proceeds			3.00%
Sale of stock price per share \| $ / shares										$ 3.21				$ 3.21		$ 3.76
Subscriptions receivable \| $										$ 46,246				$ 46,246		$ 129,159
Shares sold as receivable (in shares)																34,116
Shares subscribed and unissued (in shares)										25,000				25,000		17,869
At the Market Offering \| Aggregate
Equity
Shares issued (in shares)														2,692,190
Gross proceeds from stock issue \| $														$ 9,000,000
Net proceeds stock issuance \| $														$ 8,600,000
Sale of stock price per share \| $ / shares										$ 3.35				$ 3.35