Price Elasticity of Demand Calculator
Enter the price and the quantity demanded before and after a change, and the calculator returns the price elasticity of demand by the midpoint method, says whether demand is elastic or inelastic, shows what happened to total revenue, and draws the demand line. Switch the measure to find income or cross-price elasticity from the same kind of data.
Two observations
Enter the value before and after the change, with the quantity demanded each time. The midpoint formula gives the same answer whichever you call “before”.
Results
−1.2222
Price elasticity of demand (E)
1.2222
Absolute value |E|
−22.22%
% change in quantity demanded
18.18%
% change in price
Elastic (|E| > 1)
Verdict
Buyers respond more than proportionally: a 1% price change moves quantity demanded by about 1.22%.
Working (midpoint method)
- %ΔQ = (Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2) = (80 − 100) ÷ ((100 + 80) ÷ 2) = −20 ÷ 90 = −22.22%
- %ΔP = (P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2) = (12 − 10) ÷ ((10 + 12) ÷ 2) = 2 ÷ 11 = 18.18%
- E = %ΔQ ÷ %ΔP = −22.22% ÷ 18.18% = −1.2222
Percentages are rounded for display; the elasticity is computed from the unrounded values.
Total revenue test
Total revenue (P × Q): 1,000 → 960 (Change: −40)
Price rose and total revenue fell, which is what elastic demand does: quantity fell by a larger percentage than price rose.
Point elasticity along the straight line
If demand is the straight line through your two points, its slope is ΔQ ÷ ΔP = −10, and E = slope × P ÷ Q changes from point to point:
- At the starting point: −10 × (10 ÷ 100) = −1
- At the midpoint: −10 × (11 ÷ 90) = −1.2222
- At the end point: −10 × (12 ÷ 80) = −1.5
The midpoint answer is exactly the point elasticity at the middle of the line, so it always falls between the other two.
Show the graph data as a table
| Observation | Price (P) | Quantity demanded (Q) |
|---|---|---|
| Before | 10 | 100 |
| After | 12 | 80 |
How to Use the Price Elasticity of Demand Calculator
- 1. Choose the measure. Price elasticity of demand is the default. Choose income elasticity if the question is about how buyers respond to a change in income, or cross-price elasticity if it is about a change in the price of a different good.
- 2. Enter the before and after values. Put the price (or income) and the quantity demanded in each situation. The midpoint formula gives the same answer in either order, so you cannot get “before” and “after” the wrong way round.
- 3. Read the verdict. The signed elasticity, its absolute value, the two percentage changes and the classification appear together, with the working written out line by line so you can copy the method into your own answer.
- 4. Check the revenue test and the graph. For price elasticity the calculator compares total revenue before and after, and shows point elasticity at the start, middle and end of the straight line through your two points.
The Midpoint Formula
Elasticity compares percentage changes, so the units of price and quantity cancel. The trouble with an ordinary percentage change is that it depends on where you start: a rise from 10 to 12 is 20%, but a fall from 12 to 10 is only 16.7%. The midpoint method removes that problem by dividing each change by the average of the starting and ending values, which is the method OpenStax Principles of Economics and Mankiw's Principles of Economics both teach.
Midpoint method
Percentage change in quantity
%ΔQ = (Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2)
Percentage change in price
%ΔP = (P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2)
Price elasticity of demand
E = %ΔQ ÷ %ΔP
Along a downward-sloping demand curve, price and quantity move in opposite directions, so E is negative. Many textbooks report the absolute value |E| and say so; this calculator shows both. Income and cross-price elasticity use the same formula with income or the other good's price in the denominator, and their signs are meaningful, so they are never reduced to an absolute value.
