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Employee Option Plans (Details) - USD ($)
 1 Months Ended 12 Months Ended
Nov. 30, 2020
Feb. 28, 2019
Jan. 31, 2019
Nov. 30, 2018
Dec. 31, 2017
Aug. 31, 2017
Dec. 31, 2021
Dec. 31, 2020
Dec. 31, 2019
Aug. 03, 2021
Feb. 06, 2020
Employee Option Plans (Details) [Line Items]                      
Number of restricted shares (in Shares)                   24,222  
Description of options vest             As of December 31, 2021, Formula’s chief financial officer holds 10,834 shares.        
Total fair value of grant             $ 50,054,000        
Fair value of grant share price per share (in Dollars per share)             $ 81.8        
Total equity-based compensation expense             $ 7,373,000        
EBITDA percentage, description             (i) the EBITDA in the fiscal year immediately following the Specific Year was at least 110.25% of 75% of the Company’s EBITDA in the year preceding the Specific Year, or (ii) in case that the condition in the foregoing clause (i) was not met, then the EBITDA in the second fiscal year following the Specific Year was at least 115.7625% of 75% of the Company’s EBITDA in the year preceding the Specific Year. Accordingly, in case that either clause (i) or (ii) was met for a certain Specific Year, then the vesting with respect to such Specific Year shall be deemed to have been achieved, and those RSUs shall become vested as of the end of the Vesting Period. In the event that neither of the conditions described in clauses (i) or (ii) was met, the portion of RSUs for the applicable Specific Year shall automatically expire and terminate.        
Preceding years             2 years        
Number of vested percentage             20.00%        
Unrecognized compensation costs             $ 45,973,000 $ 51,940,000      
Selling, marketing, general and administrative expenses             289,985,000 224,188,000 $ 200,870,000    
Unrecognized compensation cost             $ 393        
Weighted average period             1 year 3 months 14 days        
Matrix [Member]                      
Employee Option Plans (Details) [Line Items]                      
Description of options vest     Matrix approved, following the approval by Matrix’s compensation committee, the grant of 1,440,000 options which are exercisable into up to 1,440,000 ordinary shares of Matrix of NIS 1 par value each, to 20 senior officers of Matrix. The exercise price of the options was NIS 41.7 at the date of their grant, subject to adjustments, including upon the distribution of dividends. 50% of the options will be vested on January 1, 2021 with the remaining amount vesting in equal parts on January 1, 2022 and 2023.                
Unrecognized compensation costs             $ 1,368,000 428,000      
Fair value options, exercise factor             70.00%        
Fair value options, expected volatility             24.00%        
Options expire periods             5 years        
Sapiens [Member]                      
Employee Option Plans (Details) [Line Items]                      
Number of restricted shares (in Shares)                     173,005
Total equity-based compensation expense             $ 5,421,000 $ 4,318,000 $ 1,125,000    
Unrecognized compensation costs             $ 8,072,000        
Options expire periods             4 years        
Employees and directors to purchase shares description             In 2019, 2020 and 2021, Sapiens granted 155,000, 315,000 and 847,000 stock options, respectively, to its employees and directors to purchase its shares.        
Weighted average grant date fair values of options (in Dollars per share)             $ 10.35 $ 7.99 $ 4.24    
Intrinsic value of options exercised             $ 8,505,000 $ 11,658,000 $ 2,301,000    
Selling, marketing, general and administrative expenses             1,130,000        
Magic [Member]                      
Employee Option Plans (Details) [Line Items]                      
Intrinsic value of options exercised             $ 628,000 765,000 537,000    
Maximum [Member]                      
Employee Option Plans (Details) [Line Items]                      
EBITDA, percentage             105.00%        
EBITDA decreasing, percentage             75.00%        
Maximum [Member] | Matrix [Member]                      
Employee Option Plans (Details) [Line Items]                      
Fair value options, risk-free interest rate             1.60%        
Minimum [Member]                      
Employee Option Plans (Details) [Line Items]                      
EBITDA, percentage             75.00%        
EBITDA decreasing, percentage             105.00%        
Minimum [Member] | Matrix [Member]                      
Employee Option Plans (Details) [Line Items]                      
Fair value options, risk-free interest rate             0.50%        
General Assembly [Member] | Matrix [Member]                      
Employee Option Plans (Details) [Line Items]                      
Description of options vest   Matrix approved, after obtaining the approval of Matrix’s compensation committee and Matrix board of directors the grant of 80,000 options which are exercisable into up to 80,000 ordinary shares of Matrix of NIS 1 par value, to the President and Vice Chairman of the Matrix board. The exercise price of the options was NIS 43.16 at the date of their grant, subject to adjustments, including upon the distribution of dividends. 50% of the options will vest on January 1, 2021, with the remaining amount vesting in equal parts on January 1, 2022 and 2023.                  
