Price Elasticity of Demand Calculator

Article — Price Elasticity of Demand Calculator

Price elasticity of demand calculator: PED, revenue, and the midpoint method

Price elasticity of demand (PED) equals the percentage change in quantity demanded divided by the percentage change in price. PED is almost always negative, so economists report and classify the absolute value: |PED| greater than 1 is elastic, |PED| less than 1 is inelastic, and |PED| = 1 is unit elastic. The midpoint (arc) method, which uses the averages of the two prices and two quantities as the base, is the version textbooks recommend whenever the price change is more than a few percent.

Enter the price and quantity before the change, then the price and quantity after. The calculator returns PED to two decimal places, classifies the result, and shows the revenue figures so the total-revenue test is one glance away. Switch between midpoint and point methods at the top.

What price elasticity of demand measures

Price elasticity of demand is a unitless number that captures how strongly buyers respond to a price change. A PED of -2 says a 1% price rise drops quantity by 2%; a PED of -0.3 says the same price rise cuts quantity by only 0.3%. Alfred Marshall introduced the elasticity concept in Principles of Economics (1890). The strength of the construct is that elasticity, a ratio of percentages, does not depend on the units chosen, which is why the gasoline figure of -0.25 travels across countries and academic studies.

The price elasticity of demand formula

The basic formula is the ratio of two percentage changes. The numerator is the percentage change in quantity demanded; the denominator is the percentage change in price. Two specifications dominate the textbooks.

A worked example: a coffee shop raises a latte from $5.00 to $5.50 and sees demand fall from 200 cups a day to 180 cups. The midpoint percentage change in price is 0.50 / 5.25 = 9.52%. The midpoint percentage change in quantity is -20 / 190 = -10.53%. PED is -10.53% / 9.52% = -1.11. The good is elastic, and the total-revenue test predicts a revenue fall: 200 × $5.00 = $1,000 before, 180 × $5.50 = $990 after. The 1% revenue dip matches the elastic classification.

Midpoint method vs point elasticity

The point method uses the starting values as the base. It is fast to compute but asymmetric: a $10-to-$12 price rise produces a different elasticity than a $12-to-$10 drop. The midpoint method, also called arc elasticity, uses the averages of the two prices and quantities. The result is symmetric and is the version every introductory textbook (Mankiw, Krugman, Perloff), Khan Academy, and MIT OpenCourseWare use for worked examples. Use the point method only for very small price changes.

Elastic vs inelastic demand bands

Marshall's three-band classification is straightforward and is still how every introductory textbook frames the topic. Inelastic goods (|PED| less than 1) see only small quantity changes when prices move; necessities, addictive goods, and goods without substitutes fall here. Elastic goods (|PED| more than 1) see large quantity moves; luxuries, branded products with generic alternatives, and discretionary services fall here.

• Perfectly inelastic |PED| = 0: quantity unchanged at any price (theoretical limit, life-saving drugs come close)
• Inelastic |PED| 0 to 1: salt, gasoline short-run, electricity, cigarettes
• Unit elastic |PED| = 1: revenue unchanged by price moves (boundary)
• Elastic |PED| 1 to infinity: restaurant meals, airline tickets, new cars, branded cereals
• Perfectly elastic |PED| = infinity: any price rise zeros demand (theoretical, identical commodities)

Price elasticity and the total revenue test

The total revenue test is the practical use of PED. Total revenue equals price times quantity, so when price changes, revenue moves with whichever percentage change is larger. If |PED| is greater than 1, the quantity drop dominates and revenue falls when price rises. If |PED| is less than 1, revenue rises when price rises.

The Federal Reserve uses this framework when analyzing how energy price shocks transmit through the economy: inelastic short-run gasoline demand means rising prices act as a tax on household budgets and reshuffle spending out of other categories.

Price elasticity by category of good

Empirical PED estimates come from controlled price experiments, natural experiments (tax changes, supply shocks), and structural econometric models. The numbers below are mid-range textbook values rather than single-study results, because PED varies with the time horizon, the substitutes available, and the share of the consumer's budget the good occupies.

The pattern across categories is consistent: goods with close substitutes or large budget shares are elastic, while necessities and addictive goods are inelastic. Time horizon matters too — elasticity grows as consumers find substitutes or replace durable goods.

Common price-elasticity mistakes

The most common mistake is ignoring the sign. A PED of -2 is elastic, not "more negative than -1" in an ambiguous sense. Always classify on the absolute value and remember that the law of demand makes negative the expected sign.

The second mistake is using the point method for large price changes. A 50% price experiment produces a meaningfully different elasticity in one direction than the other under the point method; the midpoint method removes that artifact and is what published studies use.

The third mistake is extrapolating a single elasticity estimate to a price range outside what was measured. PED is a local property of the demand curve. An estimate from a price range of $4 to $6 cannot predict behavior at $2 or $10 without extra assumptions. The fourth is confusing own-price elasticity with cross-price elasticity (sensitivity of A's demand to B's price) or income elasticity (sensitivity to income changes). The three are separate concepts with different formulas and different uses.