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Withholding allowances play a crucial role in calculating the amount of federal income tax that is deducted from an employee's paycheck. Specifically, the more allowances an employee claims on their W-4 form, the less federal income tax is withheld from their paycheck. This is because allowances are a way for employees to signal to the employer how many exemptions they qualify for, which in turn affects their tax liability.

When an employee claims more allowances, it indicates that they expect to incur more deductions when they file their tax return, thus reducing the amount of tax that needs to be withheld from their paychecks throughout the year. Conversely, fewer allowances lead to a higher amount of tax being withheld. This mechanism ensures that employees do not end up underpaying their taxes throughout the year, which could lead to a significant tax bill at tax time.

Understanding the relationship between withholding allowances and the federal income tax withheld is essential for employees as it helps them manage their take-home pay effectively and avoid unexpected tax obligations.