Marginal tax rate
Marginal tax rate is the tax rate on a change in income (i.e. change in tax/change in income). To emphasize the "change" calculation, the marginal rate is often described as the tax rate on the "next dollar" or "last dollar" of income.^{[1]} ^{[2]} ^{[3]} ^{[4]} ^{[5]} ^{[6]} However, due to the way the tax code is written (particularly the requirement to use the tax tables, but for other aspects as well), actual tax rates on a single dollar change can be misleading. For useful numbers, the marginal tax rate is often either calculated on a larger change in income, or by using an approximate form of the tax code.
The marginal tax rate is often the same as the individual's tax bracket, but not always.^{[note 1]}^{[note 2]}
A marginal tax rate is not the average (a.k.a. "effective") tax rate paid on one's entire income.^{[7]}
Marginal tax rates are useful in many contexts for making decisions, because they describe the effect of a particular change. While the average tax rate is interesting to know, it doesn't help in making decisions the same way the marginal tax rate can.
Contents
Calculation
Assuming that your marginal tax rate is equal to your tax bracket, calculated using your taxable income (Adjusted Gross Income minus deductions), is often correct. However, due to the complexity of the tax code, the actual marginal rate can be much different. Income can also phase out benefits and phase in additional taxes. For a single filer with $10K long term capital gains (LTCG), if nominally in the 12% bracket but an additional dollar of ordinary income pushes a dollar of LTCG from its 0% bracket to its 15% bracket, the marginal rate on that ordinary income is 27% as shown below. The 27% is the sum of 12% on the ordinary income dollar, plus the 15% on the LTCG dollar.
For visual learners, charts such as the one above may be generated for individual households using the personal finance toolbox Excel spreadsheet.^{[8]}, which handles most common tax situations.
Example
A single taxpayer earns $75,000 gross income. After taking the federal standard deduction of $12,200 and deducting another $10,000 contribution to a 401(k), their taxable income is $52,800, putting them in the 22% federal tax bracket. Assuming no phaseouts, their marginal tax rate is 22%, meaning each additional dollar earned results in an additional 22 cents of federal income tax. The total federal income tax due for this individual is $7,474.50 ($970 in the 10% bracket, $3,573 in the 12% bracket, and $2,931.50 in the 22% bracket; see: Tax bracket), for an "average" tax rate of only 9.966% relative to gross income.
State taxes
Your state income tax rate adds to your federal income tax rate. For example, if your federal tax bracket is 24%, your state tax bracket is 8%, you aren't affected by credits, phaseouts, etc., and can't deduct the additional state tax, an extra $1 of income would cause you to pay 8 cents in state tax and 24 cents in federal tax, so your marginal rate is 32%. If you can deduct the additional state tax, the 8 cents in state taxes mean that you pay federal tax on only 92 additional cents, which is 22.08 cents of federal tax (22.08% = 92 cents * 24%) and a marginal rate of 30.08% = (22.08% + 8%).
Social Security benefits
Taxation of Social Security benefits causes many moderateincome retirees to be subject to a much higher marginal tax rate than their tax bracket. If you are in the range in which Social Security becomes taxable, each additional $1 of income causes an extra 50 or 85 cents of Social Security to be taxable at the same tax rate, until 85% of the whole benefit is taxable. If you are in the 12% bracket and each $1 causes an extra 85 cents to be taxable, that extra $1 of income increases your taxable income by $1.85, with 22.2 cents due in tax giving you a marginal tax rate of 22.2%. If you are in the 22% bracket and each $1 causes 85 cents to be taxable, your marginal tax rate is 40.7%. This phasein of taxation can cause a "hump" in marginal rate over an income range, above which the marginal rate drops back down once the maximum 85% of Social Security benefits are taxable. Retirees near this range may choose to alter their tax strategy, to try to either fall just before the range, or far above it.
