Cross-Price Elasticity of Demand Calculator (substitutes or complements)

Understanding the cross-price elasticity of demand calculator — concept and principle

This calculator measures how the demand for one good responds to a change in the price of another, and tells you whether the two are substitutes, complements or unrelated. It uses the midpoint method and also shows the simple-percentage version for comparison. Economics students use it for exercises; marketers and pricing analysts use it to see how a competitor's or a related product's price affects their sales.

B gets dearer → more A sold — with the default inputs: +0.81.

How it is calculated

% change in quantity of A = (QA2 − QA1) ÷ ((QA1 + QA2) ÷ 2) × 100
% change in price of B = (PB2 − PB1) ÷ ((PB1 + PB2) ÷ 2) × 100
Cross-price elasticity = % change in quantity of A ÷ % change in price of B
Simple version = ((QA2 − QA1) ÷ QA1) ÷ ((PB2 − PB1) ÷ PB1)

Positive: substitutes. Negative: complements. Zero: unrelated.

The principle

If B becomes dearer and people switch to A, demand for A rises with B's price: the goods are substitutes, like coffee and tea, and the elasticity is positive. If B becomes dearer and people buy less A too, because they are used together, the goods are complements, like coffee and sugar, and the elasticity is negative. The midpoint method divides each change by the average of the two values, so you get the same answer whichever point you start from.

Worked example

Defaults: B's price rises from 4.00 to 4.40; quantity of A rises from 1,000 to 1,080.

% change in A = 80 ÷ 1,040 × 100 = 7.7%.
% change in B's price = 0.40 ÷ 4.20 × 100 = 9.5%.
Elasticity = 7.69 ÷ 9.52 = 0.81, so the goods are Substitutes (positive).
Simple version = (80 ÷ 1,000) ÷ (0.40 ÷ 4.00) = 0.08 ÷ 0.10 = 0.8.

Each point is the calculator re-run with only “Quantity of good A demanded after” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Quantity of good A demanded after	Cross-price elasticity (midpoint)
270	-12.07
540	-6.27
810	-2.2
1,080	0.81
1,350	3.13
1,620	4.97
2,160	7.71

How to read the result

The sign tells you the relationship; the size tells you its strength. Here a 1% rise in B's price raises demand for A by about 0.8%, a fairly strong substitute. Values close to zero mean the price of B hardly matters for A. A firm selling A would expect to gain customers when B's price rises, and lose them when B is discounted.

Common mistakes

Swapping the goods: the quantity is of A, the price is of B.
Reading the size without the sign, or the sign without the size.
Ignoring other changes in the period, such as income or advertising.
Comparing midpoint and simple elasticities from different sources.

Keep in mind: Two observations give only a rough estimate. Real demand responds to many factors at once, so treat the result as indicative.

Frequently asked questions

Is a positive cross-price elasticity good?

It is neither good nor bad; it means the goods are substitutes. For a seller, it shows which competitors' prices matter.

Why use the midpoint method?

It gives the same elasticity whether the price rises or falls between the same two points.

Can cross-price elasticity be greater than 1?

Yes. Close substitutes often have values above 1, meaning demand for A responds more than proportionally.

Sources: OpenStax, Principles of Economics, 3rd ed., section 5.4 "Elasticity in Areas Other Than Price"

Checked 9 Nov 2026. Cross-price elasticity = % change in Qd of good A ÷ % change in price of good B; positive for substitutes, negative for complements: OpenStax, “Principles of Economics”, 3rd ed. (2022), section 5.4 “Elasticity in Areas Other Than Price”. Midpoint percentage changes: same book, section 5.1 “Price Elasticity of Demand and Price Elasticity of Supply”.

Your numbers