Price Elasticity of Demand Calculator
Enter the price and quantity sold before and after a price change to calculate elasticity of demand, see whether demand is elastic or inelastic and find out what happened to revenue. It uses the midpoint formula by default, so the answer is the same up or down.
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Formula
- Midpoint:
E = [(Q2 - Q1) / ((Q1 + Q2) / 2)] / [(P2 - P1) / ((P1 + P2) / 2)] - Simple:
E = [(Q2 - Q1) / Q1] / [(P2 - P1) / P1] - Revenue:
price x quantity, compared before and after.
| Absolute value of E | Meaning |
|---|---|
| 0 | Perfectly inelastic |
| below 1 | Inelastic |
| exactly 1 | Unit elastic |
| above 1 | Elastic |
Worked example
The price rises from 10 to 12 and the quantity sold falls from 100 to 80.
- Midpoint: change in quantity is -20 / 90 = -0.2222, change in price is 2 / 11 = 0.1818, so E = -1.22, which is elastic.
- Simple: -20% / +20% = -1.0, unit elastic.
- Revenue goes from 10 x 100 = 1,000 to 12 x 80 = 960, a change of -40 (-4%).
Another example
The price falls from 20 to 18 and the quantity rises from 500 to 560.
- Quantity change: 60 / 530 = 0.1132. Price change: -2 / 19 = -0.1053.
- Midpoint E = -1.08, which is elastic.
- Revenue goes from 10,000 to 10,080, a change of +80 (+0.8%).
When to use it
Use it to check what a past price change did, to judge whether a discount can pay for itself, and to compare how sensitive different products are to price. Pair it with margin, since revenue is not profit.
Common mistakes
- Using two periods where something else changed, such as season or promotion.
- Mixing the simple and midpoint methods when comparing.
- Reading the sign. Elasticity is normally negative, and the verdict uses its absolute value.
How it differs
The percentage change calculator gives one change. This page divides one change by another and links the result to revenue. The discount calculator shows the price, and the profit margin calculator shows what each unit earns.
Frequently asked questions
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 change is measured against the average of the two values. A price rise from 10 to 12 with sales falling from 100 to 80 gives (-20 / 90) / (2 / 11) = -1.22.
What is the difference between the midpoint and simple method?
The simple method measures each change against the starting value, so the answer depends on the direction of the change. The midpoint method uses the average, so a rise from 10 to 12 and a fall from 12 to 10 give the same elasticity. For the example above the simple method gives exactly -1.0 and the midpoint method -1.22.
What does elastic or inelastic mean?
If the absolute value of elasticity is above 1, demand is elastic: quantity changes by a larger percentage than price, so raising the price lowers revenue. Below 1 it is inelastic and a price rise raises revenue. At exactly 1 revenue stays about the same.
Why is the elasticity negative?
Demand normally falls when price rises, so the two changes have opposite signs and the ratio is negative. Many textbooks quote the absolute value, so -1.22 is often written as 1.22. The verdict here always uses the absolute value.
How accurate is an elasticity from two points?
It is only a rough estimate for that price range. Seasonality, promotions, competitors and other changes between the two periods also move sales, so treat the result as a guide and test price changes where you can.
What is the price elasticity formula in Excel?
Midpoint elasticity is =((Q2-Q1)/AVERAGE(Q1,Q2))/((P2-P1)/AVERAGE(P1,P2)). For a price from 10 to 12 and quantity from 100 to 80 that returns -1.22. The simple method is =((Q2-Q1)/Q1)/((P2-P1)/P1), which returns -1.0 for the same data.
Which products have inelastic demand?
Products people need or cannot easily replace, such as basic utilities, medicine or fuel for a commute, tend to be inelastic. A 10% price rise with an elasticity of -0.5 cuts quantity by about 5%, so revenue rises by about 1.10 × 0.95 − 1 = 4.5%. Elastic goods behave the other way.
How do I use elasticity to set a price?
Check the revenue effect first: above 1 in absolute value, a price cut raises revenue, while below 1 a price rise does. Then check profit, because selling more units also raises costs. In the example, revenue rises 0.8% after the price cut but you sold 60 more units to get it.