Price elasticity of demand calculator
Enter two prices and quantities, get the elasticity.
How do you calculate price elasticity of demand?
Divide the percent change in quantity by the percent change in price. The midpoint method measures each change against the average of the two values, so the answer is the same whichever way the price moves (OpenStax Principles of Economics).
Example
OpenStax: the price falls from $70 to $60 and the quantity demanded rises from 2,800 to 3,000. Quantity changes 200 ÷ 2,900 = 6.9%, price 10 ÷ 65 = 15.4%, so the elasticity is 0.45.
What do elastic and inelastic mean?
Above 1, demand is elastic: quantity changes proportionally more than price. Below 1 it is inelastic. Exactly 1 is called unitary elasticity.
Why is elasticity usually negative?
Price and quantity demanded move in opposite directions. Economists usually report the absolute value, as OpenStax does; the calculator shows both.
How does elasticity affect revenue?
When demand is elastic, cutting the price raises total revenue; when it is inelastic, cutting the price lowers revenue. The calculator shows revenue at both prices.
Why use the midpoint method instead of simple percentages?
Simple percentages depend on which point you start from. On the example, measuring from the old price gives 0.50 (7.1% ÷ 14.3%), while measuring from the new price back to the old one gives 0.40 (6.7% ÷ 16.7%). The midpoint method divides each change by the average of the two values and gives 0.45 in both directions.
Does the unit of quantity change the answer?
No. Elasticity compares percentage changes, so it has no units: counting gallons, liters, boxes or thousands of boxes gives the same value as long as both quantities use the same unit.
How the midpoint formula works
Elasticity = (percent change in quantity) ÷ (percent change in price). With the midpoint method, the change in quantity is divided by the average of the two quantities and the change in price by the average of the two prices: [(Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2)] ÷ [(P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2)]. The result is negative for a normal demand curve, and the size is what is compared with 1. The number describes demand between those two points, not the whole curve, and it assumes nothing else that affects demand changed between the two observations.
Worked example: $70 to $60
Quantity rises from 2,800 to 3,000: the change is 200 and the average is 2,900, so quantity changes by 6.90%. Price falls from $70 to $60: the change is −10 and the average is $65, so price changes by −15.38%. The elasticity is 6.90 ÷ −15.38 = −0.45, which is 0.45 in absolute value and below 1: demand is inelastic. Revenue agrees: $70 × 2,800 = $196,000 falls to $60 × 3,000 = $180,000. For an elastic case with made-up numbers, a price cut from $5 to $4 that lifts quantity from 100 to 160 gives an elasticity of 2.08, and revenue rises from $500 to $640.
Common mistakes
Using a plain percentage change from the starting point gives a different answer for each direction, which the midpoint method avoids. Reading the sign as meaningful is another: the negative sign only reflects the law of demand, and a value of −2 is as elastic as +2. Treating one result as a property of the product is a third mistake, since elasticity can differ at other prices and over other periods. Finally, if something besides price changed between the two observations, such as a promotion, a competitor’s move or the season, the calculation attributes all of the change in quantity to price.
Sources: OpenStax, Principles of Economics, chapter 5, “Elasticity” (the midpoint formula, the elastic, inelastic and unit-elastic cases, and the link between elasticity and total revenue), including the $70 to $60 example above. The second example uses made-up numbers chosen to show an elastic case. The revenue arithmetic is price × quantity at each point. Compare with the break-even calculator, the margin calculator, the discount calculator and the percentage calculator.