Quick answer
Income elasticity of demand = % change in quantity demanded ÷ % change in income, using midpoints. Income rising from 30,000 to 36,000 while quantity rises from 100 to 112 gives 0.6226, a normal good.
Enter income before and after and the quantity before and after. The calculator returns the elasticity and its interpretation.
Related tools: Price Elasticity of Demand Calculator: Price elasticity of demand by the midpoint (arc) method. Price Elasticity of Supply Calculator: Price elasticity of supply by the midpoint (arc) method. Cross-Price Elasticity Calculator: Cross-price elasticity (price of the other good) by the midpoint (arc) method.
How to use the Income Elasticity of Demand Calculator
- Enter income before (above 0).
- Enter income after (above 0).
- Enter quantity before (above 0).
- Enter quantity after (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Income before | A number | > 0 |
| Income after | A number | > 0 |
| Quantity before | A number | > 0 |
| Quantity after | A number | > 0 |
Formula and method
Formula
E = [(Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2)] ÷ [(X₂ − X₁) ÷ ((X₁ + X₂) ÷ 2)]
IEEE-754 double precision; shown to the decimals indicated.
The midpoint method gives the same value whichever direction the change is measured.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Income before = 30000; Income after = 36000; Quantity before = 100; Quantity after = 112.
| Result | Value |
|---|---|
| Income Elasticity of Demand | 0.6226 |
| Interpretation | Normal good (0 < E ≤ 1) |
Example 2
Inputs: Income before = 20000; Income after = 25000; Quantity before = 80; Quantity after = 70.
| Result | Value |
|---|---|
| Income Elasticity of Demand | -0.6 |
| Interpretation | Inferior good (E < 0) |
The first line is the headline result (income Elasticity of Demand). Below it the income Elasticity of Demand Calculator lists interpretation, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Interpreting the value
Between 0 and 1: a normal necessity, demand rises less than income. Above 1: a luxury good. Negative: an inferior good that people buy less of as they earn more. 0.6226 means a 10% income rise raises demand about 6.2%.
Midpoint arithmetic
Quantity change: 12 ÷ 106 = 11.32%. Income change: 6,000 ÷ 33,000 = 18.18%. The ratio is 0.6226. The two incomes must differ.
How the result changes with income before
Holding every other input at the first worked example, this table changes only income before. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Income before | Income Elasticity of Demand | Interpretation |
|---|---|---|
| 15000 | 0.1375 | Normal good (0 < E ≤ 1) |
| 30000 | 0.6226 | Normal good (0 < E ≤ 1) |
| 60000 | -0.2264 | Inferior good (E < 0) |
| 120000 | -0.1051 | Inferior good (E < 0) |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Income after: entering "10" shows "The two values must be different." beside that field and no result.
- Income before: entering "0" shows "Income before must be greater than 0." beside that field and no result.
Choosing between the Income Elasticity of Demand Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Price Elasticity of Demand Calculator](/business/price-elasticity-demand/) | price before, price after and quantity before | Price Elasticity of Demand |
| [Price Elasticity of Supply Calculator](/business/price-elasticity-of-supply-calculator/) | price before, price after and quantity before | Price Elasticity of Supply |
| [Cross-Price Elasticity Calculator](/business/cross-price-elasticity-calculator/) | price before, price after and quantity before | Cross-Price Elasticity |
| [GDP Calculator](/business/gdp-calculator/) | consumption, investment and government spending | GDP |
| [Marginal Cost Calculator](/business/marginal-cost/) | total cost before, total cost after and quantity before | Marginal cost |
Background: business metrics
Business ratios depend on exactly which costs and revenues you include, so read each page's definition. Two common checks: break-even units = fixed costs ÷ (price − variable cost per unit), so $50,000 of fixed costs with a $10 price and $5 variable cost breaks even at 10,000 units; and net profit margin = net profit ÷ revenue, so $20,000 profit on $100,000 revenue is 20%.
Return on investment ignores time: 20% over five years is far less impressive than 20% in one, so compare returns over the same period.
Assumptions and limitations
- The two values of the driver must differ
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for income after and income before to confirm this.
Frequently asked questions
Is a luxury good elastic?
Yes, with income elasticity above 1.
Give an example of an inferior good.
Instant noodles or public transit in some markets.
Can I use percentages directly?
Use the before and after values; the calculator computes the changes.
What does the Income Elasticity of Demand Calculator calculate?
Income elasticity of demand by the midpoint (arc) method. It returns Income Elasticity of Demand and Interpretation.
What formula does the Income Elasticity of Demand Calculator use?
E = [(Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2)] ÷ [(X₂ − X₁) ÷ ((X₁ + X₂) ÷ 2)]. The midpoint method gives the same value whichever direction the change is measured.
What do I need to enter in the income Elasticity of Demand Calculator?
You enter Income before, Income after, Quantity before and Quantity after.
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. The two values of the driver must differ.
What is an example of a income Elasticity of Demand result?
With income before 30000, income after 36000, quantity before 100 and quantity after 112, the income Elasticity of Demand is 0.6226.
Where does the method come from?
The method follows: Midpoint (arc) elasticity, e.g. Mankiw, Principles of Economics.
Related calculators
- Price Elasticity of Demand Calculator — Price elasticity of demand by the midpoint (arc) method.
- Price Elasticity of Supply Calculator — Price elasticity of supply by the midpoint (arc) method.
- Cross-Price Elasticity Calculator — Cross-price elasticity (price of the other good) by the midpoint (arc) method.
- GDP Calculator — Gross domestic product by the expenditure approach.
- Marginal Cost Calculator — Extra cost of producing additional units.
- Marginal Revenue Calculator — Extra revenue from selling additional units.
Sources
- Midpoint (arc) elasticity, e.g. Mankiw, Principles of Economics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.