The two numbers a raise actually has
A percentage raise is a ratio, and every ratio needs its denominator named. The raise percentage is the increase divided by current pay: going from $60,000 to $62,400 is $2,400 ÷ $60,000 = 4.00%. Dividing by the new figure instead gives 3.85%, and that is not a smaller raise, it is a different quantity — the share of your new salary that the increase represents. Employers quote the first; the second has no useful interpretation.
The second number is what the raise is worth after prices move. If your pay rises 4% while the goods you buy rise 3%, you are better off, but not by 1%. Purchasing power is a ratio of ratios: your pay multiplies by 1.04 and prices multiply by 1.03, so what you can buy multiplies by 1.04 ÷ 1.03 = 1.0097087, a real gain of 0.9709%. Subtraction is an approximation that is close at small numbers and increasingly wrong as either figure grows — at 8% against 4% the subtraction says 4.00% and the exact relation says 3.846%.
Both matter for different decisions. The nominal figure sets your paycheck and your next negotiation's starting point. The real figure tells you whether this year's raise moved you forward at all.
From percentage to payslip, and forward through time
New pay is current pay multiplied by one plus the raise: 60,000 × 1.04 = 62,400. Reverse it when you know the new figure instead: subtract, divide by the old figure, multiply by a hundred.
The per-paycheck increase is the annual increase divided by the number of checks you receive, and it is the number that decides whether a raise feels real. $2,400 a year is $92.31 on each of 26 biweekly checks — before tax takes its share, which is why a 4% raise never shows up as 4% more money in the bank.
The hourly equivalent divides annual pay by paid hours, conventionally 2,080 for a full-time year. That conversion runs both ways, so an hourly worker can enter a rate and get the salary comparison, which is what the hourly to salary calculator does in more detail for schedules with overtime or unpaid weeks.
The projection compounds. A raise is not a one-off payment; it is a permanent change to the base every future raise is calculated on. Repeating the same percentage for t years multiplies pay by (1 + g)t, so 3% a year for ten years multiplies salary by 1.0310 = 1.343916, a cumulative 34.39% — noticeably more than the 30% that ten times three suggests. The table below carries a parallel column in today's dollars, dividing each year's salary by (1 + inflation) raised to that year, so you can see the nominal and real paths side by side.
Worked example: 4% on $60,000 with 3% inflation
You earn $60,000, are offered 4%, are paid biweekly, and consumer prices are rising 3% a year.
- Dollar increase. $60,000 × 0.04 = $2,400.
- New salary. $60,000 + $2,400 = $62,400, or $62,400 ÷ 2,080 = $30.00 an hour.
- Per paycheck. $2,400 ÷ 26 = $92.31 gross on each check.
- Real raise. 1.04 ÷ 1.03 = 1.0097087, so the raise is worth 0.9709% in purchasing power. In dollars of today's value, $62,400 ÷ 1.03 = $60,582.52, which is $582.52 more than you have now — and note that $582.52 ÷ $60,000 = 0.9709%, the same figure.
- Five years of the same raise. $60,000 × 1.045 = $60,000 × 1.2166529 = $72,999.17.
- Five years in today's dollars. $72,999.17 ÷ 1.035 = $72,999.17 ÷ 1.1592741 = $62,969.73. Five years of 4% raises against 3% inflation leaves you 4.95% better off in real terms, which is 1.00970875 − 1 = 0.049495.
That last line is the one worth sitting with. The nominal path looks like a 21.7% gain over five years; the real gain is 4.95%. Neither figure is wrong, and they answer different questions.
How to read the result
Judge the offer against inflation first, and against the market second. A raise below inflation is a real pay cut however it is described, and the calculator says so explicitly. A raise above inflation is a real gain, but that does not make it competitive — if pay for your role has moved more than yours has, you are falling behind the market while gaining against prices. The Employment Cost Index published quarterly by the Bureau of Labor Statistics is the reference series for what compensation is doing in aggregate; salary surveys for your specific role and metro are what to bring to a negotiation.
Use the per-paycheck figure carefully. It is gross, and the increment is taxed at your marginal rate, not your average one. A 4% raise on a salary already inside the 22% federal bracket delivers noticeably less than 4% more spendable income once federal, state and payroll taxes are applied — run both salaries through the take-home pay calculator to see the actual difference in the deposit.
