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Price Elasticity of Demand Calculator

Calculate price elasticity of demand (PED), percentage/midpoint methods, total revenue change, and demand elasticity classification.

Demand inputs

$
$

Price elasticity of demand (PED)

-1.57

Elastic (|E| > 1) • |E| = 1.57

Demand classification

Elastic (|E| > 1)

Quantity demanded responds more than proportionally to price

% change in quantity demanded

-28.57%

% change in price

+18.18%

Initial total revenue (P₁ × Q₁)

$1,000.00

New total revenue (P₂ × Q₂)

$900.00

Revenue impact

Revenue change-$100.00 (-10.0%)
Elasticity magnitude |E|1.5714
Pricing takeawayElastic demand: the price increase reduced total revenue

How price elasticity of demand is calculated

Step-by-step breakdown using your price and quantity inputs.

  1. Step 1: Midpoint percentage change in quantity demanded

    %ΔQ=Q2−Q1(Q1+Q2)/2×100%=75−100(100+75)/2=−28.571%\% \Delta Q = \frac{Q_2 - Q_1}{(Q_1 + Q_2) / 2} \times 100\% = \frac{75 - 100}{(100 + 75) / 2} = -28.571\%

    Average quantity is 87.50 units, so demand shifted by -28.57%.

  2. Step 2: Midpoint percentage change in price

    %ΔP=P2−P1(P1+P2)/2×100%=12−10(10+12)/2=18.182%\% \Delta P = \frac{P_2 - P_1}{(P_1 + P_2) / 2} \times 100\% = \frac{12 - 10}{(10 + 12) / 2} = 18.182\%

    Average price is $11.00, so price moved by 18.18%.

  3. Step 3: Divide quantity change by price change

    PED=%ΔQ%ΔP=−28.571%18.182%=−1.5714\mathrm{PED} = \frac{\% \Delta Q}{\% \Delta P} = \frac{-28.571\%}{18.182\%} = -1.5714

    Elastic (|E| > 1). Elastic demand: the price increase reduced total revenue.

Report tool

Understanding Price Elasticity of Demand (PED)

Price elasticity of demand measures how responsive quantity demanded is to a change in price. It is one of the most practical concepts in microeconomics for pricing managers, retailers, and financial analysts who need to forecast revenue after a price change.

A coefficient of -2.0 means that a 1% price increase is associated with roughly a 2% drop in quantity demanded. The sign is usually negative, but the magnitude |E| tells you whether demand is elastic, inelastic, or unitary. Pair this analysis with our price elasticity of supply calculator to compare buyer and seller responsiveness, or use our cross-price elasticity calculator when competitor or complement prices also move.

Formulas and calculation methods

Price elasticity of demand is the ratio of the percentage change in quantity demanded to the percentage change in price. You can compute those percentages with either the midpoint arc method or the simple percentage change method.

Midpoint (arc) elasticity

The midpoint method uses the average of the two price and quantity observations as the denominator base:

PED=Q2−Q1(Q1+Q2)/2P2−P1(P1+P2)/2\mathrm{PED} = \frac{\frac{Q_2 - Q_1}{(Q_1 + Q_2) / 2}}{\frac{P_2 - P_1}{(P_1 + P_2) / 2}}

Percentage change elasticity

The percentage method uses the initial price and quantity as the base:

PED=Q2−Q1Q1P2−P1P1\mathrm{PED} = \frac{\frac{Q_2 - Q_1}{Q_1}}{\frac{P_2 - P_1}{P_1}}

Worked example

Suppose a product moves from an initial price of $10 and quantity of 100 units to a new price of $12 and quantity of 75 units.

  1. Midpoint %ΔQ = (75 - 100) / 87.5 = -28.57%
  2. Midpoint %ΔP = (12 - 10) / 11 = 18.18%
  3. PED = -28.57% / 18.18% = -1.57 (elastic demand)
  4. Initial revenue = $10 × 100 = $1,000; new revenue = $12 × 75 = $900

Because |PED| is greater than 1, the price increase reduced total revenue. This is a common pattern for discretionary products where buyers can cut back quickly when prices rise.

Interpreting elasticity values

  • |E| > 1: Elastic demand. Quantity responds more than proportionally to price.
  • |E| = 1: Unitary elasticity. Revenue is approximately unchanged for small price moves.
  • 0 < |E| < 1: Inelastic demand. Quantity responds less than proportionally to price.
  • |E| = 0: Perfectly inelastic demand. Quantity does not change when price changes.

Practical business uses

Retailers use PED to decide whether a promotion will lift revenue or only sacrifice margin. Subscription businesses estimate churn sensitivity to annual price increases. Public policy teams model how excise taxes affect consumption of tobacco, alcohol, or fuel. For broader demand drivers beyond price, our income elasticity of demand calculator measures how sales respond to changes in consumer income.

Frequently asked questions

What does a negative price elasticity of demand mean?
Price elasticity of demand is usually negative because price and quantity demanded move in opposite directions. When price rises, quantity demanded typically falls, and when price falls, quantity demanded typically rises. Economists often focus on the absolute value |E| when classifying demand as elastic or inelastic.
What is the difference between midpoint and percentage elasticity?
The percentage method divides each change by the initial value (P₁ or Q₁). The midpoint, or arc, method divides each change by the average of the initial and final values. Arc elasticity gives the same coefficient whether you move from point A to point B or from B to A, which makes it better for comparing two observed price points.
How does elasticity affect total revenue?
When demand is inelastic (|E| < 1), a price increase tends to raise total revenue because the quantity drop is smaller than the price gain. When demand is elastic (|E| > 1), a price increase tends to lower total revenue because quantity falls by a larger percentage. At unitary elasticity (|E| = 1), total revenue stays roughly unchanged after a small price move.
What products are usually price elastic?
Luxury goods, products with many close substitutes, and non-essential items often have elastic demand. Examples include restaurant meals, airline tickets, branded apparel, and electronics where shoppers can easily compare alternatives.
What products are usually price inelastic?
Necessities, addictive goods, products with few substitutes, and items that represent a tiny share of household spending often have inelastic demand. Examples include prescription medicine, gasoline in the short run, basic utilities, and salt.
Can price elasticity change over time?
Yes. Demand is often more inelastic in the short run because consumers need time to adjust habits, find substitutes, or change budgets. Over the long run, more alternatives appear and demand usually becomes more elastic.
How is price elasticity of demand different from cross-price elasticity?
Price elasticity of demand measures how quantity demanded for one product responds to that product's own price change. Cross-price elasticity measures how demand for Good A responds when the price of a different Good B changes. Use our cross-price elasticity calculator when analyzing substitutes and complements.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.