Price Elasticity Calculator
See how much your sales react to a price change, whether demand is elastic or inelastic, and whether raising or cutting the price brings in more money.
How your sales react to a change in your own price.
Changing this converts the sales figures. Elasticity is the same whatever period you use.
Left blank, it uses the old price.
Shows the price that makes the most profit.
Left blank, it uses your result above.
Left blank, these use the new price and sales after.
How your price elasticity is worked out
Elasticity = % change in sales ÷ % change in price, each measured against the average (midpoint).
- 1
Change in sales
(800 − 1,000)÷ avg 900= −22.2%
- 2
Change in price
($12 − $10)÷ avg $11= +18.2%
- 3
Divide them
−22.2% ÷ 18.2%= −1.22elastic
- 4
Revenue
$10,000 →$9,600= −$400 (−4%)
Read more: the formula, a worked example, demand curves, cross-price and income elasticity
Price elasticity of demand measures how strongly sales react to a price change. It is the % change in the quantity sold divided by the % change in price. The answer is usually negative, because sales fall when prices rise, so people often talk about its size and ignore the minus sign.
The formula
midpoint elasticity = ((new sales − old sales) ÷ average sales) ÷ ((new price − old price) ÷ average price)
average sales = (old sales + new sales) ÷ 2, average price = (old price + new price) ÷ 2
simple elasticity = ((new sales − old sales) ÷ old sales) ÷ ((new price − old price) ÷ old price)
revenue = price × sales
straight-line demand: sales = a − b × price
point elasticity = −b × price ÷ sales
price for the most revenue = a ÷ (2 × b)
price for the most profit = (a ÷ b + cost per unit) ÷ 2
predicted sales (midpoint) = sales now × (2 + k) ÷ (2 − k), where k = elasticity × (new price − price now) ÷ average price
Worked example
A shop raises the price of a product from $10 to $12, and monthly sales fall from 1,000 to 800 units.
- Change in sales: (800 − 1,000) ÷ ((1,000 + 800) ÷ 2) = −200 ÷ 900 = −22.2%.
- Change in price: ($12 − $10) ÷ (($10 + $12) ÷ 2) = $2 ÷ $11 = +18.2%.
- Elasticity: −22.2% ÷ 18.2% = −11 ÷ 9 = −1.22. That is more than 1 in size, so demand is elastic.
- Revenue: $10 × 1,000 = $10,000 before, $12 × 800 = $9,600 after, a fall of $400 (−4%). Raising the price of an elastic product loses money.
- Simple method: −200 ÷ 1,000 = −20% of sales, $2 ÷ $10 = +20% on price, so −20% ÷ 20% = −1.00. It looks unit elastic only because it measures from the starting point; going back from $12 to $10 would give +25% ÷ −16.7% = −1.50.
What the number means
| Elasticity (size) | Type | Raise the price | Cut the price |
|---|---|---|---|
| 0 | Perfectly inelastic | Revenue up | Revenue down |
| Between 0 and 1 | Inelastic | Revenue up | Revenue down |
| Exactly 1 | Unit elastic | No change | No change |
| More than 1 | Elastic | Revenue down | Revenue up |
| Infinite | Perfectly elastic | Sales drop to 0 | You take the whole market |
Demand tends to be more elastic when there are close substitutes, when the product is a big part of people’s budget, when it’s a want rather than a need, and over a longer time, as people find alternatives.
Straight-line demand curve
A straight line through the two points ($10, 1,000) and ($12, 800) loses 200 ÷ 2 = 100 sales for each $1 rise, so b = 100 and a = 1,000 + 100 × $10 = 2,000: sales = 2,000 − 100 × price. Nobody buys at 2,000 ÷ 100 = $20.
On a straight line, elasticity changes along the curve. At $10 it is −100 × 10 ÷ 1,000 = −1.00; at $15 it is −100 × 15 ÷ 500 = −3.00. Revenue is highest where elasticity is −1: at 2,000 ÷ (2 × 100) = $10, selling 1,000 units for $10,000.
With a cost of $4 per unit, profit is highest at ($20 + $4) ÷ 2 = $12, selling 2,000 − 1,200 = 800 units for a profit of ($12 − $4) × 800 = $6,400. At that price elasticity is −100 × 12 ÷ 800 = −1.5, which fits the rule that the best markup is (price − cost) ÷ price = 1 ÷ 1.5 = 66.7%.
Predicting sales after a price change
Using the elasticity of −11 ÷ 9 (−1.22) from $12 and 800 sales, a 10% rise to $13.20 gives k = −1.22 × ($1.20 ÷ $12.60) = −0.1164, so sales = 800 × (2 − 0.1164) ÷ (2 + 0.1164) = 712 units and revenue $13.20 × 712 = $9,398.40, down $201.60. The simple method (sales change = elasticity × price change = −12.2%) gives 702.2 units.
Cross-price elasticity
When a rival raises its price from $4 to $5 and your sales go from 100 to 120, your sales change by 20 ÷ 110 = +18.2% against a price change of $1 ÷ $4.50 = +22.2%, so cross-price elasticity is 18.2% ÷ 22.2% = +0.82. Above 0 means substitutes; below 0 means complements (bought together); close to 0 means unrelated.
Income elasticity
If average income rises from $50,000 to $60,000 (+18.2% by the midpoint) and sales go from 10 to 13 (+26.1%), income elasticity is 26.1% ÷ 18.2% = 1.43, a luxury. From 0 to 1 is a necessity (sales grow more slowly than income), and below 0 an inferior good (people buy less as they earn more).
Elasticity from two points assumes nothing else changed between them: not the season, marketing, a rival’s price or people’s income. If sales rose with the price, something else probably did change. A straight-line demand curve is a simple model; real demand often curves, so use it for nearby prices and test price changes in small steps.
Common questions
How do you calculate price elasticity of demand?
Divide the % change in quantity sold by the % change in price. With the midpoint method each % change is measured against the average of the old and new values. If the price goes from $10 to $12 and sales fall from 1,000 to 800, sales change by −200 ÷ 900 = −22.2% and the price by 2 ÷ 11 = +18.2%, so elasticity is −22.2% ÷ 18.2% = −1.22.
What does an elasticity of −1.22 mean?
Each 1% rise in price cuts sales by about 1.22%. Because that is more than 1 (ignoring the minus sign), demand is elastic: raising the price brings in less revenue, and cutting it brings in more. Below 1 it is inelastic and a price rise brings in more revenue.
Why use the midpoint method instead of the simple % change?
The simple method measures from the starting values, so going from $10 to $12 gives a different answer from going $12 to $10. The midpoint (arc) method uses the averages, so you get the same elasticity in both directions. In the example the simple method gives −1.00 and the midpoint method −1.22.
What price brings in the most revenue?
On a straight-line demand curve Q = a − bP, revenue is highest at P = a ÷ 2b, where elasticity is exactly −1. For Q = 2,000 − 100P that is $10, selling 1,000 units for $10,000.
What is cross-price elasticity?
It compares the % change in sales of one product with the % change in the price of another. Above 0 the two are substitutes (people switch when the other gets dearer); below 0 they are complements (bought together, like printers and ink); close to 0 they are unrelated.
What is income elasticity of demand?
The % change in sales divided by the % change in buyers’ income. Below 0 it is an inferior good (people buy less as they earn more), from 0 to 1 a necessity, and above 1 a luxury.
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