Quick answer
Cross-price elasticity = % change in quantity of good A ÷ % change in the price of good B, using midpoints. A price rise from 2 to 2.5 with quantity rising from 100 to 120 gives 0.8182, meaning the goods are substitutes.
Enter the price of the other good before and after and the quantity of your good before and after. The calculator returns the elasticity and an 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. Income Elasticity of Demand Calculator: Income elasticity of demand by the midpoint (arc) method.
How to use the Cross-Price Elasticity 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 = 2; Price after = 2.5; Quantity before = 100; Quantity after = 120.
| Result | Value |
|---|---|
| Cross-Price Elasticity | 0.8182 |
| Interpretation | Substitutes (E > 0) |
Example 2
Inputs: Price before = 2; Price after = 2.5; Quantity before = 100; Quantity after = 85.
| Result | Value |
|---|---|
| Cross-Price Elasticity | -0.7297 |
| Interpretation | Complements (E < 0) |
The first line is the headline result (cross-Price Elasticity). Below it the cross-Price Elasticity Calculator lists interpretation, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Reading the sign
Positive: substitutes, as buyers switch to the cheaper alternative (tea when coffee gets dearer). Negative: complements that are used together (printers and ink). Near zero: unrelated. The magnitude shows how strong the link is.
The midpoint method
Percentage changes use the average of the start and end values: (120 − 100) ÷ 110 = 18.18% and (2.5 − 2) ÷ 2.25 = 22.22%, giving 0.8182. This makes the result the same whichever direction you calculate.
How the result changes with price before
Holding every other input at the first worked example, this table changes only price before. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Price before | Cross-Price Elasticity | Interpretation |
|---|---|---|
| 1 | 0.2121 | Substitutes (E > 0) |
| 2 | 0.8182 | Substitutes (E > 0) |
| 4 | -0.3939 | Complements (E < 0) |
| 8 | -0.1736 | Complements (E < 0) |
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 Cross-Price Elasticity 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 |
| [Income Elasticity of Demand Calculator](/business/income-elasticity-demand/) | income before, income after and quantity before | Income Elasticity of Demand |
| [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
Can it be greater than 1?
Yes, for close substitutes.
What if the price did not change?
The calculator needs two different prices.
Is it the same as own-price elasticity?
No, that uses the good's own price.
What does the Cross-Price Elasticity Calculator calculate?
Cross-price elasticity (price of the other good) by the midpoint (arc) method. It returns Cross-Price Elasticity and Interpretation.
What formula does the Cross-Price Elasticity 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 cross-Price Elasticity 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 cross-Price Elasticity result?
With price before 2, price after 2.5, quantity before 100 and quantity after 120, the cross-Price Elasticity is 0.8182.
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.
- Income Elasticity of Demand Calculator — Income elasticity of demand 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.