1. 
What’s a marginal tax rate, and how is it different from an average tax rate? 

Let’s say you’re a single person earning $50,000. If you have no other income and take the standard deduction, you’ll owe $6,250 in income tax, plus $2,825 in payroll taxes, for a federal tax burden of $9,075. If you divide $9,075 by $50,000, you get 18.15%  in other words, 18% of your income goes to the federal government, and your average tax burden is 18%.
What if you get a $1000 raise, and earn a total of $51,000? You might think that your tax burden would then be 18.15% times $51,000 = $9,257, but it’s more complicated than this. Your income is taxed at different rates at different levels, and if you do a detailed tax calculation, you’ll find that your federal tax burden actually comes out to $9,382. That’s $307 more than the tax you owed making $50,000, so your $1000 raise has led to a $307 increase in taxes. $307 divided by $1000 is 30.7%, so economists say that the “marginal” tax rate on that additional $1,000 is 30.7%. (It’s actually 30.65%, but all numbers on a tax return are rounded to the nearest dollar.)
There are many things that can affect the marginal rate you owe on your top dollar of income. The income tax code is divided into six different tax brackets, with rates ranging from 10% to 35%, but those don’t tell the whole story. Things like the Child Tax Credit and the Earned Income Tax Credit, which phase in and out at different income levels, will change effective marginal tax rates. If you include payroll taxes, those are slightly regressive, as the social security tax (currently 4.2%, instead of 6.2%, as a result of the tax compromise signed last year) is only applied to the first $106,800 of income.


2. 
Why are the scales on the axes all funny? 

All the axes on the graph default to a log scale. This is for a variety of reasons – primarily that a lot of the most interesting and complicated stuff in the tax code happens at lower income levels, and a log scale allows for these to be more clearly visible. Additionally, the rate scale is logarithmic (for positive rate values only), to accommodate the occasional spike in marginal rates associated with cliffs in the tax code (such as the phaseout of the child tax credit or the tuition and fees deduction.) All axes can be changed to a linear scale in the “advanced options” section. 

3. 
What is the “calculation interval” in the advanced section? 

The calculator works by running a tax calculation many times for different values of a particular variable. By default, the calculator attempts to pick values intelligently, so that it narrows down precisely on locations where marginal rates change. The alternative is to set a fixed calculation interval. For example, if you’re calculating the effects of changes in wage income from $0 to $50000, entering “1000” here will cause the calculator to run a calculation at $0, $1000, $2000, $3000, etc., up to $50000 in wage income. This is often faster, but it can “blur out” the marginal rate line in that you’re getting an average marginal rate for a particular interval rather than a precise one for each dollar. 

4. 
What is the difference between a “discrete” and “continuous” phaseout of the Child Tax Credit? 

The Child Tax Credit has a peculiar structure, in that the credit amount is reduced by exactly $50 for each $1000 interval above $110,000 (or $75,000 for head of household filers.) A credit that is worth its full value at $110,000 of income is worth $50 less at $110,001 of income. Your taxes have gone up by $50 for an increase of only $1 in income, so there’s an effective 5000% marginal tax rate on that one dollar. This gives the graph a peculiar shape where it is marked by “spikes” up to 5000% each $1000 in the phaseout range. To avoid this, there is the option to have a continuous phaseout instead, where the $50 loss is spread out over the $1000 range. This makes for a nicer graph, but is slightly less accurate. 
