Price Elasticity of Demand Calculator
Enter the price and quantity demanded before and after a price change to see the price elasticity of demand by the midpoint method, and what the change did to total revenue.
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Price Elasticity of Demand Calculator
Our Price Elasticity of Demand Calculator shows how strongly buyers react when a price changes. Type the price and the quantity demanded before the change, then the price and quantity after it. It returns the price elasticity of demand (PED) by the midpoint method, the percentage change in price and in quantity, whether demand is elastic, inelastic or unit elastic, and how total revenue moved. It is built for economics students checking homework, shop owners testing a price rise or discount, and analysts comparing how sensitive different products are to price.
Quick answer
Price elasticity of demand is % change in quantity demanded ÷ % change in price: if a coffee rises from 4 to 5 (22.2222% by the midpoint) and daily sales fall from 600 to 400 cups (−40%), PED = −40% ÷ 22.2222% = −1.8.
- |PED| above 1: demand is elastic.
- |PED| below 1: demand is inelastic.
- |PED| equal to 1: demand is unit elastic.
- PED of 0: demand is perfectly inelastic.
What Is Price Elasticity of Demand?
Price elasticity of demand (PED) measures how much the quantity buyers want changes when the price changes. Both changes are in percent, so the answer has no unit and you can compare a cup of coffee with a litre of petrol or a monthly software plan.
A PED of −1.8 means that a 1% rise in price cuts the quantity demanded by about 1.8%. A PED of −0.3 means the same 1% rise cuts it by only about 0.3%. Because people normally buy less when the price goes up, PED is normally negative. What matters for the type of demand is its size, the absolute value.
Price Elasticity of Demand Formula
%ΔQd = (Q2 − Q1) ÷ avg Q × 100
%ΔP = (P2 − P1) ÷ avg P × 100
avg Q = (Q1 + Q2) ÷ 2
avg P = (P1 + P2) ÷ 2
- P1 and Q1: the initial price and the quantity demanded at that price.
- P2 and Q2: the new price and the quantity demanded at that price.
- %ΔQd: the percentage change in quantity demanded.
- %ΔP: the percentage change in price.
This is the midpoint, or arc, formula. Dividing each change by the average of the two values means a price rise and the matching price cut between the same two points give the same elasticity.
How to Calculate Price Elasticity of Demand
A café sells 600 coffees a day at a price of 4. After it raises the price to 5, it sells 400:
= 22.2222%
%ΔQd = −200 ÷ 500 × 100
= −40%
PED = −40% ÷ 22.2222%
= −1.8
- Find the average price. (4 + 5) ÷ 2 = 4.5.
- Find the percentage change in price. (5 − 4) ÷ 4.5 × 100 = 22.2222%.
- Find the average quantity. (600 + 400) ÷ 2 = 500.
- Find the percentage change in quantity. (400 − 600) ÷ 500 × 100 = −40%.
- Divide. −40% ÷ 22.2222% = −1.8.
The PED is −1.8, so demand is elastic. Takings fell from 2,400 (4 × 600) to 2,000 (5 × 400) a day: the price rise lost the café 400 in revenue.
How to Read the Result
| |PED| | Demand is |
|---|---|
| 0 | Perfectly inelastic |
| Between 0 and 1 | Inelastic |
| Exactly 1 | Unit elastic |
| Above 1 | Elastic |
| Infinite | Perfectly elastic |
- Elastic: buyers react strongly, so quantity moves by a larger percentage than price.
- Inelastic: buyers keep buying, so quantity moves by a smaller percentage than price.
- Unit elastic: quantity and price move by the same percentage.
- Perfectly inelastic: buyers take the same amount at any price, close to how a vital medicine behaves.
- Perfectly elastic: buyers take any amount at one price and none above it.
A positive result means price and quantity moved in the same direction. That is not a movement along a normal demand curve. Usually demand itself shifted, for example because of a season, an advert or a change in income.
