Quick answer
Price elasticity of demand by the midpoint (arc) method. Enter price before, price after, quantity before and quantity after and the price elasticity of demand calculator returns price Elasticity of Demand and interpretation.
Related tools: Income Elasticity of Demand Calculator: Income 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 Price Elasticity of Demand Calculator
- Enter price before (above 0).
- Enter price 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 |
|---|---|---|
| Price before | A number | > 0 |
| Price 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: Price before = 10; Price after = 12; Quantity before = 100; Quantity after = 90.
| Result | Value |
|---|---|
| Price Elasticity of Demand | -0.5789 |
| Interpretation | Inelastic (|E| < 1) |
Example 2
Inputs: Price before = 5; Price after = 4; Quantity before = 200; Quantity after = 260.
| Result | Value |
|---|---|
| Price Elasticity of Demand | -1.1739 |
| Interpretation | Elastic (|E| > 1) |
The first line is the headline result (price Elasticity of Demand). Below it the price Elasticity of Demand Calculator lists interpretation, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Reading the number
Price elasticity of demand compares the percentage change in quantity demanded with the percentage change in price. It is normally negative, because higher prices reduce demand. Ignoring the sign: above 1 the demand is elastic (buyers are sensitive to price), below 1 it is inelastic, and 1 is unit elastic. Essentials with few substitutes tend to be inelastic.
A price rise from 10 to 12 with different falls in quantity
Every figure in this table comes from running this calculator, so it matches what the form returns.
| Quantity after | Price Elasticity of Demand | Interpretation |
|---|---|---|
| 95 | -0.2821 | Inelastic (|E| < 1) |
| 90 | -0.5789 | Inelastic (|E| < 1) |
| 80 | -1.2222 | Elastic (|E| > 1) |
| 60 | -2.75 | Elastic (|E| > 1) |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Price after: entering "10" shows "The two values must be different." beside that field and no result.
- Price before: entering "0" shows "Price before must be greater than 0." beside that field and no result.
Choosing between the Price 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 |
|---|---|---|
| [Income Elasticity of Demand Calculator](/business/income-elasticity-demand/) | income before, income after and quantity before | Income 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 price after and price before to confirm this.
Frequently asked questions
What does the Price Elasticity of Demand Calculator calculate?
Price elasticity of demand by the midpoint (arc) method. It returns Price Elasticity of Demand and Interpretation.
What formula does the Price 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 price Elasticity of Demand Calculator?
You enter Price before, Price 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 price Elasticity of Demand result?
With price before 10, price after 12, quantity before 100 and quantity after 90, the price Elasticity of Demand is -0.5789.
Where does the method come from?
The method follows: OpenStax, Principles of Economics 3e (Rice University): elasticity (price elasticity of demand).
Related calculators
- Income Elasticity of Demand Calculator — Income 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
- OpenStax, Principles of Economics 3e (Rice University): elasticity (price elasticity of demand)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.