Finance Calculator
Price Elasticity of Demand Calculator
Measure how sensitive demand is to a price change, by the standard percentage method or the midpoint (arc) method. Both are shown side by side, with the elastic or inelastic classification and what the change does to total revenue.
Price Elasticity of Demand
How quantity responds to a price change
PED = (ΔQ ÷ Q1) ÷ (ΔP ÷ P1)
Divides by the starting values, so the answer depends on direction.
Results
PED
−1.00
Unit Elastic
|PED|
1.00
|PED| = 1
Unit Elastic · |PED| = 1
Quantity changes in exactly the same proportion as price. This is the revenue-maximising point on a linear demand curve.
Total revenue is unchanged by a price move — the two effects cancel exactly.
Where This Sits
Both Methods on These Figures
Reading the Same Points in Reverse
Total Revenue
| Point | Price | Quantity | Revenue |
|---|---|---|---|
| Before | 10.00 | 100 | 1,000.00 |
| After | 12.00 | 80 | 960.00 |
| Change | −40.00 | ||
Reading the same two points in reverse gives −1.50 rather than −1.00. The standard method divides by the starting value, so the answer depends on the direction of travel. The midpoint method gives the same figure either way, which is why it is preferred for a range.
Unit Elastic: Quantity changes in exactly the same proportion as price. This is the revenue-maximising point on a linear demand curve.
Total revenue is unchanged by a price move — the two effects cancel exactly.
Revenue moves from 1,000.00 to 960.00, a change of −40.00 or −4.00%. That direction is the practical test of elasticity: revenue rising on a price increase means inelastic demand, falling means elastic.
PED is normally negative because demand curves slope downward. Economists often quote the absolute value and drop the sign, so "an elasticity of 1.8" usually means −1.8.
Elasticity is specific to a price range, a moment and a market — it is not a fixed property of a product. The same good is far more elastic over a year than over a week, because substitution takes time.
Step-by-Step Calculation
Method — Standard Percentage
PED = (ΔQ ÷ Q1) ÷ (ΔP ÷ P1)
Price: 10.00 → 12.00
Quantity: 100 → 80
Step 1 — Percentage change in quantity
%ΔQ = (80 − 100) ÷ 100 × 100 = −20.00%
Step 2 — Percentage change in price
%ΔP = (12.00 − 10.00) ÷ 10.00 × 100 = 20.00%
Step 3 — Price elasticity of demand
PED = −20.00% ÷ 20.00% = −1.0000
|PED| = 1.0000 → Unit Elastic
Result
PED = −1.00 — Unit Elastic
Understanding Price Elasticity
Price elasticity of demand answers a single practical question: if you change the price, what happens to the quantity sold? It is the percentage change in quantity divided by the percentage change in price.
A PED of −1.8 means a 1% price rise costs you 1.8% of unit sales. The value is normally negative because demand curves slope downward, and the magnitude is what matters — |PED| above 1 is elastic, below 1 is inelastic.
The practical payoff is the revenue test. Inelastic demand means a price rise increases revenue; elastic demand means it reduces it. That single fact decides whether a price increase is worth making.
Elasticity Formulas
1. The Basic Ratio
2. Standard Percentage Method
3. Midpoint (Arc) Method
Why the Midpoint Method Exists
The standard method has an awkward property: it gives a different answer depending on which direction you measure. Take the same two points — $10 with 100 units, and $12 with 80 units:
| Method | $10 → $12 | $12 → $10 | Same Either Way? |
|---|---|---|---|
| Standard | −1.0000 | −1.5000 | No — 0.5 apart |
| Midpoint | −1.2222 | −1.2222 | Yes — identical |
The standard method divides by whichever value you started from, and $2 is 20% of $10 but only 16.7% of $12. The midpoint method divides by the average, $11, so the direction cannot matter. That is its entire purpose — and the reason it is the preferred method for anything but a tiny price change.
Reading the Number
| |PED| | Classification | Price Rise Effect on Revenue |
|---|---|---|
| = 0 | Perfectly Inelastic | Revenue rises in direct proportion |
| 0 to 1 | Inelastic | Revenue rises |
| = 1 | Unit Elastic | Revenue unchanged |
| > 1 | Elastic | Revenue falls |
| = ∞ | Perfectly Elastic | Revenue collapses to zero |
Both extremes are theoretical limits. Real goods sit between them, and the useful question is which side of 1 they fall on.
Revenue Flips Sign at Unit Elasticity
Holding a 10% price rise ($10 → $11) and varying only how much quantity falls, on 100 starting units:
| New Quantity | %ΔQ | PED | Class | Revenue Change |
|---|---|---|---|---|
| 100 | 0% | 0.000 | Perfectly Inelastic | +$100 |
| 95 | −5% | −0.500 | Inelastic | +$45 |
| 91 | −9% | −0.900 | Inelastic | +$1 |
| 90 | −10% | −1.000 | Unit Elastic | −$10 |
| 89 | −11% | −1.100 | Elastic | −$21 |
| 82 | −18% | −1.800 | Elastic | −$98 |
| 50 | −50% | −5.000 | Elastic | −$450 |
The revenue column crosses zero between 91 and 90 units — exactly where PED passes −1. At 91 units revenue gains a single dollar; at 90 it loses ten. That crossing point is the whole reason elasticity matters for pricing.
Where the Revenue Rule Breaks Down
"Inelastic means a price rise raises revenue" is exact for small changes. Over a wide price range the standard method can say inelastic while revenue actually falls:
| Measure | Value | Says |
|---|---|---|
| Standard PED | −0.8000 | Inelastic — revenue should rise |
| Midpoint PED | −1.2500 | Elastic — revenue should fall |
| Actual revenue | $1,000 → $900 | Fell by $100, or 10% |
On price $10 → $15 with quantity 100 → 60, the midpoint method gets it right and the standard method does not. The exact test is the product: (15 ÷ 10) × (60 ÷ 100) = 0.90, below 1, so revenue falls 10%. For large price moves, trust the midpoint figure — or just multiply the ratios.