Treat the compounding projection as an illustration, not a plan. It assumes the same percentage every year, which is not how merit budgets work; they move with company performance and with the labour market. Its real use is to show what a one-off difference is worth over a career: taking $62,400 instead of $61,800 is $600 this year, but it also raises the base for every future raise, and after five years of 4% increases that $600 gap has become $600 × 1.045 = $730.
A promotion is a different calculation. Step changes of 10–20% are common when the job itself changes, and comparing one against an annual merit percentage is a category error. Where the new role sits in a different market, price the role rather than the increment.
Real raise by nominal raise and inflation
| Nominal raise | 2% inflation | 3% inflation | 4% inflation |
|---|---|---|---|
| 2% | 0.00% | −0.97% | −1.92% |
| 3% | 0.98% | 0.00% | −0.96% |
| 4% | 1.96% | 0.97% | 0.00% |
| 5% | 2.94% | 1.94% | 0.96% |
| 6% | 3.92% | 2.91% | 1.92% |
| 8% | 5.88% | 4.85% | 3.85% |
Compare the diagonal to the subtraction shortcut: at 8% against 4%, subtracting gives 4.00% while the exact figure is 3.85%. The gap widens as both rates rise, which is why high-inflation periods make the shortcut misleading.
Which inflation figure to enter
The default reference is the Consumer Price Index for All Urban Consumers (CPI-U), published monthly by the Bureau of Labor Statistics, measured over the twelve months your raise covers. Use the twelve-month change ending in the month your raise takes effect, not a forecast, if you are assessing a raise you have already received.
Two refinements are worth knowing. Core CPI excludes food and energy and is less volatile, which makes it a better guide to the trend but a worse guide to your grocery bill. Regional CPI series exist for major metro areas and can differ from the national figure by more than a percentage point, which matters if your costs are dominated by local housing. If you are comparing an offer in another city rather than an annual raise, the relevant adjustment is not inflation at all but a cost-of-living difference — see the cost of living comparison calculator.
Mistakes that make a raise look better or worse than it is
- Dividing by the new salary. Percentage change is always measured against the starting value. Using the new figure as the denominator understates every increase.
- Subtracting inflation instead of dividing. Fine at 2% and 3%; misleading once either figure is large. Use (1 + g) ÷ (1 + π) − 1.
- Comparing a mid-year raise against a full-year figure. A raise effective in July delivers roughly half its annual value in that calendar year, while the annualised salary figure is what carries into the next.
- Forgetting that the increment is taxed at the marginal rate. The extra dollars sit on top of your existing income, so they are taxed at your highest bracket, not your average one.
- Treating a bonus as a raise. A one-off payment does not change the base for next year's increase, and it does not compound. A 3% raise and a 3% bonus are worth very different amounts over five years.
- Ignoring the benefits side. A raise accompanied by a higher health-insurance contribution can leave less money in your pocket than the percentage implies. Compare total compensation, and check the deposit rather than the letter.
Using this before a negotiation
Run the calculation in both directions before the conversation. Forwards, from the percentage you expect to be offered, tells you what that offer is worth after inflation and after tax. Backwards, from the salary you want, tells you the percentage you are actually asking for — and a request framed as a dollar figure is easier to justify with market evidence than one framed as a percentage.
Two facts from the arithmetic are useful to have in mind. First, the base compounds: a difference agreed today is multiplied by every future raise, so the gap between two offers grows rather than staying fixed. Second, the real hurdle is inflation, not zero — a 2% raise in a 3% year is a reduction in what you can buy, and describing it that way is accurate rather than dramatic. The inflation and purchasing power calculator converts a past salary into today's dollars if you want to see what has happened over several years rather than one.
If the raise arrives, the decision that follows is what to do with it. Increases that get absorbed into monthly spending leave no trace on your balance sheet; increases routed to savings before they reach the current account are the cheapest saving you will ever do, because you have not yet adjusted to the money. That is the specific moment the 50/30/20 budget calculator is most useful, and the effect on your position shows up in the net worth calculator within a year.