Tools · Economics
Macro Formula Lab
The core macroeconomic formulas behind every data release — worked, explained, and solvable in any direction. Give it any two of the three figures and it returns the third.
Strip inflation out of an output figure — or put it back. Give any two of the three and this returns the third.
Real GDP = Nominal GDP ÷ (GDP deflator ÷ 100)
Index where the base year = 100.
Enter the values to see a result: Nominal GDP, GDP deflator.
Assumptions behind this formula
- The deflator is an index with the base year set to 100. A deflator of 120 means prices are 20% above the base year.
- The GDP deflator covers all domestic output and reweights continuously. CPI tracks a fixed consumer basket. They are different numbers and will disagree — that is not an error in either.
Worked example
Nominal GDP £2,400 · GDP deflator 120.0 → £2,000
A deflator of 120 means prices are 20% above the base year, so £2,400bn nominal is £2,000bn real.
Talk to an adviser about your portfolio
Understanding the data is the first step. Our advisers can discuss what it means for your own holdings, currency exposure and long-term plan.
What this tool does and who it's for
Most market-moving economic news reduces to a handful of relationships. A GDP print, an inflation release, a jobs report and a budget announcement are each built on formulas that fit on a single sheet — and once you can work them, the headline number stops being something you take on trust. This lab holds thirteen of those relationships and lets you solve each one with your own figures, in whichever direction you happen to need.
It is built for investors reading data releases rather than for students sitting an exam. Every formula carries a “why this matters” note that connects it to a decision you might actually face, and four of the thirteen — real return, purchasing power, the real interest rate, and the nominal-to-real conversion — are there because they are the arithmetic that turns an economic statistic into something about your own money.
Solving in any direction
Several of these relationships are one equation with three terms, and in practice you usually hold two of them. Real GDP, nominal GDP and the deflator are the clearest case: a statistics release might give you two, and the third is what you want. Rather than making you rearrange the algebra, the lab offers each rearrangement as a “solve for” option with its own inputs. The formula being applied is printed above the fields so you can see exactly what is being calculated, and the same expression appears in your emailed results.
Assumptions are stated, not buried
Every formula that rests on a simplification says so directly beneath the result. This matters most for the multipliers. The expenditure multiplier of 1 ÷ (1 − MPC) and the lump-sum tax multiplier of −MPC ÷ MPS are the closed-economy forms: they assume saving is the only way money leaks out of the circular flow. Real economies also leak through tax and imports, so genuine multipliers are substantially smaller — a point that is frequently lost when these formulas are quoted in commentary. The tool shows the textbook figure and tells you plainly that it is an upper bound on the mechanism, not a forecast.
The same discipline applies elsewhere. The marginal propensity to consume is defined against disposable income rather than gross income. Real returns use the exact Fisher relation rather than the subtract-inflation shortcut. Opportunity cost is expressed in units of the good given up. Each of these is a place where a casually stated version of the formula would give you a subtly wrong answer.
When a formula has no answer
Some inputs make a formula genuinely undefined rather than merely awkward. An MPC of exactly 1 makes the expenditure multiplier infinite; a base-year basket costing nothing makes CPI meaningless; an unchanged quantity of X gives opportunity cost a denominator of zero. In every one of those cases the lab says no answer exists and explains which denominator collapsed. It will not show a zero, an infinity, or a blank — a plausible-looking number in place of an undefined one is the most dangerous output a calculator can produce.
Reading a data release with these
Take a typical sequence. A growth figure is published: use the deflator formula to establish whether it is real or nominal, because a 5% nominal rise alongside a 4% deflator increase is an economy that barely moved. An inflation print follows: convert the index change into a rate, and remember that a falling rate still means rising prices. A jobs report lands: calculate the unemployment rate, then calculate participation, because unemployment falling while participation falls is discouraged workers leaving rather than a strengthening market. Then a budget: apply the appropriate multiplier to the announced change, noting the sign convention that a tax rise produces a negative effect on output.
Finally, bring it back to your own position. If your portfolio returned 7.5% while inflation ran at 3.2%, the real return calculator shows you made 4.17% in purchasing power, not 4.3% and certainly not 7.5%. If you are holding cash at 4.5% while inflation runs at 6%, the real interest rate is about −1.4% and the balance is shrinking in real terms while the statement shows it growing. That gap between the nominal number and the real one is the single most useful thing on this page.
