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Summary of Significant Accounting Policies - Reconciliation of Numerators and Denominators used in Computing Basic and Diluted Net Income Per Share (Detail) - USD ($)
 3 Months Ended 9 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2024
Sep. 30, 2023
Accounting Policies [Abstract]        
Net income (loss) attributable to Odyssey Marine Exploration, Inc. $ 18,688,236 $ (3,813,285) $ 20,659,157 $ 13,562,793
Numerator:        
Basic net income (loss) available to stockholders 18,688,236 (3,813,285) 20,659,157 13,562,793
Income (loss) on equity method investment 746,505 0 (256,062) 0
Fair value change inof debt instruments (5,285,472) 0 (5,528,725) (214,339)
Fair value change of warrants (10,798,965) 0 (17,394,715) (3,398,976)
Fair value change of convertible debt (6,279) 0 (360,690) 0
Diluted net income (loss) available to stockholders $ 3,344,025 $ (3,813,285) $ (2,881,035) $ 9,949,478
Denominator:        
Weighted average common shares outstanding - Basic 20,665,783 20,025,067 20,524,779 19,871,381
Dilutive effect of options 24,862 0 0 5,236
Dilutive effect of restricted stock awards 3,871,880 0 3,871,880 174,754
Dilutive effect of warrants 519,690 0 1,386,386 91,459
Dilutive effect of convertible instruments 137,043 0 131,488 1,394,132
Weighted average common shares outstanding - Diluted 25,219,258 20,025,067 25,914,533 21,536,962
Net income (loss) per share:        
Basic $ 0.9 $ (0.19) $ 1.01 $ 0.68
Diluted $ 0.13 $ (0.19) $ (0.11) $ 0.46