Why a real return is not nominal minus inflation
Your investment return and inflation are both multiplicative processes, and you cannot combine multiplicative processes by subtracting them. A portfolio that grows 7% turns each dollar into 1.07 dollars. Prices that rise 3% turn each 1.00 of cost into 1.03. What you can buy at the end is 1.07 ÷ 1.03 = 1.038835 times what you could buy at the start — a real return of 3.8835%, not 4%.
The 0.1165 percentage point difference looks trivial and is not. Compounded over a 30-year retirement horizon, 1.0430 = 3.24340 turns $100,000 into $324,340 while 1.038835030 = 3.13589 turns it into $313,589 — a gap of $10,751, more than a tenth of the starting balance, created entirely by an arithmetic shortcut.
The gap widens with both inputs. Because the exact error equals (r − π) × π ÷ (1 + π), it grows with the size of the real return and with inflation. At 10% nominal and 4% inflation the shortcut overstates the real return by 0.2308 percentage points; at 4% nominal and 2% inflation, by only 0.0392.
The second thing this calculator does matters more than the first. It takes your projected balance and divides it by the cumulative price level, so a $38,697 balance twenty years out is shown as the $21,426 of today's purchasing power it actually represents. That is the number to compare against today's cost of living, and it is the number almost every projection quietly omits.
The Fisher equation, term by term
Irving Fisher's relation states that the nominal growth factor is the product of the real growth factor and the inflation factor:
(1 + rnominal) = (1 + rreal) × (1 + π)
Rearranged for the quantity you want, rreal = (1 + rnominal) ÷ (1 + π) − 1. Each factor is a growth ratio, not a rate, which is why the operation is division rather than subtraction.
Expand the exact form and the approximation appears naturally. (1 + rreal)(1 + π) = 1 + rreal + π + rrealπ, so rnominal = rreal + π + rrealπ. Drop the cross-term rrealπ and you get rreal ≈ rnominal − π. The cross-term is exactly what the shortcut throws away, and it is small only when both rates are small.
Deflating a balance uses the same logic across t years. The price level after t years is (1 + π)t, so dividing your nominal balance by that factor restates it in the purchasing power of today. Equivalently, you can compound the starting balance at the real rate directly — both routes give the same answer, and the calculator's worked example checks one against the other.
Note what this does not handle: contributions. If you add a flat $6,000 a year for twenty years, the last contribution is worth far less in real terms than the first. This calculator treats the contribution as a constant nominal amount and deflates the whole ending balance, which is the correct treatment for a fixed-dollar standing order. If you intend to raise your contribution with inflation each year, model it with the step-up SIP calculator instead, setting the step-up rate equal to inflation.
Worked example: $10,000 for 20 years at 7% nominal, 3% inflation
Every figure below comes from the calculator's default inputs, so you can reproduce it on the page.
- Find the real rate. 1.07 ÷ 1.03 = 1.0388350, so rreal = 3.88350% a year. The subtraction shortcut would have said 4%, overstating by 0.11650 percentage points.
- Grow the balance nominally. 1.0720 = 3.8696845. $10,000 × 3.8696845 = $38,696.84.
- Find the price level. 1.0320 = 1.8061112. A basket costing $100 today costs $180.61 in twenty years.
- Deflate. $38,696.84 ÷ 1.8061112 = $21,425.51 in today's dollars.
- Cross-check with the real rate. 1.038835020 = 2.1425505, and $10,000 × 2.1425505 = $21,425.51. The two routes agree exactly, which is the arithmetic proof that the Fisher form is the right one.
- Read the loss. $38,696.84 − $21,425.51 = $17,271.33 of the headline balance is not new purchasing power — it is compensation for a price level that rose 80.6% while you waited.
- Value of a dollar. 1 ÷ 1.8061112 = $0.5537. Every dollar in that ending balance buys about 55 cents of what a dollar buys today.
