Free formula sheets
Every formula you need for AP, A-Level, IB and first-year university economics and statistics, with a one-line note on what each one tells you. Print it, or keep this page open while you revise.
Microeconomics formulas
| Concept | Formula | What it tells you |
|---|---|---|
| Price elasticity of demand | \( PED=\dfrac{\%\Delta Q_d}{\%\Delta P} \) | |PED| > 1 elastic, < 1 inelastic, = 1 unit elastic |
| Percentage change | \( \%\Delta X=\dfrac{X_{new}-X_{old}}{X_{old}}\times 100 \) | Use the starting value as the base |
| Midpoint (arc) elasticity | \( PED=\dfrac{(Q_2-Q_1)/\tfrac{1}{2}(Q_1+Q_2)}{(P_2-P_1)/\tfrac{1}{2}(P_1+P_2)} \) | Same answer whichever way the price moves |
| Income elasticity of demand | \( YED=\dfrac{\%\Delta Q_d}{\%\Delta Y} \) | Positive: normal good; negative: inferior good; > 1: luxury |
| Cross elasticity of demand | \( XED=\dfrac{\%\Delta Q_{d,A}}{\%\Delta P_B} \) | Positive: substitutes; negative: complements |
| Price elasticity of supply | \( PES=\dfrac{\%\Delta Q_s}{\%\Delta P} \) | How quickly producers can respond |
| Total revenue | \( TR=P\times Q \) | Rises with a price cut only if demand is elastic |
| Opportunity cost | \( \text{OC of }X=\dfrac{\text{units of }Y\text{ given up}}{\text{units of }X\text{ gained}} \) | Lower opportunity cost = comparative advantage |
| Consumer surplus (linear demand) | \( CS=\tfrac{1}{2}\times Q^*\times(P_{max}-P^*) \) | Area of the triangle under demand, above price |
| Total cost | \( TC=TFC+TVC \) | Fixed costs do not change with output |
| Average total cost | \( ATC=\dfrac{TC}{Q}=AFC+AVC \) | |
| Marginal cost | \( MC=\dfrac{\Delta TC}{\Delta Q} \) | Cuts AVC and ATC at their minimum |
| Marginal revenue | \( MR=\dfrac{\Delta TR}{\Delta Q} \) | |
| Profit | \( \pi=TR-TC=(P-ATC)\times Q \) | Normal profit when P = ATC |
| Profit-maximising rule | \( MR=MC \) | Holds for every market structure |
| Shutdown rule (short run) | \( P<AVC\Rightarrow\text{shut down} \) | Long run: exit if P < ATC |
| Lerner index | \( L=\dfrac{P-MC}{P} \) | 0 under perfect competition |
| Concentration ratio | \( CR_n=\text{sum of the top }n\text{ firms\’ market shares} \) | CR4 above 60% suggests oligopoly |
| Marginal revenue product of labour | \( MRP_L=MP_L\times MR \) | Firms hire until MRP = wage |
| Tax incidence | \( \text{consumer share}=\dfrac{PES}{PES+|PED|} \) | The less elastic side pays more of the tax |
Learn each formula with worked examples in the step-by-step guide.
Macroeconomics formulas
| Concept | Formula | What it tells you |
|---|---|---|
| GDP (expenditure method) | \( Y=C+I+G+(X-M) \) | |
| Real GDP | \( \text{Real GDP}=\dfrac{\text{Nominal GDP}}{\text{Deflator}}\times 100 \) | |
| GDP per capita | \( \dfrac{\text{GDP}}{\text{population}} \) | |
| Growth rate | \( g=\dfrac{Y_t-Y_{t-1}}{Y_{t-1}}\times 100 \) | |
| Rule of 70 | \( \text{doubling time}\approx\dfrac{70}{g} \) | g in percent per year |
| Unemployment rate | \( u=\dfrac{\text{unemployed}}{\text{labour force}}\times 100 \) | Labour force = employed + unemployed |
| Participation rate | \( \dfrac{\text{labour force}}{\text{working-age population}}\times 100 \) | |
| Inflation rate | \( \pi=\dfrac{CPI_t-CPI_{t-1}}{CPI_{t-1}}\times 100 \) | |
| Price index | \( CPI=\dfrac{\text{cost of basket now}}{\text{cost of basket in base year}}\times 100 \) | Base year = 100 |
| Real interest rate (Fisher) | \( r\approx i-\pi^e \) | |
| Marginal propensities | \( MPC+MPS=1 \) | With taxes and imports: MPC + MPS + MPT + MPM = 1 |
| Spending multiplier | \( k=\dfrac{1}{1-MPC}=\dfrac{1}{MPS} \) | |
| Open-economy multiplier | \( k=\dfrac{1}{MPS+MPT+MPM} \) | Leakages shrink the multiplier |
| Tax multiplier | \( k_T=\dfrac{-MPC}{1-MPC} \) | Smaller than the spending multiplier |
| Change in GDP | \( \Delta Y=k\times\Delta\text{AD injection} \) | |
| Money multiplier | \( m=\dfrac{1}{rr} \) | rr = required reserve ratio |
| Quantity theory of money | \( MV=PQ \) | |
| Budget balance | \( \text{balance}=T-G \) | Negative = deficit |
| Current account | \( CA=(X-M)+\text{net primary income}+\text{net transfers} \) | |
| Terms of trade | \( ToT=\dfrac{\text{export price index}}{\text{import price index}}\times 100 \) | |
| Okun’s law (rule of thumb) | \( \Delta u\approx -\tfrac{1}{2}(g-g^*) \) | g* = trend growth |
Learn each formula with worked examples in the step-by-step guide.
