What an equivalent salary actually means
The equivalent salary is the amount that buys, at destination prices, the same basket of things you buy today. It is not a measure of how nice the city is, what you would enjoy, or what the market pays for your job. It answers one narrow question precisely: if nothing about your life changed except the prices, what would the number on the offer letter have to be?
The method is the one national statistical agencies use for price indices. Take the quantities you buy now, price them where you are, price the identical quantities at the destination, and divide. That is a Laspeyres index, and its defining property is that it holds the basket fixed. It is the right basis for a relocation decision because you are asking about your life, not an average household's.
Which is also why the weights matter more than the indices. A renter who spends 40% of income on housing and a homeowner with a paid-off house facing the same city see completely different numbers, because the housing index — the category that varies most between cities — is multiplied by a completely different weight. The default weights here are a broadly typical urban split, with housing as the largest single share; change them to your own spending before trusting the result.
How the composite index is built
Each category index is expressed with your current city at 100, so 145 means housing costs 45% more at the destination and 80 means it costs 20% less. The composite is the weighted average of those five numbers, using your budget shares as the weights: composite = Σ(wi × Ii) ÷ Σwi.
Dividing by the sum of the weights means they do not have to add to 100. Enter 33, 13, 17, 8 and 29 and nothing is rescaled; enter 66, 26, 34, 16 and 58 and you get exactly the same composite, because doubling every weight leaves every share unchanged. That also means you can enter dollars per month instead of percentages if that is easier — the arithmetic only cares about the ratios.
Two properties are worth internalising. First, the composite is linear in each index, so a category with a 10% weight moves the composite by one point for every ten points its index moves. Second, the relationship between the cost difference and the purchasing-power change is not symmetric: a city 25% more expensive needs a 25% higher salary, but a salary held flat in a city 20% cheaper is worth 1 ÷ 0.8 − 1 = 25% more, not 20%. The percentages point in opposite directions and have different denominators, which is exactly the trap in reading a headline "20% cheaper" as a 20% raise.
Worked example: $85,000 moving to a city with 45% higher housing
You earn $85,000. The destination indexes at 145 for housing, 108 for food, 112 for transport, 102 for healthcare and 106 for everything else, and your budget splits 33 / 13 / 17 / 8 / 29. The offer is $95,000.
- Weights sum. 33 + 13 + 17 + 8 + 29 = 100, so each weight is already a share.
- Contributions. Housing 0.33 × 145 = 47.85. Food 0.13 × 108 = 14.04. Transport 0.17 × 112 = 19.04. Healthcare 0.08 × 102 = 8.16. Everything else 0.29 × 106 = 30.74.
- Composite index. 47.85 + 14.04 + 19.04 + 8.16 + 30.74 = 119.83, so the destination is 19.83% more expensive on your basket.
- Equivalent salary. 85,000 × 119.83 ÷ 100 = $101,855.50.
- Judge the offer. 95,000 − 101,855.50 = −$6,855.50. The $10,000 raise is a real pay cut of 95,000 ÷ 101,855.50 − 1 = −6.73%, about $571 a month of lost purchasing power.
- Find the housing share of the damage. Housing contributes 0.33 × (145 − 100) = 14.85 of the 19.83 points, or 75% of the entire difference. Every other category combined accounts for 4.98 points.
That last step is the one that changes decisions. If you could take a home that indexes at 120 rather than 145 — a smaller place, a different neighbourhood, a longer commute — the composite falls to 111.58 and the equivalent salary to $94,843, which the offer clears.
Reading the result honestly
A negative gap means the offer buys less than your current salary buys today; a positive gap means it buys more. The percentage version, the real change in purchasing power, is the one to quote, because it is comparable across offers of different sizes.
Three adjustments the composite does not make, all of which can be larger than the index difference itself. State and local income tax is the biggest: moving between a state with no income tax and one charging 5–10% changes take-home pay by more than most cost-of-living gaps, and it is not in any price index because it is not a price. Run both salaries through the take-home pay calculator with the right state rates and compare the net figures against the composite. Housing tenure is the second: if you own outright, your housing weight is not 33% and the whole calculation changes. And commuting is the third — a cheaper housing index bought with an extra hour a day is a real cost the transport index only partly captures.
Finally, treat the equivalent salary as a floor for negotiation rather than a target. It restores your current standard of living exactly; it does not compensate you for moving, for a smaller professional network, or for the risk of the new job. If the offer only just clears the equivalent salary, the move is, financially, a lateral one.
What a composite index does to a salary
| Composite index | $60,000 becomes | $85,000 becomes | $120,000 becomes | Purchasing power on an unchanged salary |
|---|---|---|---|---|
| 70 | $42,000 | $59,500 | $84,000 | +42.9% |
| 85 | $51,000 | $72,250 | $102,000 | +17.6% |
| 100 | $60,000 | $85,000 | $120,000 | 0.0% |
| 115 | $69,000 | $97,750 | $138,000 | −13.0% |
| 130 | $78,000 | $110,500 | $156,000 | −23.1% |
| 160 | $96,000 | $136,000 | $192,000 | −37.5% |
Note the asymmetry: an index of 70 is 30% cheaper but raises purchasing power by 42.9%, because the comparison divides by the smaller number.
What this comparison leaves out
- Income tax. State and local income taxes are not prices and appear in no cost-of-living index, yet they can swing net pay by ten points between states. Compare after-tax figures separately.
- Property tax and insurance. Housing indices usually reflect rents or prices, not the annual cost of holding a home. Two cities with identical house prices can differ sharply once tax rates and hurricane or wildfire insurance are included.
- Your actual housing choice. Within-metro variation in housing cost is often larger than the difference between metros. A citywide index is a starting point; the rent on the specific home you would take is the real number.
- Substitution. A fixed-basket index overstates the pain of a price rise, because in real life you buy less of what became expensive. That bias is why national agencies publish chained indices alongside fixed-basket ones.
- One-off moving costs. Removals, deposits, breaking a lease, a duplicate month of rent and a vehicle registration are real and are not annual.
- Quality differences. An index compares prices for a comparable basket; it cannot price a shorter commute, better schools or a climate you like.
Where to get the index numbers
This calculator deliberately does not ship city data, because cost-of-living indices are proprietary, revised regularly and disagree with each other. Use a source you can name and date. The Bureau of Economic Analysis publishes Regional Price Parities, which measure price levels for states and metropolitan areas against the national average and are free; converting two RPPs into an index with your origin at 100 is one division. The Council for Community and Economic Research's ACCRA Cost of Living Index is the commercial standard and is what most media comparisons are built on. The Bureau of Labor Statistics publishes Consumer Expenditure Survey shares, which is the right source for your weights if you do not want to work them out from your own bank statements.
Whatever you use, take all five indices from the same source and the same period. Mixing a housing figure from one provider with a food figure from another produces a composite that means nothing, because the providers define their baskets differently. And once you have a shortlist of cities, sanity-check the housing index against real listings — it is the term that dominates the answer, and it is the one you can verify in ten minutes. When you have chosen, size the housing payment itself with the home affordability calculator or check the rent against a mortgage with the rent vs buy calculator.