Your 401(k) contribution has no effect on your ability to contribute to a Roth IRA. You only need to make sure you meet the eligibility requirements for funding a Roth IRA.
Another question arises if you want to contribute to a traditional IRA and take a tax deduction for that contribution. Depending on your income, contributing to your employer's 401(k) plan may affect your ability to take a tax deduction for traditional IRA contributions. It will not affect the amount you are able to contribute (up to an annual $5,500/$6,500 if you’re age 50 or older, for 2018; up to $6,000/$7,000 for 2019).
Factors to Consider
Basically, if you are covered by a 401(k) (or any employer-sponsored plan), your modified adjusted gross income (MAGI) becomes a factor in the deductibility of IRA deposits. For example, In 2018, single taxpayers covered by plans can't take an IRA deduction if their MAGI is $73,000 or over; those making more than $63,000 but less than $73,000 can take a partial deduction. Those making $63,000 or less can take a full deduction – regardless of their 401(k) participation. For 2019, those figures rise by $1,000: no deduction for an MAGI of $74,000 or more; partial deductions for more than $64,000 and less than $74,000 and full deductions for $64,000 or less.
Publication 590-A from the IRS explains the deductibility of IRA contributions; it provides the formula you need to calculate how your 401(k) plan contributions affect your IRA contributions. If you are single, you only have to calculate your own contributions, but if you are married and filing jointly, you must take into consideration whether your spouse contributes to an spouse’s employer plan and any deductible contributions your spouse makes to IRAs, too. Calculate your IRA contributions and your spouse’s contributions separately using the worksheet that is available on the IRS website.
If you complete the worksheet and discover that some or all of your IRA contributions are nondeductible, you may want to take out the amount you overcontributed. There is no additional tax or penalty to remove the excess contribution as long as you do so before you file your taxes for the year in which the contribution was made.
What's more, any investment gain or income you made on the contribution also needs to be added to your gross income for the year and may be subject to a 10% early withdrawal penalty if you are under 59½. For these reasons, it is wise to determine your eligibility for IRA contributions before you make them.
In short, depending on your income, participating in a company 401(k) can limit your ability to deduct contributions to an individual retirement account. If you are what is called an “active participant” in an employer-sponsored plan, or your spouse is, you need to follow a formula to determine whether you can make deductible traditional IRA contributions.