Section 199A deductions
The 2018 Tax Cuts and Jobs Act allows certain types of businesses to deduct 20% of certain types of income, called Qualified Business Income (QBI). Every $1 of QBI causes only 80 cents of additional taxable income. So, if you are in the 24% tax bracket, it results in 19.2 cents of additional tax, and your marginal federal tax rate is 19.2%. For a "Specified Service Trade or Business" subject to the phaseouts of the Section 199A deduction ($160,700$210,700 single and $321,400$421,400 married filing jointly, as of 2019), the marginal tax rate gets more complicated and varies over the phaseout range; see the discussion page for an analysis. Maximum federal marginal tax rates in the phaseout range can be 66.2% or higher.
Child Tax Credit phaseout
The 2018 Tax Cuts and Jobs Act offers a tax credit of $2,000 per qualifying child, with phaseout of $50 credit reduction for every $1,000 above the limits of $200,000 Modified Adjusted Gross Income for single filers and $400,000 MAGI for married filers. Each additional dollar of income over these limits reduces the credit by 5 cents ($50/$1,000), raising the marginal tax rate by 5% until the credit is phased out completely, over a range of $40,000 per child.
Student loan interest deduction phaseout
Qualifying student loan interest is capped at $2,500 per return for either single or married joint filers (married separate filers can't deduct student loan interest). The phaseout for this deduction is between $65,000$80,000 Adjusted Gross Income for single filers and $135,000$165,000 for married joint filers. Both of these phaseouts are in the 22% bracket. For single filers, each additional dollar of income causes ~16.67 cents ($2,500/$15,000) of interest to become nondeductible, generating ~3.67 cents (~16.67 * 22%) of addition tax, so the marginal tax rate is increased by ~3.67%. For married joint filers, each additional dollar of income causes ~8.33 cents ($2,500/$30,000) of interest to become nondeductible, generating ~1.83 cents (~8.33 * 22%) of addition tax, so the marginal rate is increased by ~1.83%. If the taxpayer paid less than $2,500 in qualifying student loan interest, the marginal rate increase would be proportionally less.
Longterm capital gains and qualified dividends
Longterm capital gains and qualified dividends are taxed at a reduced rate by the IRS: either 0%, 15%, or 20% depending on income. Additionally, the IRS assesses the Net Investment Income Tax (NIIT) on the lesser of investment income and MAGI over $200,000 for single filers or $250,000 for married joint filers. For high earners this can result in a federal marginal rate on longterm capital gains and qualified dividends of up to 23.8%.
Payroll taxes
The IRS assesses Payroll Taxes (also called FICA Taxes) on earned income (wages). The tax has three components:
 Social Security tax on individual wages up to the Social Security Wage Base ($132,900 as of 2019): 6.2% paid by the employee and 6.2% paid by the employer
 Medicare tax on all individual wages: 1.45% paid by the employee and 1.45% paid by the employer
 Additional Medicare Tax on wages in excess of $200,000 for single taxpayers and $250,000 for married couples filing jointly: 0.9% paid by the employee
Payroll taxes increase one's marginal tax rate on earned income above the level of just income tax. Most sources do not include payroll taxes when discussing marginal tax rates. The reason is that the most common use of marginal tax rates is making investment decisions, either calculating aftertax rates of return or deciding between Traditional and Roth contributions. For both of these purposes, payroll taxes do not come into play, because payroll taxes are not assessed against investment income, and Traditional contributions are not payroll taxdeductible. However, for other purposes (see below, using the marginal rate), payroll taxes would need to be included.
Selfemployed payroll taxes
Selfemployed taxpayers (either sole proprietors or incorporated) are required to pay both halves of payroll taxes. Sole proprietors pay payroll tax on IRS Schedule SE (Form 1040). Schedule SE scales down selfemployed business income by a factor of 92.35%, so that the employer half of payroll tax is taxdeductible, the same as it would be for a corporation. Therefore, the marginal tax rate on selfemployment income is not exactly the same as the payroll tax rates.
For income less than the Social Security Wage Base (SSWB), each additional dollar of business income results in ~14.13 cents (92.35% * 15.3%) of payroll tax, of which half (~7.06 cents) is deductible against income tax. If the taxpayer has a marginal income tax rate of 22%, the total marginal tax rate on business income would be ~34.57% ((1  7.06%)*22% + 14.13%), significantly less than the 37.3% (22% + 15.3%) which would result if employer payroll taxes were not deductible.