Limitations, and what this tool is not
This is arithmetic on figures you supply. It holds no live economic data, so nothing here updates when a statistics agency publishes — you enter the numbers from the release. It makes no forecast and expresses no view on any market, asset class or product. The multiplier models are deliberately simplified textbook forms, and the purchasing-power calculation assumes a constant inflation rate that no real period ever delivers. Treat the outputs as a way to read published data accurately, not as an input to a specific investment decision. For that, and for anything touching your own tax position or objectives, take regulated advice. You can find the rest of our calculators across our financial tools, and the wider context in our investment guides.
Important — This is an educational calculator. It performs arithmetic on figures you enter, contains no market or economic data, and makes no forecast. The multiplier formulas are the simple closed-economy versions, which assume saving is the only leakage and therefore overstate real-world multipliers. Nothing here is a recommendation to buy, sell or hold any investment.
This tool is a general illustration based on the figures you enter. It does not constitute financial, investment, tax or legal advice, and the results are estimates rather than guarantees. Global Investments is not authorised or regulated by the Financial Conduct Authority. Where the amounts involved are material, take advice from a suitably qualified professional in each relevant jurisdiction before acting.
Related tools & guides
- Real Return Calculator — the same arithmetic aimed squarely at a portfolio
- Investment services — how these figures feed into portfolio construction
- Investment guides — the wider library on markets and strategy
- Portfolio Yield Calculator — blended yield across a multi-asset portfolio
- Cost of Living Calculator — price levels applied to a relocation decision
- All financial tools — the full calculator and eligibility library
Macroeconomic formulas — common questions
6 questions
What is the difference between CPI and the GDP deflator?
Both measure the price level, but over different things. CPI tracks the cost of a fixed basket of consumer goods and services, so it answers "what has happened to household living costs?". The GDP deflator covers everything a country produces — consumer goods, capital equipment, government services, exports — and reweights continuously as the mix of output changes. Because their coverage and weighting differ, the two will report different inflation figures for the same period, and neither is wrong. CPI is the number central banks usually target and the one index-linked contracts reference; the deflator is what you use to convert nominal GDP into real GDP.
Link to this questionWhy does the real return calculation not just subtract inflation?
Subtracting is an approximation that is close enough at low inflation and increasingly wrong as inflation rises. The exact relationship divides rather than subtracts: real = ((1 + nominal) ÷ (1 + inflation) − 1). With a 7.5% return and 3.2% inflation, subtracting gives 4.3% while the exact form gives 4.17% — a small gap. At 20% nominal and 15% inflation, subtracting gives 5% while the correct figure is 4.35%. The tool uses the exact form throughout, which is why it may disagree slightly with a mental calculation.
Link to this questionWhy is the tax multiplier smaller than the spending multiplier?
Because the first round differs. When a government spends a pound, the whole pound enters the economy as demand. When it cuts taxes by a pound, households receive the pound but only spend a fraction of it — the marginal propensity to consume — and save the rest. That saved portion never enters the circular flow, so the chain of subsequent spending starts from a smaller base. The arithmetic reflects this exactly: the tax multiplier is always smaller in magnitude than the expenditure multiplier by precisely one. This asymmetry is the core of most arguments about whether a stimulus should be delivered through spending or tax cuts.
Link to this questionAre these multiplier figures realistic for a real economy?
No, and that is deliberate. These are the simple closed-economy multipliers, which assume saving is the only leakage from the circular flow. Real economies also leak through taxation and through imports, both of which reduce how much of each round is respent domestically. A simple multiplier of 4 from an MPC of 0.75 would be far lower once those leakages are included — empirical estimates for developed economies typically fall well below 2, and vary with the state of the economy and the type of spending. Use the figure here to understand the mechanism and the direction, not to forecast a policy outcome.
Link to this questionWhy does the unemployment rate sometimes fall for bad reasons?
Because the denominator is the labour force, not the population. The labour force counts people who are either employed or actively seeking work. Someone who gives up looking leaves the labour force entirely, so they disappear from both the numerator and the denominator — and the unemployment rate falls. That is why the participation rate matters as a companion figure. Unemployment falling while participation also falls usually indicates discouraged workers leaving the market rather than a strengthening jobs picture. Calculate both here and read them together.
Link to this questionCan I use this to value an investment or decide what to buy?
No. This is an educational tool that performs arithmetic on figures you supply. It contains no market data, makes no forecast, and offers no view on any asset, sector or product. Its purpose is to let you read an economic data release accurately — to see that a 5% nominal return in a 5% inflation year has gained nothing, or that a headline growth figure is nominal rather than real. Investment decisions depend on your own circumstances, objectives and tax position, and warrant regulated advice. Global Investments is not authorised by the Financial Conduct Authority.
Link to this question