Negative Sign or Absolute Value?
Textbooks handle the minus sign in two ways. Some keep it, so a typical PED is −1.8. Others drop it and quote 1.8, because demand almost always slopes down. Both describe the same buyers.
The calculator shows the signed value as the main result, as the formula gives it, and the absolute value as a separate row. Use the absolute value when you compare with 1 or when your course quotes elasticities without a sign.
Elasticity and Total Revenue
Total revenue is price × quantity. Elasticity tells you which way it moves when you change the price. The table shows what happens to revenue:
| Demand | Price up | Price down |
|---|---|---|
| Elastic | Falls | Rises |
| Inelastic | Rises | Falls |
| Unit elastic | Same | Same |
The café lost revenue when it raised its price, which fits elastic demand. A petrol station whose sales dip from 1,000 to 950 litres when the price goes from 100 to 120 takes in 114,000 instead of 100,000, which fits inelastic demand. The calculator works out both revenue figures for you.
Elastic and Inelastic Demand on a Graph
Both lines pass through the same starting point. When the price rises from P1 to P2, buyers on the flat line cut their purchases sharply, while buyers on the steep line barely change. Elasticity is not the same as slope, though: along one straight demand line, PED changes from point to point, because the same unit change is a bigger percentage where prices are high and quantities are low.
Midpoint Method vs Start-Point Method
The start-point method divides each change by the starting value, so the answer depends on which way the price moved. Here is the café going from 4 to 5 and back:
| Price move | Start point | Midpoint |
|---|---|---|
| 4 to 5 | −1.3333 | −1.8 |
| 5 to 4 | −2.5 | −1.8 |
The midpoint method gives −1.8 both ways. The calculator still shows the start-point figure as a row, so you can match a course or report that uses it. For small price changes the two methods are close.
Price Elasticity of Demand Examples
Inelastic demand. Petrol rises from 100 to 120 a litre and a station sells 950 litres a day instead of 1,000:
= 18.1818%
%ΔQd = −50 ÷ 975 × 100
= −5.1282%
PED = −0.2821
Unit elastic demand. A cinema raises tickets from 10 to 15 and sells 200 instead of 300. Both changes are 40% of their average, so PED = −40% ÷ 40% = −1 and revenue stays at 3,000.
A price cut. A shop cuts a jacket from 100 to 90 and sells 560 instead of 500:
= −10.5263%
%ΔQd = 60 ÷ 530 × 100
= 11.3208%
PED = −1.0755
Demand is just elastic, so the cut raised revenue from 50,000 to 50,400.
Perfectly inelastic demand. A patient needs 200 doses of a medicine a year. When the price goes from 30 to 40 a dose they still buy 200, so the quantity change is 0% and the PED is 0.
What Makes Demand Elastic or Inelastic?
- Substitutes. If buyers can switch easily to another brand or product, demand is elastic.
- Necessity or luxury. Basics such as medicine, water and power are inelastic. Treats and holidays are more elastic.
- Share of the budget. A rise in the price of salt goes unnoticed. A rise in rent or a car price does not.
- Time. Buyers find alternatives given longer, so demand is more elastic in the long run.
- How narrow the market is. Demand for one brand of coffee is far more elastic than demand for coffee in general.
- Habit. Habit-forming goods such as cigarettes have inelastic demand.
Short Run vs Long Run
Take the petrol station again, with the price staying at 120 instead of 100. In the first month drivers still have the same cars and commutes. After a few years some have switched to smaller cars, car shares or public transport:
| Time allowed | Litres a day | PED |
|---|---|---|
| First month | 950 | −0.2821 |
| A few years | 800 | −1.2222 |
The same price rise looks inelastic in the short run and elastic in the long run. Revenue rises at first (114,000) and then falls below where it started (96,000), so always state the period a PED covers.
Common Mistakes
- Dividing the wrong way round. The quantity change goes on top and the price change underneath.
