Employee Option Plans (Details)			1 Months Ended								12 Months Ended
	Jan. 12, 2023	Mar. 12, 2011 shares	Dec. 31, 2022 USD ($) $ / shares shares	Nov. 30, 2020 shares	Feb. 28, 2019	Jan. 31, 2019	Nov. 30, 2018 shares	Dec. 31, 2017	Aug. 31, 2017 USD ($) $ / shares shares	Mar. 31, 2011 ₪ / shares shares	Dec. 31, 2022 USD ($) $ / shares shares	Dec. 31, 2021 USD ($) $ / shares	Dec. 31, 2020 USD ($) $ / shares	Dec. 31, 2022 ILS (₪) shares	Mar. 31, 2022 USD ($) $ / shares shares	Aug. 31, 2021 shares	Aug. 03, 2021 shares	Feb. 06, 2020 shares	Aug. 17, 2017 shares	Nov. 13, 2014 shares
Employee Option Plans (Details) [Line Items]
Number of restricted shares (in Shares) | shares										545,000					21,000	48,378	24,222		10,000
Shares incentive plan (in Shares) | shares		1,200,000
Options expire periods		10 years
Aggregate restricted shares (in Shares) | shares																350,000
Options purchase shares (in Shares) | shares										1,122,782
Exercisable per share | (per share)			$ 81.8							₪ 0.01	$ 81.8				$ 96.7
Description of options vest												As of December 31, 2022, Formula’s chief financial officer holds 31,834 Ordinary shares, of which 16,834 are fully vested.
Total fair value of grant			$ 7,914								$ 7,914			₪ 27,851	$ 232
Total equity-based compensation expense											7,089,000
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			1 year 1 month 17 days	2 years
Number of vested percentage				20.00%
Unrecognized compensation costs			$ 2,885
Compensation Cost											$ 5,550
Weighted average period											1 year 10 months 2 days
Selling, marketing, general and administrative expenses											$ 317,956,000	$ 289,985,000	$ 224,188,000
Unrecognized compensation cost											112
Options Shares (in Shares) | shares			4,028
Purchase Shares (in Shares) | shares			4,028
Formula [Member]
Employee Option Plans (Details) [Line Items]
Number of restricted shares (in Shares) | shares															2,400
Exercisable per share | $ / shares															$ 96.7
Total fair value of grant															$ 232
Unrecognized compensation costs											$ 34,972,000	45,973,000
Matrix [Member]
Employee Option Plans (Details) [Line Items]
Number of restricted shares (in Shares) | shares			375,000								375,000			375,000
Number of vested percentage											40.00%
Unrecognized compensation costs											$ 0	428,000
Maximum [Member]
Employee Option Plans (Details) [Line Items]
Total fair value of grant | ₪														₪ 170,684
EBITDA, percentage				105.00%
EBITDA decreasing, percentage				75.00%
Maximum [Member] | Events After Reporting Period [Member]
Employee Option Plans (Details) [Line Items]
Number of vested percentage	66.67%
Minimum [Member]
Employee Option Plans (Details) [Line Items]
Total fair value of grant			$ 50,054,000								50,054,000
EBITDA, percentage				75.00%
EBITDA decreasing, percentage				105.00%
Minimum [Member] | Events After Reporting Period [Member]
Employee Option Plans (Details) [Line Items]
Number of vested percentage	33.33%
2011 Plan [Member]
Employee Option Plans (Details) [Line Items]
Number of restricted shares (in Shares) | shares				611,771			10,000		10,000
Exercisable per share | $ / shares									$ 37.1
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, 2022, 2021 and 2020 was $21, $52 and $98, respectively. As of December 31, 2022 Formula’s chief operational officer holds 10,000 restricted shares from this grant.		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
Total equity-based compensation expense											$ 973,000	0
Chief Financial Officers [Member]
Employee Option Plans (Details) [Line Items]
Number of restricted shares (in Shares) | shares										10,000										10,000
Matrix [Member]
Employee Option Plans (Details) [Line Items]
Options expire periods											5 years
Description of options vest						Matrix IT’s board of directors approved, following the approval by Matrix IT’s compensation committee, the grant of 1,440,000 options which are exercisable into up to 1,440,000 ordinary shares of Matrix IT of NIS 1 par value each, to 20 senior officers of Matrix IT. 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.
Fair value options, exercise factor											70.00%
Fair value options, expected volatility											24.00%
Matrix [Member] | Maximum [Member]
Employee Option Plans (Details) [Line Items]
Fair value options, risk-free interest rate											(1.60%)
Matrix [Member] | Minimum [Member]
Employee Option Plans (Details) [Line Items]
Fair value options, risk-free interest rate											0.50%
Matrix [Member] | General Assembly [Member]
Employee Option Plans (Details) [Line Items]
Description of options vest					Matrix IT approved, after obtaining the approval of Matrix IT’s compensation committee and Matrix IT’s board of directors the grant of 80,000 options which are exercisable into up to 80,000 ordinary shares of Matrix IT of NIS 1 par value, to the President and Vice Chairman of the Matrix IT 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.
Matrix [Member] | Mr. Moti Gutman [Member]
Employee Option Plans (Details) [Line Items]
Description of options vest								Matrix IT extended its agreement with Revava Management Company Ltd. through which its chief executive officer, Mr. Moti Gutman, provides services to Matrix IT, for five years’ term starting on January 1, 2018. As part of the new agreement in January 2018, Matrix IT 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 IT’s financial statements for each respective year, and subject to certain conditions. In 2022, 51,378 restricted share units (RSU) were vested and exercised. As of December 31, 2022 Mr. Gutman holds 51,378 restricted share units (RSUs) from this grant.
Sapiens [Member]
Employee Option Plans (Details) [Line Items]
Number of restricted shares (in Shares) | shares																		173,005
Total equity-based compensation expense											$ 4,317,000	$ 5,421,000	$ 4,318,000
Employees and directors to purchase shares description											In 2022, 2021 and 2020, Sapiens granted 404,500, 847,000 and 315,000 stock options, respectively, to its employees and directors to purchase its shares.
Weighted average grant date fair values of options (in Dollars per share) | $ / shares											$ 7.22	$ 10.35	$ 7.99
Intrinsic value of options exercised											$ 250,000	$ 8,505,000	$ 11,658,000
Selling, marketing, general and administrative expenses											794	1,130,000
Magic [Member]
Employee Option Plans (Details) [Line Items]
Intrinsic value of options exercised											$ 344,000	$ 628,000	$ 765,000