Statistics formulas
| Concept | Formula | What it tells you |
|---|---|---|
| Mean | \( \bar{x}=\dfrac{\sum x_i}{n} \) | |
| Weighted mean | \( \bar{x}_w=\dfrac{\sum w_ix_i}{\sum w_i} \) | |
| Variance (sample) | \( s^2=\dfrac{\sum (x_i-\bar{x})^2}{n-1} \) | |
| Standard deviation | \( s=\sqrt{s^2} \) | |
| Interquartile range | \( IQR=Q_3-Q_1 \) | Outliers: below Q1 − 1.5·IQR or above Q3 + 1.5·IQR |
| Coefficient of variation | \( CV=\dfrac{s}{\bar{x}}\times 100 \) | |
| z-score | \( z=\dfrac{x-\mu}{\sigma} \) | How many standard deviations from the mean |
| Addition rule | \( P(A\cup B)=P(A)+P(B)-P(A\cap B) \) | |
| Multiplication rule | \( P(A\cap B)=P(A)\,P(B\mid A) \) | Independent: P(A)P(B) |
| Conditional probability | \( P(A\mid B)=\dfrac{P(A\cap B)}{P(B)} \) | |
| Expected value | \( E(X)=\sum x\,P(x) \) | |
| Variance of X | \( Var(X)=\sum (x-\mu)^2P(x) \) | |
| Binomial probability | \( P(X=k)=\binom{n}{k}p^k(1-p)^{n-k} \) | Mean np, variance np(1 − p) |
| Standard error of the mean | \( SE=\dfrac{\sigma}{\sqrt{n}} \) | Central limit theorem: sample means are near-normal for large n |
| Standard error of a proportion | \( SE=\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}} \) | |
| Confidence interval (mean) | \( \bar{x}\pm t^*\dfrac{s}{\sqrt{n}} \) | Use z* when σ is known |
| Confidence interval (proportion) | \( \hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}} \) | 95%: z* = 1.96 |
| One-sample t statistic | \( t=\dfrac{\bar{x}-\mu_0}{s/\sqrt{n}} \) | df = n − 1 |
| Two-sample t statistic | \( t=\dfrac{\bar{x}_1-\bar{x}_2}{\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2}}} \) | |
| Chi-square statistic | \( \chi^2=\sum\dfrac{(O-E)^2}{E} \) | Expected count: row total × column total ÷ grand total |
| Correlation | \( r=\dfrac{1}{n-1}\sum\left(\dfrac{x_i-\bar{x}}{s_x}\right)\left(\dfrac{y_i-\bar{y}}{s_y}\right) \) | −1 ≤ r ≤ 1 |
| Regression slope | \( b_1=r\dfrac{s_y}{s_x} \) | |
| Regression intercept | \( b_0=\bar{y}-b_1\bar{x} \) | Line: ŷ = b0 + b1x |
| Coefficient of determination | \( R^2=1-\dfrac{SS_{res}}{SS_{tot}} \) | Share of variation in y explained |
| ANOVA F statistic | \( F=\dfrac{MS_{between}}{MS_{within}} \) |
Learn each formula with worked examples in the step-by-step guide.
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