Price elasticity calculator — PED & cross-price elasticity

Midpoint (arc) formula: PED = (%ΔQ / average Q) ÷ (%ΔP / average P). It uses averages so the answer does not flip when you reverse the direction of the change.

Example: Price rises from $10 to $12 and quantity falls from 100 to 80. %ΔQ = −20/90 = −22.22%; %ΔP = 2/11 = 18.18%; PED ≈ −1.22 (elastic). Total revenue falls from $1,000 to $960.

Load the Textbook (elastic) preset in the calculator to reproduce this example instantly.

Use the absolute value |PED| to classify demand (economics classes often report magnitude as a positive number — toggle that in Advanced):

• |PED| > 1 — elastic: quantity is relatively responsive to price
• |PED| = 1 — unit elastic: proportional response
• |PED| < 1 — inelastic: quantity is relatively unresponsive
• |PED| = 0 — perfectly inelastic (theoretical)

The calculator labels your result automatically and shows step-by-step midpoint math.

PED is not fixed forever — it depends on context. The main determinants economists use in exams and pricing analysis:

• Substitutes — more close substitutes → more elastic demand
• Necessity vs luxury — essentials tend to be inelastic
• Share of income — expensive items (as a % of budget) tend to be more elastic
• Time horizon — demand is usually more elastic in the long run
• Market definition — narrow markets (one brand) are often more elastic than broad categories

For competitive structure (how concentrated a market is), pair elasticity with our HHI calculator. For generic percentage math behind %ΔQ and %ΔP, use the percentage calculator.

Total revenue = price × quantity. The total revenue test links elasticity to pricing decisions for retail, SaaS, and menu pricing:

• If demand is elastic (|PED| > 1), price and total revenue move in opposite directions — a price cut can raise revenue.
• If demand is inelastic (|PED| < 1), price and total revenue move in the same direction — a price increase can raise revenue.

The calculator shows revenue before and after for PED mode. For margin after a price change, use our profit margin calculator or break-even calculator.

Cross-price elasticity (XED) measures how demand for product B changes when the price of product A changes. Switch to Cross-price elasticity mode in the calculator above.

Positive XED → substitutes (when A gets pricier, B sells more). Negative XED → complements (when A gets pricier, B sells less). Near zero → weak or no relationship.

This is different from price elasticity of supply — supply elasticity measures how quantity supplied responds to a product’s own price, not a related good. For market-structure context, see our HHI calculator or comparative advantage calculator.

The midpoint method (also called arc elasticity) is the safest default for homework, AP Microeconomics, and university exams because it is direction-neutral. The simple percentage method divides by the initial value only — reversing the price change can give a different number.

Use Direct % changes when a problem already gives percentage changes (e.g. price −10%, quantity +20%). Use Point elasticity when you have a linear demand function Q = a − bP and need elasticity at one price.

For a linear demand curve Q = a − bP, point elasticity at price P is PED = (dQ/dP) × (P/Q) = (−b) × (P/Q). On a straight-line demand curve, elasticity varies by price: above the midpoint price tends to be elastic; below tends to be inelastic.

Example: Q = 100 − 2P at P = 20 → Q = 60 → PED = (−2) × (20/60) = −0.67 (inelastic at that point).