Cross Price Elasticity Calculator

Background.

When a competitor raises its price, some of its customers drift to you; when the price of something your product is used with goes up, some of yours disappear. Cross-price elasticity puts a number on that link. It divides the percentage change in the quantity of one good by the percentage change in the price of another, and the sign tells you the relationship before the size does: positive for substitutes such as two brands of cola, negative for complements such as printers and ink cartridges, close to zero for goods that have little to do with each other.

The percentages here are taken by the midpoint, or arc, method: each change is measured against the average of the old and new values rather than against the starting value. That small choice makes the answer symmetric. A move from 100 units to 110 and a move from 110 back to 100 produce the same elasticity, which is not true if you divide by the starting point.

The page works from just two observations, before and after. That is enough to describe what happened, but not to prove why. If incomes rose, the season changed, or the first product's own price moved at the same time, the quantity change carries those effects too, and the elasticity will attribute all of it to the other good's price. Estimating a reliable elasticity from many data points, with the other influences held constant, is a regression exercise this page does not attempt.

What is cross price elasticity calculator?

Cross-price elasticity of demand is the ratio of the percentage change in the quantity demanded of one good to the percentage change in the price of a different good. A value of 0.5 means a 1% rise in the other good's price goes with about a 0.5% increase in this good's quantity. The arc version computed here measures both percentage changes against midpoints, so the result describes the whole stretch between two observations rather than one end of it.

How to use this calculator.

1. 01Enter the old and new quantity of the good whose sales you are tracking, in any consistent unit such as units sold per week. Both must be above zero.
2. 02Enter the old and new price of the other good, the competitor's or partner product's price, in the same currency for both. The two prices must differ, since an elasticity is undefined without a price change.
3. 03Choose periods that are otherwise comparable: the same length, the same season, and no change in your own price between them.
4. 04Read the sign first, positive for substitutes and negative for complements, then the size for how strongly the two goods are linked.

The formula.

E = [(Q2 − Q1) ÷ ((Q1 + Q2) ÷ 2)] ÷ [(P2 − P1) ÷ ((P1 + P2) ÷ 2)]. Q1 and Q2 are the quantities of the first good before and after; P1 and P2 are the other good's prices before and after. The top bracket is the quantity change as a fraction of the average quantity, the bottom bracket the price change as a fraction of the average price. Using averages means swapping before and after leaves the answer unchanged, and the result has no units because both brackets are pure ratios. The sign is set by the directions of the two changes: quantity and price moving together give a positive value, moving in opposite directions a negative one.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Principles of Finance, 2022. Chapters 6–10. Retrieved 2026-08-06.
2. [2]U.S. Internal Revenue Service. Tax guidance current 2026. Official forms, instructions and tax topics. Retrieved 2026-08-06.
3. [3]U.S. Securities and Exchange Commission. Investor.gov current 2026. Investment products and risk. Retrieved 2026-08-06.