The formula
Cost of living is one ratio, not a feeling: the equivalent salary is your current salary times the new city’s cost index divided by your current city’s cost index. A cost index of 100 is the US average, so a city at 120 costs about 20% more than the average and a city at 85 costs about 15% less. The difference is the equivalent minus your current salary, the percent change is the difference over your current salary, and the monthly figures are the annual figures divided by 12. Whichever of the two cities you are solving for, the same seven steps give the answer — and the cost of living calculator runs them for you.
Step 1 — Find your current salary
Start with the salary you actually earn, before tax, on a full year. Our worked example uses $75,000.00, a round number near the middle of the US pay scale — but the steps work at any salary, from $45,000.00 to $1,000,000.00. Use the gross salary, not the take-home pay: the cost index compares what things cost, not what tax takes, so the tax math belongs in a separate step. If your pay includes a bonus or overtime, use the base salary first and add the variable pay afterwards, or the comparison will flatter the new city.
Step 2 — Find your current city’s cost index
Look up the cost index for the city you live in now. The US average is 100, and most published indexes put the big coastal cities far above it — New York at about 168, San Francisco at about 169, Honolulu at about 165, Boston at about 148, Los Angeles at about 147, Seattle at about 145, Chicago at about 113 and Dallas at about 100. The index is a blend of housing, food, transport and other spending, and housing is the biggest driver: two neighborhoods in the same city can differ more than two cities. Use the index for the exact city and the exact year.
Step 3 — Find the new city’s cost index
Look up the same index for the city you would move to, from the same source and the same year — mixing sources is how a comparison goes wrong. Our worked example moves to a city at index 120, a fifth above the average. Write both indices down side by side: the current city at 100 and the new city at 120. If the new city’s index is lower than the current one, the equivalent salary will be lower than your salary — that is not a pay cut, it is the same life for less money.
Step 4 — Multiply and divide
Multiply your salary by the new city’s index, then divide by your current city’s index. On the worked example that is $75,000.00 × 120 ÷ 100 = $90,000.00. The order does not matter — $75,000.00 ÷ 100 × 120 gives the same $90,000.00 — but do the multiply first if you are working by hand, because it keeps the numbers whole for longer. The result is the salary that buys the same life in the new city: the equivalent salary.
Step 5 — Work out the difference
Subtract your current salary from the equivalent salary. On the worked example that is $90,000.00 − $75,000.00 = +$15,000.00 — the new city costs $15,000.00 a year more to live the same life. A negative difference is good news, not bad: at index 85 the equivalent is $75,000.00 × 85 ÷ 100 = $63,750.00, so the difference is $63,750.00 − $75,000.00 = −$11,250.00, and the cheaper city pays you $11,250.00 less in nominal terms while buying the same life.
Step 6 — Work out the percent change
Divide the difference by your current salary and multiply by 100. On the worked example that is +$15,000.00 ÷ $75,000.00 × 100 = +20.00%. The percent is the honest way to compare moves of different sizes: a $15,000.00 rise on a $75,000.00 salary is 20.00%, while the same $15,000.00 on a $100,000.00 salary is only 15.00%. Moving from a city at 130 to a city at 100, the equivalent is $75,000.00 × 100 ÷ 130 = $57,692.31, so the difference is −$17,307.69 and the percent change is −23.08%.
Step 7 — Check the monthly gap and the calculator
Divide both annual figures by 12 and compare the monthly gap. On the worked example the monthly equivalent is $90,000.00 ÷ 12 = $7,500.00 against $75,000.00 ÷ 12 = $6,250.00 — $1,250.00 more a month. The monthly gap is the number that decides whether the move fits your budget, because rent and bills are monthly. Then run the same numbers through the cost of living calculator and check that it gives the same $90,000.00, $15,000.00 and 20.00% — if it does not, one of the two indices is wrong, and that is the number to re-check.
Three worked examples
A cheaper city. A $75,000.00 salary at index 100, moving to index 85: $75,000.00 × 85 ÷ 100 = $63,750.00, a difference of −$11,250.00 and a percent change of −15.00%. Monthly, that is $5,312.50 against $6,250.00.
Moving home to a cheaper city. A $75,000.00 salary at index 130, moving to index 100: $75,000.00 × 100 ÷ 130 = $57,692.31, a difference of −$17,307.69 and a percent change of −23.08%. Monthly, that is $4,807.69 against $6,250.00 — the same life for $1,442.31 less a month.
New York. A $75,000.00 salary at index 100, moving to index 168: $75,000.00 × 168 ÷ 100 = $126,000.00, a difference of +$51,000.00 and a percent change of +68.00%. Monthly, that is $10,500.00 against $6,250.00 — and that is why a New York offer that looks generous can still feel tight.
When the answer surprises you
The most common surprise is a big number that feels wrong. A $75,000.00 salary that becomes $126,000.00 at index 168 is not a raise — it is the same life, repriced. The second surprise is a small number that looks like a pay cut: $57,692.31 at index 100 after earning $75,000.00 at index 130 is the same life for less money, and the $17,307.69 you “lose” is rent you no longer pay. The third surprise is the index itself: a city at 120 can be cheap on groceries and dear on rent, and the single number hides the mix. If the mix matters — and it usually does, because rent is the biggest bill — compare the housing cost separately before you sign anything.
What the index hides
A cost index hides two things. The first is tax: the index blends housing, food, transport and other spending, but it does not count state income tax, and tax alone can move the answer by thousands a year — so run the take-home math separately. The second is the mix: two cities at the same index can feel very different if one is dear on rent and cheap on food while the other is the reverse. Use the index to shortlist the cities, then price the rent, the commute and the tax before you decide.