Your ability to directly fund a Roth IRA is dependent on your Federal Income Tax filing status and the amount of your income. There is a “backdoor Roth” strategy that could still be pursued as discussed in another question.
There is a maximum dollar amount you can deposit each tax year to an IRA. It may take more than one tax year’s contribution to have enough money in the Roth equal to the amount needed for an Emergency Fund.
The Roth IRA should NOT be part of your strategy of saving for retirement. The Roth contribution is money that would specifically go towards your Emergency Fund; and you would not otherwise have funded the Roth but for your need to have an Emergency Fund.
Withdrawals from a Roth IRA for emergencies benefit from favorable IRS rules that dictate the order in which money is considered withdrawn when determining if a withdrawal is taxable: first, from regular, annual contributions; second, from amounts contributed to the Roth through conversion; and last, earnings. (Be forewarned: the order of withdrawals for taxation purposes from other IRAs is very different from those of a Roth.).
Emergency Funds should be restricted to the amount you deem appropriate as reserves in an emergency. This may be as 3-6 months living expenses. Don’t keep any more than is necessary because such an account is normally invested very conservatively. Consequently, the amount of earnings can be relatively little. You need your money working hard for you whenever possible!
If you are forced to tap into your Roth for an emergency, try not to withdraw the earnings. If you do withdraw the earnings, they will only be tax-free and penalty free if withdrawn after age 59 ½ AND after the fifth year of the Roth account’s existence.
You ask, “If there might be so little earnings as you suggest, why go to all the trouble?”
Once you have fully funded your Emergency Fund, your savings strategies might argue for continuing to fund the Roth. Account balances in excess of your “emergency reserves” can be invested less conservatively—and those earnings could longer-term be tax-free!
Developing good habits makes it easier to achieve financial success.