Ira contribution limits: When I search for this, I am given a table that reads "partial deduction", but nothing says what the amount is.

Only contributions to a traditional IRA can be deducted on your return.  For 2018 the most that can be contributed to a traditional IRA is the smaller of:

• $5,500 ($6,500 if you are age 50 or older); or
• your taxable compensation.

In 2019, Traditional and Roth IRA contribution limits will go up by $500 to $6,000 in 2019. The age 50 catch up limit is fixed by law at $1,000 in all years.

Even though you are covered by a retirement plan, you can still contribute to a traditional IRA and get a deduction --  it just may be reduced.

If you are--

Single, and your modified adjusted gross income is:

• $61,000 or less - You get the full deduction
• more than $618,000 but less than 71,000 - partial deduction
• $71,000 or more - no deduction

Married filing joint return, and your modified adjusted gross income is:

• $98,000 or less  - You get the full deduction
• more than $98,000 but less than $118,000 - partial deduction
• $118,000 or more - no deduction

Married filing separately*, and your modified adjusted gross income is:

• less than $10,000 - partial deduction
• $10,000 or more - no deduction

[NOTE:  There is no impact on Roth IRA contributions if you are covered by an employer retirement plan.  These contributions, however, are not deductible on your return.]

For 2019, if you are covered by a retirement plan at work, your deduction for contributions to a traditional IRA is reduced (phased out) if your modified AGI is:

• More than $103,000 but less than $123,000 for a married couple filing a joint return or a qualifying widow(er),

• More than $64,000 but less than $74,000 for a single individual or head of household, or

• Less than $10,000 for a married individual filing a separate return. Modified AGI

 To calculate your reduced IRA deduction, see page 15 of IRS Publication 590-A - Contributions to Individual Retirement Arrangements (IRAs)

For more details on IRAs, please see the following IRS Publications:

• Publication 590-A - Contributions to Individual Retirement Arrangements (IRAs)
• Publication 590-B - Distributions from Individual Retirement Arrangements (IRAs)

This still did not answer my question. I can't enter "partial deduction" into my calculator to see how much I can deduct.

In my original answer I've attached the IRS worksheet, Figuring Your Reduced IRA Deduction for 2018.  You can open and print the form to calculate your deduction.
I hope this will answer your question.