Liabilities, Convertible Preferred Stock and Stockholders' (Deficit) Equity - Narrative (Details) - USD ($)				1 Months Ended		3 Months Ended		9 Months Ended		12 Months Ended	39 Months Ended	40 Months Ended
	Dec. 31, 2023	Sep. 29, 2023	Jun. 22, 2023	May 31, 2022	Jul. 31, 2020	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2023	Sep. 30, 2022	Dec. 31, 2016	Sep. 30, 2023	May 31, 2022	Jan. 01, 2023	Jan. 01, 2022
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Warrants to purchase shares (in shares)				694,892								694,892
Offering price of warrant (in dollars per share)				$ 39.9975								$ 39.9975
Exercise price per warrant (in dollars per share)				$ 0.0025								$ 0.0025
Net proceeds from sale of common stock				$ 42,900,000
Placement agent fees and offering costs				$ 2,100,000
Maximum ownership percentage of common stock shares for outstanding warrants to be exercised												4.99%
Ownership percentage for outstanding warrants to purchase shares of common stock to be exercised to certain holders												9.99%
Revised ownership percentage, period to take effect after notice												61 days
Stock-based compensation expense						$ 4,785,000	$ 1,565,000	$ 8,405,000	$ 5,684,000
Options granted (in shares)						1,044,667	50,806	3,867,366	153,686
Stock-based compensation								$ 8,405,000	$ 5,684,000
Maximum
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Maximum ownership percentage of common stock shares for outstanding warrants to be exercised												19.99%
2016 Equity Incentive Plan
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Annual percentage of additional shares										4.00%
Additional number of shares available for issuance													104,560	78,968
Stock options granted to certain members of board of directors, contingent on stockholder approval (in shares)			2,720,033
Expense on contingent awards			$ 0
Common stock available for future issuance (in shares)						293,497		293,497			293,497
2016 Equity Incentive Plan | Restricted Stock Units (RSUs)
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Equity instruments other than options, granted (in shares)					9,128
Equity instruments other than options, vested (in shares)											0
Stock-based compensation expense								$ 0
2018 Equity Inducement Plan
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Additional number of shares available for grant								2,800,000
Options granted (in shares)								3,583,880
Vest period grant date								4 years
Share-based payment award, term								10 years
Spyre 2023 Equity Incentive Plan | Asset Acquisition
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Number of outstanding and unexercised stock options to purchase (in shares)			2,734
Parapyre Option Obligation
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Annual percentage of additional shares			1.00%
Share-based payment award, term		10 years
Fair value of contingent consideration assumed			$ 100,000
Stock-based compensation						$ 2,700,000	$ 0	$ 2,900,000	$ 0
Unamortized expense						$ 2,100,000		$ 2,100,000			$ 2,100,000
Parapyre Option Obligation | Forecast
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Pro-rated estimated fair value of options	$ 3,000,000
2016 Employee Stock Purchase Plan
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Number of shares issued								2,496	6,073
Aggregate cash proceeds from sale of shares									$ 200,000
2016 Employee Stock Purchase Plan | Maximum
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Aggregate cash proceeds from sale of shares								$ 100,000
Common Stock
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Number of shares issued				430,107
Public offering price (in dollars per share)				$ 40.00								$ 40.00