2011 Plan [Member]                      
Employee Option Plans (Details) [Line Items]                      
Number of restricted shares (in Shares) 611,771     10,000   10,000          
Description of options vest 66.67% of the RSUs (i.e., 407,847 RSUs) are subject to time-based vesting that shall start as of the grant date and shall end at December 31, 2027, subject to the continued engagement of Formula’s chief executive officer with the Company as of that date (the “Vesting Period”); and up to 33.33% of the RSUs (i.e., 203,924 RSUs as of the date hereof) are subject to performance-based vesting, and shall vest at December 31, 2027 on a pro-rata basis with respect to each fiscal year (starting as of January 1, 2020) during the Vesting Period in which the Target EBITDA (as defined below) is achieved, subject to the continued engagement of Formula’s chief executive officer with the Company. At the end of the vesting period, the number of performances-based RSUs that vests shall be equal to (i) the number of fiscal years in which the Target EBITDA was achieved multiplied by (ii) 25,490.50 RSUs (rounded to the nearest whole number, up to a cap of 203,924 RSUs in total). The “Target EBITDA” in a given fiscal year during the Vesting Period means the Company’s EBITDA in that certain fiscal year (as reflected in the Company’s annual audited consolidated financial statements), excluding the cost attributed to the applicable portion of the RSUs in the Company’s annual audited consolidated financial statements for the applicable fiscal year (as to which the review of performance is made to determine whether one-eighth of the Performance Based RSUs (i.e., 25,490.50 RSUs) shall become vested at the end of the Vesting Period).     These restricted shares vest on an annual basis over a four-year period, commencing on November 19, 2018 and concluding on November 19, 2022, provided that during such time the chief operational officer will continue to serve as (i) an officer of the Company and/or (ii) an officer in one of the directly held affiliates. The total fair value of the grant was calculated based on the Formula share price on the grant date and equaled $382 ($38.2 per share). The total compensation expense the Company recorded in its statement of profit or loss for the years ended December 31, 2019, 2020 and 2021 were $191, $98 and $60, respectively. As of December 31, 2021 Formula’s chief operational officer holds 10,000 restricted shares from this grant, of which 7,500 are fully vested.   These restricted shares vest on a quarterly basis over a three-year period, commencing on August 17, 2017 and concluding on August 17, 2020, provided that during such time the chief financial officer will continue to serve as (i) an officer of the Company and/or (ii) an officer in one of the directly held affiliates, except that if he fails to meet the service condition due to the request of the board of directors of either Formula or any of its directly held affiliates (other than a termination of his provision of services which is based on actions or omissions by him that will constitute “cause” under his grant agreement with Formula), then, the chief financial officer will be deemed to have complied with clauses (i) or (ii) above.          
Total fair value of grant           $ 371,000          
Fair value of grant share price per share (in Dollars per share)           $ 37.1          
Total equity-based compensation expense               $ 21,000 $ 66,000    
Mr. Moti Gutman [Member] | Matrix [Member]                      
Employee Option Plans (Details) [Line Items]                      
Description of options vest         Matrix extended its agreement with Revava Management Company Ltd. through which its chief executive officer, Mr. Moti Gutman, provides services to Matrix, for five years’ term starting on January 1, 2018. As part of the new agreement in January 2018, Matrix awarded Mr. Gutman 256,890 (RSUs), which vest on an annual basis over a five-year period, commencing on January 16, 2018 and concludes on December 31, 2022, but not before the publication of Matrix’s financial statements for each respective year, and subject to certain conditions. In 2021, 51,378 restricted share units (RSU) were vested and exercised. As of December 31, 2021 Mr. Gutman holds 102,756 restricted share units (RSU) from this grant.