What Makes Demand Elastic
- Close substitutes are available
- The good is discretionary
- It takes a large share of the budget
- The time horizon is long
- The market is competitive
- No real substitute exists
- The good is a necessity
- It is a trivial share of spending
- The purchase is urgent
- Brand loyalty or habit is strong
Time is the most underrated factor. A petrol price rise barely dents demand this week, because people still have to commute — but over a year they buy a different car, move closer to work, or change habits. The same product has very different elasticity depending on the window you measure.
Benefits of Using the Elasticity Calculator
Example Calculations
Three cases worked through step by step:
Example Scenario 1 — Standard Method
Price $10 → $12, quantity 100 → 80 units.
%ΔQ = (80 − 100) ÷ 100 × 100 = −20.00%
%ΔP = (12 − 10) ÷ 10 × 100 = +20.00%
PED = −20% ÷ 20% = −1.0000 → Unit Elastic
Revenue: $1,000 → $960, a fall of $40
The midpoint method on the same figures gives −1.2222
Read in reverse ($12 → $10) the standard method gives −1.5000
Example Scenario 2 — Midpoint Method
Price $8 → $10, quantity 150 → 120 units.
Quantity base = (150 + 120) ÷ 2 = 135
Price base = (8 + 10) ÷ 2 = 9
%ΔQ = −30 ÷ 135 × 100 = −22.22%
%ΔP = +2 ÷ 9 × 100 = +22.22%
PED = −22.22% ÷ 22.22% = −1.0000 → Unit Elastic
Revenue is unchanged at $1,200, which confirms unit elasticity
Example Scenario 3 — Elastic Demand
Price $10 → $11, quantity 100 → 82 units.
%ΔQ = −18.00%, %ΔP = +10.00%
PED = −18% ÷ 10% = −1.8000 → Elastic
Quantity fell proportionally more than price rose
Revenue: $1,000 → $902, a fall of $98 or 9.80%
Falling revenue on a price rise is the signature of elastic demand
The midpoint method gives −2.0769 on the same figures
Two Points Are Not a Demand Curve
Calculating elasticity from two observations assumes the price change caused the quantity change, when income, competitor pricing, seasonality, advertising and simple novelty all move demand at the same time. A measured elasticity is a correlation over one interval, not a law about the product. It is also specific to a range: elasticity is not constant along a demand curve, so a figure derived between $10 and $12 says little about behaviour at $30. The time horizon matters as much as the price range, because substitution takes time — demand that looks inelastic over a week is often elastic over a year. Over wide price ranges the standard and midpoint methods can disagree on the classification itself, which is why both are shown; where they differ, the midpoint figure is the more reliable and the product test settles the revenue question outright. Treat the result as one input to a pricing decision rather than the answer. This is general information, not business advice.
Frequently Asked Questions
- What is price elasticity of demand?
- A measure of how much the quantity demanded responds to a price change. It is the percentage change in quantity divided by the percentage change in price. A PED of −1.8 means a 1% price rise cuts quantity by 1.8%.
- How do you calculate price elasticity of demand?
- Divide the percentage change in quantity by the percentage change in price. With price $10 → $12 and quantity 100 → 80, that is −20% ÷ 20% = −1.0. The midpoint method uses the average of the two values as the base instead of the starting value.
- Why is PED usually negative?
- Because demand curves slope downward — a higher price means lower quantity, so the two percentage changes have opposite signs. Economists often quote the absolute value and drop the sign, so "an elasticity of 1.8" generally means −1.8.
- What is the difference between the standard and midpoint methods?
- The base they divide by. The standard method uses the starting value, so the answer depends on which end you travel from — $10 → $12 gives −1.0 but $12 → $10 gives −1.5 for the same pair of points. The midpoint method uses the average of both values, giving −1.2222 either way.
- Which method should I use?
- The midpoint method for any meaningful price range, because it gives one answer rather than two. The standard method is fine for small changes and is simpler to explain, which is why textbooks introduce it first. Over a wide range the two can even disagree on the elastic/inelastic classification.
- What do elastic and inelastic mean?
- Elastic means |PED| > 1 — quantity responds proportionally more than price, typical of discretionary goods with substitutes. Inelastic means |PED| < 1 — quantity responds proportionally less, typical of necessities. At exactly 1 the two effects cancel and demand is unit elastic.
- How does elasticity affect my revenue?
- If demand is inelastic, raising the price raises revenue, because the quantity lost is proportionally smaller. If it is elastic, raising the price lowers revenue. At unit elasticity revenue is unchanged, which is the revenue-maximising point on a linear demand curve.
- Why did my revenue fall even though demand looked inelastic?
- The revenue rule is exact only for small changes. Over a wide price range the standard method can read inelastic while revenue falls — price $10 → $15 with quantity 100 → 60 gives a standard PED of −0.8 yet revenue drops 10%. The midpoint method gives −1.25 there, which matches what revenue actually did.
- What makes demand more or less elastic?
- Substitutes are the main driver — the more alternatives, the more elastic. Necessity reduces elasticity, as does a small share of the buyer's budget and brand loyalty. Time matters too: demand is far more elastic over a year than over a week, because substitution takes time to arrange.
- Can PED be positive?
- Mathematically yes, if quantity rises with price, but it contradicts normal demand behaviour and usually signals a data error. Genuine cases exist — Veblen goods bought for status, and speculative assets where rising prices attract buyers — but they are exceptions worth verifying.