Price Elasticity of Demand Calculator

Calculate price elasticity of demand (PED) using the midpoint or point method. Enter two price–quantity pairs to find elasticity and classify demand.

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$
$
≥ 0

Results

%
%

Revenue insight: when demand is elastic (|PED| > 1), a price cut raises total revenue — the gain in quantity more than offsets the lower price. When demand is inelastic (|PED| < 1), a price cut reduces total revenue.

Price elasticity of demand is a theoretical measure derived from two observed price–quantity pairs. Real-world demand curves are rarely linear; elasticity typically varies along the curve. This tool is for educational and analytical purposes only, not as a basis for pricing decisions without additional market research.

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What is price elasticity of demand?

Price elasticity of demand (PED) is the ratio of the percentage change in quantity demanded to the percentage change in price. It measures how responsive consumer demand for a good is to a change in its price: a PED of −2 means a 1% price increase reduces quantity demanded by 2%. Under the law of demand, price and quantity move in opposite directions, so PED is normally negative; the absolute value is what determines the elasticity category.

The two formulas

Point method

The simplest form uses the initial value as the base:

PED=(Q1−Q0)/Q0(P1−P0)/P0\text{PED} = \frac{(Q_1 - Q_0) / Q_0}{(P_1 - P_0) / P_0}

The limitation is that measuring from $10 to $12 gives a different result than measuring from $12 back to $10 (a 20% price rise vs. a 16.7% price fall). The same real-world change produces two different elasticity numbers depending on the direction of measurement.

Midpoint (arc) method

The textbook standard divides by the average of the two values:

PED=(Q1−Q0) / Q‾(P1−P0) / P‾whereQ‾=Q0+Q12,P‾=P0+P12\text{PED} = \frac{(Q_1 - Q_0) \,/\, \overline{Q}}{(P_1 - P_0) \,/\, \overline{P}} \quad\text{where}\quad \overline{Q} = \frac{Q_0+Q_1}{2},\quad \overline{P} = \frac{P_0+P_1}{2}

Because the denominator is symmetric, measuring in either direction gives the same result. The midpoint method is the default choice unless the initial point is specifically required as the base.

Interpreting the result

PED rangeClassificationWhat it means
0Perfectly inelasticQuantity does not respond to price at all
0 < |PED| < 1InelasticQuantity changes less than proportionally
|PED| = 1Unit elasticQuantity changes by the same proportion as price
|PED| > 1ElasticQuantity changes more than proportionally

PED is typically negative under the law of demand (price up → quantity down). Economists often discuss the absolute value when classifying elasticity.

Worked example

A coffee shop raises the price of a latte from $4.50 to $5.00. Weekly orders fall from 840 to 780.

Midpoint method:

  • %ΔQ = (780 − 840) / ((840 + 780) / 2) = −60 / 810 ≈ −7.41%
  • %ΔP = (5.00 − 4.50) / ((4.50 + 5.00) / 2) = 0.50 / 4.75 ≈ 10.53%
  • PED = −7.41% / 10.53% ≈ −0.70

|PED| = 0.70 < 1 → demand is inelastic. Consumers are not very price-sensitive for their morning coffee, so the price rise increases total revenue despite the drop in orders.

Revenue check: Revenue before = $4.50 × 840 = $3,780. Revenue after = $5.00 × 780 = $3,900. The price increase raised weekly revenue by $120, consistent with inelastic demand.

Rationale for the midpoint base

Demand curves slope downward, but the full curve is rarely known — only two points are observed. The midpoint method finds the elasticity of the chord connecting those two points, producing a single consistent value for that price range. It became standard in introductory economics texts because it eliminates the directional ambiguity of the simpler point formula, making it a more reliable estimate when only two observations are available.

Elasticity and total revenue

The connection between elasticity and revenue is one of the most practically useful results in microeconomics:

  • Elastic demand (|PED| > 1): A price cut increases revenue; a price rise decreases it. The quantity gain (or loss) outweighs the price effect.
  • Inelastic demand (|PED| < 1): A price cut decreases revenue; a price rise increases it. The price effect dominates.
  • Unit elastic (|PED| = 1): Total revenue is at a local maximum — small price changes in either direction leave revenue approximately unchanged.

This is why firms with market power often charge more for necessities (inelastic) and discount luxuries or substitutable goods (elastic) to maximize revenue.

To see how elasticity interacts with fixed costs and profitability thresholds, use the Break-Even Calculator alongside this calculator. For a refresher on percentage-change arithmetic, see the Percent Change Calculator.

Frequently Asked Questions (FAQ)

What is price elasticity of demand?

Price elasticity of demand (PED) measures how responsive the quantity demanded of a good is to a change in its price. It is defined as the percentage change in quantity demanded divided by the percentage change in price.

A PED of −2, for example, means that a 1% price increase reduces quantity demanded by 2%. Under the standard law of demand, PED is negative (price and quantity move in opposite directions), though economists often discuss the absolute value for classification purposes.

What is the difference between the midpoint and point elasticity formulas?

The point method calculates percentage changes relative to the initial values: %ΔQ = (Q₁ − Q₀) / Q₀ and %ΔP = (P₁ − P₀) / P₀. The problem is that going from $10 to $12 gives a different result than going from $12 to $10 (20% vs. −16.7%).

The midpoint (arc) method resolves this by dividing by the average of the two values: %ΔQ = (Q₁ − Q₀) / ((Q₀ + Q₁) / 2). This produces a symmetric result regardless of direction and is the textbook standard for comparing two discrete price points.

What does it mean for demand to be elastic or inelastic?

Demand is elastic (|PED| > 1) when consumers are very responsive to price — a small price change causes a proportionally larger quantity change. Luxury goods, goods with many substitutes, and non-essential items tend to be elastic.

Demand is inelastic (|PED| < 1) when consumers are less responsive — a price change causes a smaller proportional quantity change. Essential goods, habit-forming products, and goods with few substitutes tend to be inelastic.

Unit elastic (|PED| = 1) is the boundary where the percentage changes are exactly equal. Perfectly inelastic (|PED| = 0) means quantity does not respond to price at all — often a theoretical limit, approached by life-saving medications with no substitutes.

How does price elasticity affect total revenue?

Total revenue equals price × quantity. When demand is elastic, a price increase reduces quantity by a larger percentage than the price rose, so total revenue falls; a price cut raises revenue. When demand is inelastic, a price increase raises revenue (quantity falls by a smaller percentage); a price cut reduces it.

At unit elasticity, total revenue is at a local maximum — small price changes in either direction leave revenue approximately unchanged. This is why firms with market power often charge more for necessities (inelastic) and discount substitutable goods (elastic).

Disclaimer

Price elasticity of demand is a theoretical measure derived from two observed price–quantity pairs. Real-world demand curves are rarely linear; elasticity typically varies along the curve. This tool is for educational and analytical purposes only, not as a basis for pricing decisions without additional market research.

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