For income above the the SSWB, each additional dollar of business income results in ~2.68 cents (92.35% * 2.9%) of payroll tax, of which half (~1.34 cents) is deductible against income tax. If the taxpayer has a marginal income tax rate of 22%, the total marginal tax rate on business income would be ~24.38% ((1  1.34%)*22% + 2.68%).
If the additional business income were also deductible under Section 199A, then the marginal tax rates would be ~30.18% ((1  7.06%  20%)*22% + 14.13%) and ~19.98% ((1  1.34%  20%)*22% + 2.68%) respectively.
Special cases
Marginal rate less than zero
A negative marginal tax rate means that the government, in effect, subsidizes additional income, rather than taxes it. For example, with a marginal tax rate of 10%, an additional $100 of income results in a decrease of tax liability by $10. Negative marginal federal income tax rates commonly occur in the United States due to the Earned Income Tax Credit (EITC). The EITC is a refundable credit, meaning it can lower an individual's total tax liability below zero, so they can receive an overall refund for the tax year. If one includes FICA taxes, the marginal (federal income plus FICA) tax rates do not go negative.
Marginal rate of zero
A tax with a marginal rate of zero is a fixedamount tax, such as a tax of $100 on every house rather than a percentage of the value of the house.
Flat rate tax
A flat rate tax has a constant marginal tax rate. Sales taxes and property taxes are normally flat, a fixed percentage of the value. Income taxes in some states are almost flat; typically, there is a fixed amount (such as a standard deduction) which is exempt from tax, and everyone making more than that fixed amount pays the same marginal tax rate, so the average tax rate varies.
Marginal rate greater than 100%
A marginal tax rate of greater than 100% means that a taxpayer's total tax liability increases faster than their income, meaning they take home less money the more they earn. Generally, tax codes are written to try to avoid situations where marginal tax rates are greater than 100%, due to the obvious disincentive for work and economic productivity it would create. Nonetheless, tax analysts sometimes find cases under current or proposed tax laws where a combination of additional tax, loss of subsides, and other factors combine to create effective marginal tax rates greater than 100%.^{[9]} When they do occur, most often such rates are for rare situations and over only a small range of income.
Abrupt changes in tax liability with income can produce "spikes" in marginal tax rates far greater than 100%, see below.
Spikes in marginal tax rate
When a tax kicks in or a benefit is lost abruptly, as opposed to being phased in or out gradually, the calculated marginal tax rate on the income that causes the change can be very large. For example, in a case analyzed in the Traditional versus Roth article, an additional $200 Saver's credit is earned for a $12,500 retirement savings contribution. The last dollar that gains the additional credit has a calculated marginal savings rate of 20,000% ($200/$1), and if calculated using the last cent the marginal savings rate is 2,000,000% ($200/$0.01). These numbers are correct, but are not as useful for making decisions because they only apply to a tiny amount of savings or income. In this case, it would be more useful to calculate the rate over the entire contribution necessary to gain the credit; that rate is 1.6% ($200/$12,500) in addition to other components of the overall rate. This figure is a better reflection of the value in making that contribution. For those very close to a spike in a marginal rate, even the rate over the entire change may be high; if only $500 savings were necessary to earn a $200 credit, the savings rate would be the rate on the $500 plus 40% ($200/$500).
