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Stockholders' Equity (Common Stock Shares Activity) (Details) (USD $)
0 Months Ended 9 Months Ended 12 Months Ended
Nov. 05, 2014
Dec. 31, 2014
Mar. 31, 2014
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Treasury stock, shares, beginning of period   609,625us-gaap_TreasuryStockShares 405,843us-gaap_TreasuryStockShares
Repurchase of common stock 1,000,000us-gaap_TreasuryStockSharesAcquired 1,377,001us-gaap_TreasuryStockSharesAcquired 203,782us-gaap_TreasuryStockSharesAcquired
Treasury stock, shares, end of period   1,986,626us-gaap_TreasuryStockShares 609,625us-gaap_TreasuryStockShares
Repurchase of common stock, price per share $ 25.10us-gaap_TreasuryStockAcquiredAverageCostPerShare    
Common stock, Class A      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Common stock, shares issued, beginning of period   143,962,073us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassAMember
136,457,444us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassAMember
Issuance of common stock   1,315,400us-gaap_StockIssuedDuringPeriodSharesNewIssues
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassAMember
1,047,160us-gaap_StockIssuedDuringPeriodSharesNewIssues
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassAMember
Stock options exercised   3,099,729us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassAMember
5,299,501us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassAMember
Share exchange   1,517,951bah_StockIssuedDuringPeriodSharesShareExchange
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassAMember
1,157,968bah_StockIssuedDuringPeriodSharesShareExchange
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassAMember
Common stock, shares issued, end of period   149,895,153us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassAMember
143,962,073us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassAMember
Non-voting common stock, Class B      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Common stock, shares issued, beginning of period   582,080us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassBMember
1,451,600us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassBMember
Share exchange   (582,080)bah_StockIssuedDuringPeriodSharesShareExchange
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassBMember
(869,520)bah_StockIssuedDuringPeriodSharesShareExchange
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassBMember
Common stock, shares issued, end of period   0us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassBMember
582,080us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassBMember
Restricted common stock, Class C      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Common stock, shares issued, beginning of period   935,871us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassCMember
1,224,319us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassCMember
Share exchange   (935,871)bah_StockIssuedDuringPeriodSharesShareExchange
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassCMember
(288,448)bah_StockIssuedDuringPeriodSharesShareExchange
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassCMember
Common stock, shares issued, end of period   0us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassCMember
935,871us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassCMember
Special voting common stock, Class E      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Common stock, shares issued, beginning of period   4,424,814us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= bah_CommonClassEMember
7,478,522us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= bah_CommonClassEMember
Stock options exercised   (2,573,225)us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
/ us-gaap_StatementClassOfStockAxis
= bah_CommonClassEMember
(3,053,708)us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
/ us-gaap_StatementClassOfStockAxis
= bah_CommonClassEMember
Common stock, shares issued, end of period   1,851,589us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= bah_CommonClassEMember
4,424,814us-gaap_SharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= bah_CommonClassEMember