Price elasticity of demand calculator
Price elasticity of demand tells you how strongly the quantity sold reacts to a price change. Enter the old and new price and the quantity at each. The calculator gives the elasticity by the midpoint (arc) method or by simple percent change, says whether demand is elastic or inelastic and shows what happened to revenue.
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How to use it
- Choose the method: midpoint (recommended) or simple percent change.
- Enter the old and the new price.
- Enter the quantity sold at each price, for the same length of time.
- Read the elasticity, the type of demand and the revenue at both prices.
Midpoint method:
- %ΔQ = (Q2 − Q1) ÷ ((Q1 + Q2) ÷ 2) × 100
- %ΔP = (P2 − P1) ÷ ((P1 + P2) ÷ 2) × 100
- E = %ΔQ ÷ %ΔP
The simple method divides by Q1 and P1 instead of the averages. Revenue is price × quantity.
Worked example
The price goes from 10 to 12 and weekly sales fall from 1,000 to 800 units.
- %ΔQ = −200 ÷ 900 × 100 = −22.22 %.
- %ΔP = 2 ÷ 11 × 100 = 18.18 %.
- E = −22.22 ÷ 18.18 = −1.222: demand is elastic.
- Revenue falls from 10,000.00 to 9,600.00, a change of −400.00.
With the simple method the same data give −20% ÷ 20% = −1, unit elastic: the two methods can classify a borderline case differently.
Tips
- Compare equal periods: a week of sales at one price with a week at the other.
- Elasticity changes along a demand curve, so an estimate from a small price step is most useful near that price.
- If quantity does not change at all, demand is perfectly inelastic over that range (E = 0).
Frequently asked questions
What is the midpoint formula for elasticity?
E = [(Q2 − Q1) ÷ ((Q1 + Q2) ÷ 2)] ÷ [(P2 − P1) ÷ ((P1 + P2) ÷ 2)]. Dividing by the average of the two values gives the same answer whether the price goes up or down.
Why is the elasticity negative?
For most goods a higher price means a lower quantity, so the two changes have opposite signs. Economists often quote the absolute value; the classification here uses it too. A positive result is unusual and worth checking.
What do elastic and inelastic mean?
Elastic (|E| > 1): quantity changes by a larger percentage than price, so a price rise lowers revenue. Inelastic (|E| < 1): quantity changes less, so a price rise raises revenue. Unit elastic (|E| = 1): revenue stays about the same.
Which method should I use?
The midpoint method is the usual choice for two observed points, as in most textbooks. The simple method measures changes from the old values, which is fine for small changes but gives a different number if you swap the points.
Does the result prove that price caused the change?
No. Seasons, competitors or advertising can also change sales. The figure is reliable only when other conditions stayed roughly the same.