Multiple rates and combined rates
Note that you may have a different marginal tax rate on different types of income and savings. Consider the State Tax example above, with a marginal rate on ordinary income of 32%. The marginal tax rate on Treasury bonds (which are fully taxed by federal, not taxed by the state) is only 24%. The marginal tax rate on capital gains is 15% federal but probably fully taxed by the state at 8%. If additional state tax is deductible, then the marginal rate on capital gains will be 21.08% (15% + 8%  (24% x 8%) for deduction of the state tax), otherwise 23%. For either single or married joint filers, Section 199A Qualified Business Income (QBI) will have a different marginal rate than nonQBI, and if the Section 199A deduction is being phased out, the rates will be variable. An investor with a small business and a reasonably simple portfolio could have at least eight separate marginal rates for different types of income and savings:
 Earned income, subject to income tax, phaseouts, and payroll tax (including the Additional Medicare Tax)
 Investment income, subject to income tax, phaseouts, and Net Investment Income Tax (NIIT)
 Longterm capital gains and qualified dividends, subject to reduced income tax rates, phaseouts, and NIIT
 Section 199A Qualified Business Income (QBI), subject to income tax and phaseouts but offering the QBI deduction
 Social Security income, taxed as income at a rate determined by the Social Security Benefits Worksheet in IRS Form 1040 Instructions
 Treasury bond income, subject to federal income tax and phaseouts, but exempt from state income tax
 Municipal bond income, taxfree, except for the phasein of Social Security benefits
 Marginal savings rate for taxdeferred contributions may be different from the marginal tax rate on income due to the Saver's Credit
Combining this effect with Social Security benefits can produce even higher rates. For a single person age 65, with $12,000 in qualified dividends, $27,000 from social security, and $24,000 in traditional IRA distributions, the marginal rate for more^{[8]}
 traditional IRA distributions is 49.95%
 qualified dividends is 37.95%
 social security income is 11.475%
Not all high marginal rates are unfavorable. E.g., due to the saver's and earned income credits, marginal savings rates can be much higher than the tax bracket would suggest.
Using the marginal rate
Understanding how marginal rates affect the consequences of your financial choices can help you make better choices. Some examples are given below.
Marginal return of additional income
The marginal tax rate tells the taxpayer how much of each additional dollar they earn they get to keep. For this reason, those who can control how much income they earn might choose to work just up to the point that their marginal tax rate jumps up.
Aftertax value of investments
The marginal tax rate determines the relative aftertax value of different investments. The aftertax rates of return using the formula:
Consider the individual from the State Taxes section above, considering three bond investments: a corporate bond, a Treasury bond, and a municipal bond from the individual's state. The corporate bond is fully taxable at both federal and state levels, and state income tax is federally deductible. The Treasury bond is taxable at the federal level, but not state. The municipal bond is taxfree at both federal and state levels. Assume each bond is purchased at par value. The aftertax returns of each investment are as follows:
Investment  Yield  Marginal Tax Rate  AfterTax Return 

Corporate Bond  4.00%  30.08%  2.797% 
Treasury Bond  3.50%  24%  2.660% 
Municipal Bond  3.00%  0%  3.000% 
Assuming no other factors (eg. risk) are being considered, the municipal bond has the highest aftertax return and would therefore be the best investment.
Traditional vs. Roth
Deciding between Traditional and Roth contributions is another use for marginal rates. In general, Traditional contributions are better as long as your predicted marginal tax rate in the future is lower than your marginal tax rate now. Roth contributions are better when your predicted marginal tax rate in the future is higher than your marginal tax rate now. Predicting future tax rates can be difficult; it depends on future tax laws, longterm investment performance, and your ability to continue to make contributions over many years. See that article for more details and strategy.
One should also recognize that, over the range of allowable retirement contributions, the marginal tax rate may vary considerably, at breakpoints in the tax bracket structure and when phaseouts come into play. In those cases, splitting contributions between Traditional and Roth may be the best strategy.
Appendix: Marginal rates explained
This section explains why the differential calculus concept of a derivative for tax rate is often not useful in personal finance, but calculating the marginal rate with a difference equation is useful. It is intended for those familiar with calculus and is not necessary for understanding the concepts presented in the previous sections. 
The tax code, particularly when taxable income is under $100,000 and Tax Tables are used, produces a very nonsmooth function of tax vs. income. With the Tax Tables, for most changes in income the tax does not change at all, but every $50 there is a step change.
Comparison of difference vs. derivative
Your income increases from $20,000 to $20,100; which provides you with $100 of extra income. This additional $100 of income results in $15 of additional tax. The marginal rate is therefore 15% = $15 / $100.
