For the married couples when their income is between $183,000 and $193,000 and for the single taxpayers is $116,000 to $131,000.
The IRS severely limits the ability to contribute to a Roth IRA for individuals that are married but file separately. If you do not have income you will not be allowed to contribute to a Roth IRA. If your income is less than $10,000 you cannot contribute up to the limit. Your contribution is reduced. If your earned income for the year is less than the contribution limit (in 2014, $5,500 for those under 50), you can only contribute up to your earned income. Roth IRA Income Limits. You may contribute the full amount to your Roth IRA if your 2015 modified adjusted gross income is below $116,000 for singles ($183,000 for married). You may make partial contributions until your income hits $131,000 ($193,000 for married). If your income is above that, you cannot contribute to a Roth IRA. If you are interested, there is a workaround called the Backdoor Roth IRA if your income is above the limits. Limits on contributions depend on your annual earned income amount and your filing status. If you are married and filing a joint return, you can contribute the annual maximum as long as your modified adjusted gross income (MAGI) amount, for both spouses, is $181,000 or less as of tax year 2014. Above this figure, your contribution limit begins to phase out until you reach a MAGI of $191,000. In 2014, the same income limit for those filing as single or head of household reached $129,000. At $114,000 or less, a full contribution is allowed, while the contribution limit begins to phase out between $114,000 an Roth IRA Income Limits for Single Filers. If you file as single, head of household, or married filing separately (if you did not live with your spouse at any time during the year) your income must be less than $116,000 to contribute up to the limit. If your earned income for the year is less than the contribution limit (in 2014, $5,500 for those under 50), you can only contribute up to your earned income. Roth IRA contribution earning limits. In 2014, the phaseout range of income limits for making a Roth IRA contribution was between $181,000 and $191,000 for jointly filing married couples; and $114,000 to $129,000 for single taxpayers. If your income falls in those ranges for your filing status, the amount you can contribute to a Roth IRA is reduced. For the 2015 tax year, the Roth IRA income contribution ranges are increased a bit. Married couples filing jointly face the phaseouts when their income is between $183,000 and $193,000. The earning range for single taxpayers is $116,000 to $131,000. Contribution Limits vs. Deduction Limits. The maximum you can contribute to a traditional IRA depends on your age. For the 2015 tax year, the limit is five thousand five hundred dollars for those 49 and younger. If you turn 50 or older in 2015, then your upper limit raises to six thousand five hundred dollars.  If you file as married filing joint or as a qualifying widow(er) your income must be less than $183,000 to contribute up to the limit. If your income falls between $183,000 and $193,000 you cannot contribute up to the limit. Your contribution is reduced. If your earned income for the year is less than the contribution limit (in 2014, $5,500 for those under 50), you can only contribute up to your earned income. The IRS recently released its 2015 update to income and contribution limits for Roth IRAs. As detailed below, the contribution limits for a Roth IRA are unchanged for 2015–still $5,500. The catch-up contribution for those 50 or older, which is not indexed for inflation, remains $1,000. The income limits to qualify for a Roth IRA, however, have risen. Here are the details. 2015 Roth IRA Rules-Eligibility, Income, Contribution Limits, and More. Note: The article below refers to the 2015 tax year. Assuming your IRA was opened by Dec. 31, 2015, you have until the tax filing deadline–April 15, 2016–to make a 2015 contribution. The income/contribution limits may increase for the 2016 tax year. Click here for current contribution limits. 
http://www.rothira.com/roth-ira-limits http://www.mydollarplan.com/roth-401k-and-roth-ira-limits/ http://www.ehow.com/info_8085292_maximum-income-roth-ira.html http://www.rothira.com/roth-ira-limits http://www.bankrate.com/finance/taxes/retirement-plan-contribution-limits.aspx http://iracontributionlimits2010.com/2010-ira-income-limits/2010/07/ http://www.rothira.com/roth-ira-limits http://www.doughroller.net/retirement-planning/roth-ira-contribution-limits/ http://www.rothira.com/roth-ira-rules
max income for a roth ira