- Comparing the signed value with 1. −1.8 is elastic. Compare the absolute value with 1.
- Using changes in units. 200 cups ÷ 1 is a slope, not an elasticity. Convert both changes to percent first.
- Mixing methods. Use the midpoint for both changes or the start point for both, never one of each.
- Ignoring other changes. The formula assumes only the price changed. A holiday, a rival's sale or an advert in the same week distorts the result.
The result is for education and planning and is not economic or financial advice.
Key Terms
- Price elasticity of demand
- Percentage change in quantity demanded divided by percentage change in price.
- Quantity demanded
- The amount buyers want to purchase at a given price.
- Midpoint method
- Measuring each percentage change from the average of the two values.
- Elastic demand
- |PED| above 1: buyers respond more than in proportion to price.
- Inelastic demand
- |PED| below 1: buyers respond less than in proportion to price.
- Total revenue
- Price times quantity sold.
How to Use the Price Elasticity of Demand Calculator
- Enter the initial price. Type the price per unit before the change, such as 4.
- Enter the initial quantity. Type the quantity demanded at the initial price, such as 600.
- Enter the new price. Type the price per unit after the change, such as 5.
- Enter the new quantity. Type the quantity demanded at the new price, such as 400.
- Read and copy the result. The price elasticity of demand appears as you type, with the percentage changes, the type of demand, total revenue before and after and the start-point figure. Press Copy to copy it, or Clear or Esc to start again.
Example: a jacket is cut from 100 to 90 and sales rise from 500 to 560. The result is about −1.0755, so demand is elastic and revenue rises from 50,000 to 50,400.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you calculate price elasticity of demand?
Divide the percentage change in quantity demanded by the percentage change in price. With the midpoint method, each percentage change is the change divided by the average of the old and new values, times 100.
What is the price elasticity of demand formula?
PED = % change in quantity demanded ÷ % change in price. With the midpoint method, % change in quantity = (Q2 − Q1) ÷ ((Q1 + Q2) ÷ 2) × 100 and % change in price = (P2 − P1) ÷ ((P1 + P2) ÷ 2) × 100.
What is the PED if the price rises from 4 to 5 and sales fall from 600 to 400?
It is −1.8. The price changes by 22.2222% of its average and the quantity by −40% of its average, so PED = −40% ÷ 22.2222% = −1.8. Demand is elastic.
Why is price elasticity of demand negative?
Because buyers normally purchase less when the price rises, so the quantity change and the price change have opposite signs. Many textbooks drop the minus sign and quote the absolute value.
When is demand elastic or inelastic?
Demand is elastic when the absolute value of PED is above 1, inelastic when it is below 1 and unit elastic when it equals 1. A PED of 0 is perfectly inelastic demand.
How does elasticity affect total revenue?
With elastic demand, a price rise lowers revenue and a price cut raises it. With inelastic demand, a price rise raises revenue and a price cut lowers it. With unit elastic demand, revenue stays the same.
What does a positive price elasticity of demand mean?
It means price and quantity moved in the same direction. Along a normal demand curve that does not happen, so real data with a positive result usually means demand itself shifted at the same time.
Why use the midpoint method?
It gives the same elasticity whether the price rises or falls between the two points. The start-point method gives two different answers for the same pair of points.
Is the Price Elasticity of Demand Calculator free?
Yes. It is free to use, with no sign-up and no limit on how many times you use it.
Sources
- Wikipedia. Price elasticity of demand.
- OpenStax. Principles of Economics 3e, 5.1 Price Elasticity of Demand and Price Elasticity of Supply.
- OpenStax. Principles of Economics 3e, 5.3 Elasticity and Pricing.
- Lumen Learning. Calculating Price Elasticities Using the Midpoint Formula.
- Lumen Learning. Elasticity and Total Revenue.
- WallStreetMojo. Price Elasticity of Demand: Formula and Examples.
Try our Price Elasticity of Demand Calculator to see how buyers and revenue respond to any price change.