Elastic: above 1
Units change by more than the price. A lower price raises revenue and a higher price lowers it. Decision: whether a price cut can win enough extra units to pay.
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Price elasticity of demand calculator
Enter two prices and the units you sold at each. The calculator gives the price elasticity of demand by the midpoint (arc) method or the simple percentage method, says whether demand is elastic, unit elastic or inelastic, and shows what the price change did to revenue and, with a unit cost, to profit.
Berend Vrakking, founder. Last updated .
Your results
Elastic: units changed by more than the price did, so revenue moves opposite to the price.
Revenue rose by €400.00 (+8.0%).
- Price elasticity
- -1.73
- % change in units ÷ % change in price
- Absolute value
- 1.73
- Elasticity without its sign
- Demand is
- Elastic
- Above 1 elastic, equal to 1 unit elastic, below 1 inelastic
- Change in price
- -10.5%
- Change in units
- +18.2%
Revenue effect
- Revenue beforeOld price × old units
- €5,000.00
- Revenue afterNew price × new units
- €5,400.00
- Revenue changeRevenue after − revenue before
- +€400.00
Profit effect
- Profit before(Old price − unit cost) × old units
- €2,000.00
- Profit after(New price − unit cost) × new units
- €1,800.00
- Profit changeProfit after − profit before
- -€200.00
- Units needed to keep the old profitProfit before ÷ (new price − unit cost)
- 66.7
Profit-maximising price
€142.50
Unit cost × e ÷ (e − 1), where e is the absolute elasticity
If demand keeps this elasticity at every price, profit is highest at €142.50: the unit cost times 2.375. That is outside the €90.00 to €100.00 you entered, so it extrapolates beyond your data.
Assumes demand keeps this elasticity at every price and your unit cost stays constant.
Elasticity compares units sold at two prices. Anything else that changed between the two periods (season, stock, ads, competitor prices) is in the number too.
The start values are illustrative data.
How it works
Every step behind the numbers, worked through for the start values.
Illustrative data. A shop lowered a product from €100.00 to €90.00. It sold 50 units at the old price and 60 units at the new price. One unit costs €60.00.
| Step | Calculation | Result |
|---|---|---|
| Change in units (midpoint) | (60 − 50) ÷ ((50 + 60) ÷ 2) | +18.18% |
| Change in price (midpoint) | (€90.00 − €100.00) ÷ ((€100.00 + €90.00) ÷ 2) | -10.53% |
| Elasticity | +18.18% ÷ -10.53% | -1.73 |
| Demand is | 1.73 is above 1 | Elastic |
| Elasticity (simple method) | +20.00% ÷ -10.00% | -2.00 |
| Revenue before | €100.00 × 50 | €5,000.00 |
| Revenue after | €90.00 × 60 | €5,400.00 |
| Revenue change | €5,400.00 − €5,000.00 | +€400.00 (+8.0%) |
| Profit before | (€100.00 − €60.00) × 50 | €2,000.00 |
| Profit after | (€90.00 − €60.00) × 60 | €1,800.00 |
| Profit change | €1,800.00 − €2,000.00 | -€200.00 (-10.0%) |
| Units needed to keep the old profit | €2,000.00 ÷ (€90.00 − €60.00) | 66.7 |
Demand is elastic, so the cut raised revenue by €400.00. Profit still fell by €200.00: each unit now earns €30.00 instead of €40.00, and 60 units fall short of the 66.7 needed to keep the old profit. Elasticity says how units respond. Your margin decides whether the response pays.
What the result means
How to read the result, and what to check next.
Unit elastic: equal to 1
Units change by as much as the price, so revenue stays the same. Decision: none from revenue alone; read profit.
Inelastic: below 1
Units change by less than the price. A higher price raises revenue and a lower price lowers it. Decision: whether a price rise is worth the units you lose.
The sign
Elasticity is normally negative: a higher price sells fewer units. Read the absolute value for the class. A positive value means something besides the price moved the units.
Revenue is not profit
Revenue can rise while profit falls. Enter a unit cost to see both, and the units a new price needs to keep your profit.
Midpoint or simple
The midpoint method divides by the average of old and new, so direction does not matter. The simple method divides by the old value. For small changes they agree; for large ones they do not.
Profit-maximising price
The price that maximises profit, under one strong assumption.
If demand has the same elasticity at every price and your unit cost is constant, profit is highest at a price of unit cost × e ÷ (e − 1). Here e is the absolute elasticity, and it must be above 1. This is a reference point from a model, not a forecast.
Why the formula holds
Profit is (price − cost) × units. With units falling as a constant power of the price, its slope is zero where price − cost equals price ÷ e. Rearranged, that is price = cost × e ÷ (e − 1).
Worked example
Illustrative data. With e = 1.7273 and a unit cost of €60.00, the price is €60.00 × 1.7273 ÷ (1.7273 − 1) = €60.00 × 2.375 = €142.50.
Elasticity of 1 or below
Under this assumption profit keeps rising with the price, so there is no highest point. Real demand drops off at some price, and this model cannot find it.
Where it breaks
Elasticity measured between €90.00 and €100.00 says little about €142.50. It also changes with season, stock, ad spend and competitor prices. Change prices in small steps and measure again.
Competitor prices
Your own price is one lever, competitor prices are another.
This calculator measures how your units respond to your own price. How your units respond to a competitor’s price is cross-price elasticity: % change in your units ÷ % change in their price. A positive value means the products are substitutes.
Competitor Prices in Product Metrics shows your price position against comparable competitor products. It makes no price recommendations and does not measure elasticity.
Limits
What this number cannot tell you, and how to make it more reliable.
Why units changed
Two periods give one number, and every change in between is in it: season, stock, ads, promotions and competitor prices. Change one product at a time and compare periods of equal length.
Other price points
Elasticity from two prices describes that range only. It is not a demand curve.
A whole shop
Elasticity belongs to one product. A shop-wide figure describes none of its products.
Small volumes
A few sales per week make the number noisy. Treat a result from low volumes as a hint, not a measurement.
Price elasticity questions, answered.
How do you calculate price elasticity of demand?
Divide the percentage change in units sold by the percentage change in price. With the simple method, €100.00 to €90.00 is -10.0% and 50 to 60 units is +20.0%, so the elasticity is -2.00.
What is the midpoint method for price elasticity?
It divides each change by the average of the old and new values instead of the old value. Units: 10 ÷ 55 = +18.18%. Price: -€10.00 ÷ €95.00 = -10.53%. Elasticity: -1.73. Swap old and new and you get the same result.
What counts as elastic, unit elastic and inelastic?
Look at the absolute value. Above 1 is elastic: units change by more than the price. Exactly 1 is unit elastic. Below 1 is inelastic: units change by less than the price. An elasticity of -1.73 has an absolute value of 1.73, so demand is elastic.
Does a price cut always raise revenue?
No. It raises revenue only when demand is elastic. Even then, profit can fall. In the example the cut raised revenue by €400.00 and lowered profit by €200.00, because each unit earns €10.00 less and 60 units are fewer than the 66.7 needed.
How do you find the price that maximises profit?
Only under an assumption: demand with the same elasticity at every price and a constant unit cost. Then the price is unit cost × e ÷ (e − 1) for an absolute elasticity e above 1. With e = 1.7273 and a unit cost of €60.00 that is €142.50. Real elasticity changes with price, so use it as a reference point and test in small steps.
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