The progressive federal income tax, which is supposed to hit the rich harder than it hits the poor, isn't the great income leveler that it is commonly thought to be, according to new figures.

While the income tax does take proportionally more from wealthier taxpayers than from less affluent ones, it has relatively little effect on the distribution of income in this country.

It's only when government "transfer payments" - such as Social Security benefits, welfare and other major programs - are included that the system actually shifts significant amounts of income from the rich to the poor.

And even that is offset to a large degree by the impact of federal Social Security taxes and state and local taxes. When all federal, state and local taxes and benefits are considered, the system is only virtually proportional - with most taxpayers bearing about the same tax burden.

These conclusions are based on statistics compiled from several sources - the Treasury, the congressional Joint Committee on Taxation and computer studies by the Brookings Institution. Experts caution that the figures are not precise, but they're the best that are available.

The ineffectiveness of the federal income tax system in redistributing income stems from its basic structure:

Although wealthier persons are taxed at higher rates than poorer ones - and pay the lion's share of the total income tax tab - taxpayers in almost all brackets wind up with roughly the same portion of the nation's income pie after income taxes as they had before.

A major reason is that while the effective tax rates vary somewhat for persons in different income brackets, they aren't sharply higher or lower except for those in the very top or bottom brackets - groups that may be extremely rich or poor but comprise relatively small numbers of taxpayers.

For the large group of taxpayers in the $10,000 to $30,000 income bracket the effective federal tax rates vary very little, from a low of 9 percent to a high of 13.8 percent. Above that, the rates rise to 17, 24, 29 and 30 percent - but only 5 percent of taxpayers fall in that group.

The figures provided by the Joint Committee on Taxation show these results:

he richest one-fourth of American households - those with incomes of $17,000 a year or higher - took home 55.5 percent of the income in this country in 1977. After federal income taxes, they still had 53.2 percent. This is so despite that fact that they paid 74.3 percent of all personal income taxes.

The poorest one-fourth - wage-earners making less than $5,000 a year - received 4.6 percent of the income that year. After federal income taxes, their share rose to 5.2 percent. (These taxpayers paid less than 0.1 percent of personal income taxes.)

Those in the richest 5 percent of the country - taxpayers with income of $30,000 or more - earned 22.1 percent of the income in 1977. After federal income taxes, they still had 19.7 percent of all income. (These figures include all income from capital gains - profits from the sale of stocks or other assets.)

The richest half of American households received 82.1 percent of all income before taxes. After taxes, they still held 80.4 percent. For the poorest half, the icome tax boosted their share only modestly, to 19.6 percent, from 17.9 percent before taxes. (The dividing point between these groups was an income of $10,000 a year.)

Moreover, figures compiled by Benjamin A. Okner, a former Brookings tax specialist now at the Treasury Department, show that when all federal, state and local taxes are taken into account, even this modest income redistribution is almost totally offset.

Using 1970 income levels, Okner has estimated the share of national income held by the poorest fifth of the population edges from 4.9 percent to 5 percent, while that of the richest fifth moves from 45.8 percent to 44 percent.

The biggest changes stem from government transfer payments, such as Social Security and welfare benefits. When these are included, the income share of the poorest fifth of the population nearly doubles, to 8.2 percent, while that of the richest fifth moves from 45.8 percent to 44.

These findings were bolstered in an updated study by another Brookings tax analyst, joseph J. Minarik, using 1977 data. Minarik found the federal income tax burden varied only slightly last year for households in the $17,000 to $50,000 brackets - ranging between 10 and 17 percent.

When the employe's share of Social Security payroll taxes and state and local taxes of all sorts were included, the figures showed the tax burden is proportional for most of the nation's households. Everyone in the $8,000 to $50,000 categories paid roughly 30 to 32 percent of his income in taxes.

The reason is that the mild progressivity of the federal income tax is offset entirely by Social Security and state and local taxes, which tend to hit lower-income families proportionally harder. State and local sales and excise taxes, for example, took 3.8 percent of a $50,000-a-year family's income in 1977, but 10.7 percent of the earnings of a $5,000-a-year household.

Minarik's study shows that the federal income tax has become somewhat more progressive in the past 11 years - both because of recent changes in the tax law and the fact that inflation has pushed taxpayers into higher brackets, where their income is taxed more heavily. And taxpayers in all groups are paying proportionally more in taxes.

However, the increased progressivity in the federal income tax has been offset by the rising share of the tax burden going to Social Security and state and local taxes. As a result, the total tax burden - federal, state and local - still in proportional.

The combination of these figures appears to dispute one of the longstanding impressions about the federal income tax - specifically that it is so progressive that it results in a major redistribution of income between wealthier taxpayers and poorer ones.

Joseph A. Pechman, the Brookings Institution's top tax expert, says the effect of the income tax is redistributing income is small. "Substantial redistribution through the income tax system is not very popular," he notes. Other tax authorities agree.

Nevertheless, conservatives point out while the impact of the income tax in altering the portion of the income pie held by various categories of taxpayers may seem small in percentage terms, it often can mean substantial dollar losses for some taxpayers.

For example, for taxpayers in the $17,000-a-year bracket and up, the income tax produces a shift of only 2.3 percentage points. In dollar terms, however, that amounts to a change of $22.3 billion - or an average $5,000 a taxpayer.

By contrast, for those in the $5,000-and-below brackets, the income tax produces a gain of 0.7 percentage points. However, because there are so many more taxpayers in that category, the already scant amount is spread even thinner. The increase amounts to $263 a taxpayer.

Along with the fact that the tax rates vary so little for the bulk of American taxpayers, there are other factors that tend to reduce the impact of the income tax system in shifting income between rich and poor tax payers.

To begin with, the tax rates so often cited - the 14 to 70 percent minimum and maximum - are only the marginal rates, and do not apply to all of a taxpayer's income. (The first several thousand dollars is taxed at a lower rate than the second, and so on.)

As a result, the effective tax rates that various income groups pay - the percentage of income that taxpayers actually pay in taxes - is substantially lower, raging from 5.5 percent in the $5,000-to-$10,000 brackets to a maximum of 30 percent in the $200,000-and-over bracket.

Then, too, taxpayers in higher brackets get a larger share of the tax breaks and deductions - a factor that tends to reduce the amount of taxes they have to pay. For example, only half the income from capital gains is subject to taxation.

The question is, if the income tax system is taxing middle and upper-income groups at higher rates, and it isn't redistributing that income to the poor, where is the money going?

The answer: Into government coffers, where some is spent on social benefits (which go mainly to the poor) and some on general government. But the tax system itself, while progressive, is only modestly so.