Worked Example: Price Rises From $10 to $12
The calculator opens with this example: the price rises from $10 to $12 and the quantity demanded falls from 100 to 80.
| Step | Calculation | Result |
|---|---|---|
| %ΔQ | (80 − 100) ÷ ((100 + 80) ÷ 2) = −20 ÷ 90 | −22.22% |
| %ΔP | (12 − 10) ÷ ((10 + 12) ÷ 2) = 2 ÷ 11 | 18.18% |
| E | −22.22% ÷ 18.18% (exactly −11 ÷ 9) | −1.2222 |
| Total revenue | $10 × 100 = $1,000 before; $12 × 80 = $960 after | −$40 |
|E| = 1.2222 is greater than 1, so demand is elastic over this range, and the revenue test agrees: the price rose and total revenue fell. The point elasticities along the straight line through the two observations are −1 at the starting point, −1.2222 at the midpoint and −1.5 at the end. The midpoint formula is exactly the point elasticity at the middle of the line, which is why it is the fair single answer for a move between two points.
Reading the Result
| |E| | Name | What it means | If price rises, total revenue |
|---|---|---|---|
| 0 | Perfectly inelastic | Quantity does not respond (vertical demand) | Rises |
| Between 0 and 1 | Inelastic | Quantity changes by a smaller percentage than price | Rises |
| 1 | Unit elastic | The percentage changes are equal | Stays the same |
| Above 1 | Elastic | Quantity changes by a larger percentage than price | Falls |
| Infinite | Perfectly elastic | Any price rise loses every buyer (horizontal demand) | Falls to zero |
The revenue rule is not a separate fact. With midpoint percentages, the change in revenue P₂Q₂ − P₁Q₁ equals the average price times the change in quantity plus the average quantity times the change in price, so it has the sign of %ΔQ + %ΔP. When price rises, revenue rises exactly when the quantity falls by a smaller percentage, that is, when |E| < 1.
Income and Cross-Price Elasticity
- Income elasticity of demand is %ΔQ ÷ %Δincome. A negative value marks an inferior good (instant noodles, bus travel for some households): people buy less as they earn more. A value from 0 to 1 is a necessity, and a value above 1 is a luxury.
- Cross-price elasticity of demand is %ΔQ of one good ÷ %ΔP of another. A positive value means substitutes (tea and coffee), a negative value means complements (printers and ink), and a value near zero means the goods are unrelated.
Frequently Asked Questions
- What is the midpoint method for elasticity?
- It calculates each percentage change as the change divided by the average of the starting and ending values, rather than by the starting value alone. That makes the elasticity the same whether the price rises from A to B or falls from B to A. It is the standard arc-elasticity method in most introductory textbooks.
- Is price elasticity of demand negative?
- Usually, yes. The law of demand means price and quantity demanded move in opposite directions, so the ratio of their percentage changes is negative. Economists often drop the minus sign and talk about the absolute value, so |E| = 1.5 means elastic. Always check which convention your course uses.
- What is the difference between midpoint (arc) and point elasticity?
- Point elasticity measures responsiveness at one price on a demand curve, using the slope: E = (ΔQ ÷ ΔP) × (P ÷ Q). Arc elasticity measures it over a stretch between two points. On a straight line, the midpoint formula equals the point elasticity at the middle of that stretch.
- How do I know if demand is elastic or inelastic?
- Take the absolute value of E. Above 1, demand is elastic: quantity responds by a larger percentage than price. Below 1, it is inelastic. Exactly 1 is unit elastic. Goods with close substitutes, a large share of the budget, and a long time to adjust tend to have more elastic demand.
- What does the total revenue test say?
- If price and total revenue move in opposite directions, demand is elastic; if they move in the same direction, it is inelastic; if revenue does not change, demand is unit elastic. The calculator runs this test on your two observations and it always agrees with the midpoint elasticity.
- Can the elasticity of a straight-line demand curve be constant?
- No. A straight line has a constant slope, but elasticity is slope × P ÷ Q, and P ÷ Q falls as you move down the line. Demand is elastic in the upper half, unit elastic at the midpoint of the line between its intercepts, and inelastic in the lower half. Only a curve of the form Q = A × P^−b has constant elasticity, equal to −b.
- Why does the calculator reject two equal prices?
- If the price did not change, its percentage change is zero and the elasticity would divide by zero. A change in quantity at an unchanged price is a shift of the demand curve, not a movement along it, so there is no price elasticity to measure.