Notice how much of the headline number is illusory: 44.6% of the ending balance exists only to offset price increases. That is with a benign 3% assumption. At 5% inflation over the same twenty years the price level is 1.0520 = 2.6533, and the same nominal balance is worth $14,584 in today's money.
What real return should you plan on?
Plan in real terms and you never have to guess at inflation twice. If you set a retirement target of “$60,000 a year in today's money” and you project the portfolio at a real rate, the target and the projection are in the same units and no further adjustment is needed. That is exactly how the Coast FIRE calculator and the safe withdrawal rate calculator are set up, and it is why the well-known 4% withdrawal guideline is quoted as an inflation-adjusted spending rule rather than a nominal one.
Read the sign first. A negative real return is not a rounding detail — it means the balance is shrinking in what it buys even while the statement shows a gain. Cash deposits spent most of the 2010s and early 2020s in that regime in many countries, and a saver reading only the nominal interest credit would never have seen it.
Then read the magnitude against the risk you are taking. A real return of 1% to 2% is what investment-grade bonds have historically been priced to deliver; 4% to 5% real is an equity-like assumption and carries equity-like variability. If your plan only works at 7% real, the plan is doing the work, not the portfolio.
Finally, be honest about which price index applies to you. Headline CPI measures a national average basket. If your spending is concentrated in health care, higher education, or housing in a supply-constrained city, your personal inflation rate can run well above the published figure, and the correct input for this calculator is yours rather than the country's.
Real return by nominal return and inflation
| Nominal | 2% inflation | 3% inflation | 4% inflation | Largest shortcut error |
|---|---|---|---|---|
| 4% | 1.9608% | 0.9709% | 0.0000% | 0.0392 pp |
| 6% | 3.9216% | 2.9126% | 1.9231% | 0.0874 pp |
| 8% | 5.8824% | 4.8544% | 3.8462% | 0.1538 pp |
| 10% | 7.8431% | 6.7961% | 5.7692% | 0.2308 pp |
The shortcut error is exactly (r − π)·π/(1 + π). For 10% nominal and 4% inflation: 0.06 × 0.04 ÷ 1.04 = 0.2308 percentage points.
Assumptions and limits worth knowing
- A single constant inflation rate is a simplification. Real inflation arrives in bursts. The arithmetic here is exact for a constant rate and a good approximation for an average rate over a long horizon, but it says nothing about sequence.
- Taxes come before inflation, not after. Tax is charged on nominal gains, so in a taxable account you must deduct tax from the nominal return first and only then deflate. Skipping that order flatters the answer; the capital gains tax calculator gives you the after-tax nominal figure to feed in here.
- Fees are nominal too. Subtract the expense ratio from the nominal return before the Fisher step, for the same reason.
- Deflation flips the direction. With a negative inflation input the real return exceeds the nominal return, because the same dollars buy more later.
- Contributions are treated as constant in nominal dollars. A $500-a-month standing order that is never increased delivers steadily less real saving each year.
- Index choice matters more than most people assume. CPI, chained CPI and personal spending baskets diverge, and over thirty years small index differences compound into large ones.
Where the real rate shows up elsewhere
Once you have a real rate, most other planning questions become easier rather than harder. Doubling time is one: feed the real rate into the Rule of 72 calculator and you learn how long purchasing power takes to double rather than how long the account statement takes to double. At 7% nominal and 3% inflation, the nominal doubling is 10.24 years and the real doubling is 18.2 years — nearly twice as long.
Bond markets price the same relationship explicitly. Inflation-protected government bonds quote a real yield directly, and the gap between a nominal government bond yield and the matching inflation-linked yield of the same maturity is the market's breakeven inflation rate. That breakeven is a defensible input for the inflation field here, and it has the advantage of being observable rather than assumed.
For accumulation work, run your compound interest or future value projections twice, once nominal and once real, and present the real one to anybody making a decision. The nominal figure is larger and more exciting; the real figure is the one that tells you whether the plan works.