| Document and Entity Information | Jul. 14, 2023 |
| Document Information [Line Items] | |
| Document Type | 8-K |
| Document Period End Date | Jul. 14, 2023 |
| Entity Registrant Name | ALPHA HEALTHCARE ACQUISITION CORP III |
| Entity Incorporation, State or Country Code | DE |
| Entity File Number | 001-40228 |
| Entity Tax Identification Number | 86-1645738 |
| Entity Address, Address Line One | 2403 Sidney Street |
| Entity Address, Address Line Two | Suite 300 |
| Entity Address, City or Town | Pittsburgh |
| Entity Address, State or Province | PA |
| Entity Address, Postal Zip Code | 15203 |
| City Area Code | 919 |
| Local Phone Number | 313-9633 |
| Entity Information, Former Legal or Registered Name | Alpha Healthcare Acquisition Corp. III |
| Written Communications | false |
| Soliciting Material | false |
| Pre-commencement Tender Offer | false |
| Pre-commencement Issuer Tender Offer | false |
| Entity Emerging Growth Company | true |
| Entity Ex Transition Period | false |
| Current Fiscal Year End Date | --12-31 |
| Amendment Flag | false |
| Entity Central Index Key | 0001842939 |
| Former Address [Member] | |
| Document Information [Line Items] | |
| Entity Address, Address Line One | 1177 Avenue of the Americas |
| Entity Address, Address Line Two | 5th Floor |
| Entity Address, City or Town | New York |
| Entity Address, State or Province | NY |
| Entity Address, Postal Zip Code | 10036 |
| Common Stock [Member] | |
| Document Information [Line Items] | |
| Title of 12(b) Security | Common Stock, par value $0.0001 per share |
| Trading Symbol | CTCX |
| Security Exchange Name | NASDAQ |
| Warrant [Member] | |
| Document Information [Line Items] | |
| Title of 12(b) Security | Redeemable Warrants, each whole warrant exercisable for one share of Common Stock at an exercise price of $11.50 |
| Trading Symbol | CTCXW |
| Security Exchange Name | NASDAQ |
