What is the cross price elasticity?
Type two prices of one good and the quantities of another good at those prices. The cross price elasticity calculator applies the cross price elasticity formula with the midpoint method and says whether the goods are substitutes or complements.
- Cross price elasticity
- 0.8182
The cross price elasticity is 0.8182: the goods are substitutes.
- The goods are
- substitutes
- % change in quantity of good A
- 18.18%
- % change in price of good B
- 22.22%
Cross price elasticity: 0.8182. The cross price elasticity is 0.8182: the goods are substitutes.
The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use
How to calculate
Finds the cross price elasticity of demand by the midpoint method from two prices of one good and the quantities of another, and says whether the goods are substitutes or complements.
Example with the default inputs (Starting price of good B $4.00, New price of good B $5.00, Starting quantity of good A 200, New quantity of good A 240): The cross price elasticity is 0.8182: the goods are substitutes.
Method: Elasticity = (% change in quantity of good A) ÷ (% change in price of good B), where each % change = (new − old) ÷ ((new + old) ÷ 2) × 100 (the midpoint method).
- The midpoint (arc) method, so going from A to B gives the same elasticity as going from B to A.
- Everything else that affects demand for good A stays the same between the two points.
- Prices are at least $0.01; quantities are 0 or more, not both 0.
Worked examples
Each example is checked against the calculator on every build.
- Starting price of good B $4.00, New price of good B $5.00, Starting quantity of good A 200, New quantity of good A 240 gives Cross price elasticity 0.8182, The goods are substitutes, % change in quantity of good A 18.18%, % change in price of good B 22.22%.Source: OpenStax, Principles of Economics 3e, section 5.4 Elasticity in Areas Other Than Price (cross-price elasticity of demand = % change in Qd of good A ÷ % change in price of good B; substitutes positive, complements negative), https://openstax.org/books/principles-economics-3e/pages/5-4-elasticity-in-areas-other-than-price (retrieved 2026-11-01); OpenStax, Principles of Economics 3e, section 5.1 (midpoint method), https://openstax.org/books/principles-economics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply (retrieved 2026-11-01)
- Starting price of good B $2.50, New price of good B $3.00, Starting quantity of good A 100, New quantity of good A 80 gives Cross price elasticity −1.2222, The goods are complements, % change in quantity of good A −22.22%, % change in price of good B 18.18%.Source: OpenStax, Principles of Economics 3e, section 5.4 Elasticity in Areas Other Than Price (cross-price elasticity of demand = % change in Qd of good A ÷ % change in price of good B; substitutes positive, complements negative), https://openstax.org/books/principles-economics-3e/pages/5-4-elasticity-in-areas-other-than-price (retrieved 2026-11-01); OpenStax, Principles of Economics 3e, section 5.1 (midpoint method), https://openstax.org/books/principles-economics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply (retrieved 2026-11-01)
- Starting price of good B $4.00, New price of good B $5.00, Starting quantity of good A 50, New quantity of good A 50 gives Cross price elasticity 0, The goods are neither: the quantity did not change.Source: OpenStax, Principles of Economics 3e, section 5.1 (midpoint method), https://openstax.org/books/principles-economics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply (retrieved 2026-11-01)
How it works
With prices P₁ and P₂ of good B, and quantities Q₁ and Q₂ of good A:
- % change in quantity of good A = (Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2) × 100
- % change in price of good B = (P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2) × 100
- Cross price elasticity = % change in quantity ÷ % change in price, with its sign
- The goods are substitutes when it is positive, complements when it is negative, and "neither: the quantity did not change" when it is exactly 0.
Rules
- Prices are $0.01 to $1 trillion. Quantities are 0 to 10¹⁵.
- With two equal prices there is no answer, with the message "The two prices are the same. Elasticity needs a change in price."
- With both quantities 0 there is no answer, with the message "Both quantities are 0, so there is no average quantity to compare."
- Each % change is exact on the decimals as typed; the elasticity is an exact fraction, rounded once for display. Its sign and its class are read from that exact fraction.
- The elasticity shows up to 4 decimals and each percent change up to 2, rounded half up.
Worked examples by hand
Coffee $4 to $5, tea 200 to 240. % change in quantity = 40 ÷ 220 × 100 = 18.18%; % change in price = 1 ÷ 4.5 × 100 = 22.22%. Elasticity = 0.8182: substitutes.
Price $2.50 to $3, quantity 100 to 80. % change in quantity = −20 ÷ 90 × 100 = −22.22%; % change in price = 0.5 ÷ 2.75 × 100 = 18.18%. Elasticity = −1.2222: complements.
Price $4 to $5, quantity 50 both times. Elasticity = 0: neither: the quantity did not change.
Other questions people ask
What is cross price elasticity of demand?
It measures how the quantity of one good responds to a change in the price of another: the percent change in the quantity of good A divided by the percent change in the price of good B.
How do I calculate cross price elasticity?
If coffee rises from $4 to $5 and tea sales rise from 200 to 240, the % change in tea is 40 ÷ 220 = 18.18% and the % change in coffee’s price is 1 ÷ 4.5 = 22.22%. The cross price elasticity is 18.18 ÷ 22.22 = 0.8182.
What does a positive cross price elasticity mean?
The goods are substitutes: when one gets more expensive, buyers want more of the other.
What does a negative cross price elasticity mean?
The goods are complements: they are used together, so when one gets more expensive, buyers want less of the other.
Why does this page use the midpoint method?
Each percent change is measured against the average of the two values, so a move from A to B gives the same result as a move from B to A. OpenStax defines the method in section 5.1, and this page applies it to the formula in section 5.4.
Why is the sign kept here?
The sign is the point of this measure, since it separates substitutes from complements. So unlike price elasticity of demand, it is not shown as an absolute value.