What this calculator does
The midpoint method calculates price elasticity of demand using the average of the two prices and the average of the two quantities as the base for each percentage change, rather than the original value alone. It answers exactly the same question as the standard elasticity calculation, how much quantity demanded responds to a price change, but avoids a known quirk in the simpler version.
The quirk is this: with the ordinary percentage-change formula, calculating the elasticity from price A to price B gives a different number than calculating it from price B back to price A, purely because the base of the percentage changes depending on direction. The midpoint formula uses the same base either way, so a textbook or a study covering the same two points will always report the same elasticity, which is why it is the standard taught in most introductory economics courses.
The formula
Work out the percentage change in quantity using the average of the old and new quantity as the base, and the percentage change in price the same way, using the average of the old and new price. Divide the quantity percentage change by the price percentage change to get the elasticity.
| Term | Meaning |
|---|---|
| Midpoint %ΔQ | (Q2 − Q1) divided by the average of Q1 and Q2, times 100. |
| Midpoint %ΔP | (P2 − P1) divided by the average of P1 and P2, times 100. |
| Elasticity | Midpoint %ΔQ divided by midpoint %ΔP. Values above 1 in magnitude are elastic, below 1 are inelastic. |
The inputs explained
| Field | What to enter |
|---|---|
| Original price ($) | The price before the change. |
| New price ($) | The price after the change. Must differ from the original price. |
| Original quantity demanded | The quantity demanded at the original price. |
| New quantity demanded | The quantity demanded at the new price. |
When to use it
Comparing elasticity across studies
Two analyses of the same product using the same two price points should agree on elasticity. The midpoint method guarantees that agreement regardless of which price either analyst treated as the "starting" one.
Setting a price and expecting a symmetric answer
A retailer testing a price rise, then later reversing it back to the original price, gets one consistent elasticity figure for that price range, not two different figures depending on which direction was calculated first.
Teaching or checking coursework
The midpoint formula is the version most economics courses expect for elasticity problems, so it is the one to reach for when checking a textbook-style calculation.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How elasticity compares to the simple percentage-change method at different price rises
The same price rise and quantity fall, calculated with the midpoint method, for a range of new prices.
| New price | Elasticity of demand (midpoint method) | Classification |
|---|---|---|
| $11.00 | -2.333 | Elastic: quantity demanded responds more than proportionally to price |
| $12.00 | -1.222 | Elastic: quantity demanded responds more than proportionally to price |
| $13.00 | -0.852 | Inelastic: quantity demanded responds less than proportionally to price |
| $14.00 | -0.667 | Inelastic: quantity demanded responds less than proportionally to price |
| $15.00 | -0.556 | Inelastic: quantity demanded responds less than proportionally to price |
| $20.00 | -0.333 | Inelastic: quantity demanded responds less than proportionally to price |
How elasticity changes with the size of the quantity response
A fixed price rise from $10 to $12, with the new quantity demanded varying.
| New quantity demanded | Elasticity of demand (midpoint method) | Classification |
|---|---|---|
| 95 | -0.282 | Inelastic: quantity demanded responds less than proportionally to price |
| 90 | -0.579 | Inelastic: quantity demanded responds less than proportionally to price |
| 85 | -0.892 | Inelastic: quantity demanded responds less than proportionally to price |
| 80 | -1.222 | Elastic: quantity demanded responds more than proportionally to price |
| 70 | -1.941 | Elastic: quantity demanded responds more than proportionally to price |
| 60 | -2.750 | Elastic: quantity demanded responds more than proportionally to price |
Questions
Why does the midpoint method give a different answer to the simple formula?
The simple formula divides the change by the original value, so calculating from A to B uses a different base than calculating from B to A. The midpoint method divides by the average of the two values instead, which is the same average regardless of direction, so the result matches either way.
Which method should I use?
The midpoint method is the standard taught in most introductory economics courses and is the safer default when the direction of the price change is not fixed by the question. The simple percentage-change method is still valid for a single, clearly directional calculation.
Does the midpoint method change whether demand is elastic or inelastic?
It can, particularly for large percentage changes, because the two formulas can produce noticeably different numbers even though they describe the same two data points. For small changes the two methods converge to nearly the same result.
What does a negative elasticity mean?
A negative sign reflects the normal inverse relationship between price and quantity demanded: price up, quantity down, or vice versa. Economists often quote elasticity by its absolute value, since the negative sign is expected for almost all ordinary goods.
For the simpler percentage-change version of this formula, see the price elasticity of demand calculator. For how demand responds to income rather than price, see the income elasticity of demand calculator.