The last equation above is the general form for calculating the tax rate for the given change of income.
The step below will be familiar to those who remember differential calculus, but is not recommended for use with tax calculations when the tax function is nonsmooth, due to the lack of useful information it provides.
As a partial derivative
A partial derivative indicates that the tax is not a function of one income, e.g. total income, but several different types of income. For example, wages and capital gains. So we have not a function of one variable tax(income) but a function of two variables tax(wages,gains).
A partial derivative of a function of two or more variables is just the derivative if we change one variable and leave the others constant. This is how marginal tax rates are usually calculated. Refer to the previous example. At an income of $20,000, the marginal tax rate on wages is 15% because an extra $100 of wages increase taxes by $15. However, the marginal tax rate on capital gains is 0% because an extra $100 of capital gains results in $0 extra tax.
The same concept applies to the difference form of the calculation: one independent variable changes while the others are held constant.
Notes
 ↑ Since the income tax structure includes various types of income, deductions, exclusions, credits, and taxes that are not subject to the same treatment under tax laws, the marginal tax rate is not always apparent. See: Individual Income Tax Rates and Shares, 2010, Statistics of Income Bulletin, Winter 2013, page 23 (printed), from the IRS.
 ↑ A "taxbracket" is not formally defined, but inspection of US law shows the intended usage. Note that the term "rate bracket" is also used. From 26 U.S. Code § 1  Tax imposed:
 (f) Phaseout of marriage penalty in 15percent bracket;
 ...maximum dollar amounts for each rate bracket...
 (7) Special rule for certain brackets
See also
References
 ↑ Kitces, Michael (August 20, 2014). "Why A Roth Conversion May Be A Bad Idea Even If Taxes Are Higher In The Future". https://www.kitces.com/blog/whyarothconversionmaybeabadideaeveniftaxesarehigherinthefuture/.
 ↑ Reynolds, Alan. "Marginal Tax Rates". https://www.econlib.org/library/Enc/MarginalTaxRates.html.
 ↑ Melendez, Steven (March 9, 2019). "Tax Rate vs. Marginal Tax Rate". https://finance.zacks.com/taxratevsmarginaltaxrate3045.html.
 ↑ Pomerleau, Kyle (April 2, 2015). "There are More Marginal Income Tax Rates than Advertised". https://taxfoundation.org/therearemoremarginalincometaxratesadvertised.
 ↑ The Finance Buff (November 23, 2009). "What Is Your Marginal Tax Rate?". https://thefinancebuff.com/whatisyourmarginaltaxrate.html.
 ↑ Average vs. Marginal Tax Rates, a YouTube video by the Tax Foundation
 ↑ Kitces, Michael (January 30, 2013). "Understanding Marginal Tax Rate Vs Effective Tax Rate And When To Use Each". https://www.kitces.com/blog/understandingmarginaltaxratevseffectivetaxrateandwhentouseeach/.
 ↑ ^{8.0} ^{8.1} ^{8.2} The MMM Case Study Spreadsheet, The Mr. Money Mustache Community, viewed May 10, 2019.
 ↑ "An Average American Family Can Face +100% Marginal Tax Rates". April 21, 2018. https://www.corporatemonkeycpa.com/2018/04/21/highestmarginaltaxrateinamerica/.
External links
 Average vs. Marginal Tax Rates, a YouTube video by the Tax Foundation
 Tax rate  Wikipedia
 Definitions from Google
Forum discussions
 Bogleheads® forum topic: Important to know Marginal Tax Rate? Effective Tax Rate?
 Explains the importance of understanding the difference between marginal and effective tax rates.
 Bogleheads® forum post: Re: Effective Tax Rate [How to Calculate?]
 Bogleheads® forum topic: Marginal tax rate: statutory 15%, effective 30%
 Bogleheads® forum topic: Seeking comment on proposed revisions to Marginal Tax Rate and Traditional v. Roth wiki articles, fyre4ce. May 17, 2019
