Economic Midpoint Formula Calculator
Raise a price from $10 to $12 and quantity falls from 100 to 80: how elastic is demand? The simple percentage method gives one answer going up and a different answer coming back down, which makes it useless for comparing two points. This economic midpoint formula calculator uses the arc method instead, dividing each change by the average of the two prices and the average of the two quantities, so the elasticity is the same in either direction. It is an economics tool for price elasticity, not the geometry midpoint between two points on a graph.
Quick Answer
When price rises from $10 to $12 and quantity demanded falls from 100 to 80, midpoint elasticity is -1.222. Read by absolute value, 1.22 is above 1, so demand is elastic: the 22.22% midpoint fall in quantity outweighs the 18.18% midpoint rise in price, and total revenue falls from $1,000 to $960.
- Quick Answer
- How to use the midpoint formula calculator
- The midpoint formula, step by step
- Worked example: a $10 to $12 price rise
- Reading the result: elasticity bands and revenue
- Not the geometry midpoint: read this before you calculate
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the midpoint formula calculator
Enter the two prices and the two quantities that go with them, then click Calculate. The order matters less than the pairing: the old quantity must be the quantity at the old price, and the new quantity the quantity at the new price.
- Old and new price: the price before and after the change, in the same currency. Either can be the larger one.
- Old and new quantity: units demanded or sold at each price, over the same period. A week against a week, a month against a month.
- Read the sign, then the size: the result is normally negative for demand. Judge responsiveness by the absolute value against 1, using the verdict badge and the bands table below.
The midpoint formula, step by step
Elasticity is the percentage change in quantity divided by the percentage change in price. The midpoint twist is the base: each change is divided by the average of the two values, not by the starting value. The OpenStax Principles of Economics chapter on price elasticity presents this as the standard way to measure elasticity between two points on a demand or supply curve.
% change in price = (P2 − P1) ÷ ((P1 + P2) ÷ 2)
Elasticity = % change in quantity ÷ % change in price
Because the average is the same whichever point you start from, reversing the move gives exactly the same elasticity. Run the worked example backwards, price falling from $12 to $10 and quantity rising from 80 to 100, and the calculator still returns -1.222. The simple method cannot do that, as the comparison below shows. Elasticity has no units: it is a ratio of two percentages, a point the OpenStax chapter stresses and the reason a single number can be compared across products priced in different currencies and sold in different pack sizes. If you want the broader family of elasticity measures beyond price, a coefficient of elasticity calculator covers the general coefficient form this price version is built from.
Simple percentage method
- Going up, $10 to $12 and 100 to 80: quantity -20%, price +20%, elasticity -1.00
- Coming back, $12 to $10 and 80 to 100: quantity +25%, price -16.67%, elasticity -1.50
- Two different answers for the same two points, depending on direction
Midpoint (arc) method, this calculator
- Going up: quantity -22.22%, price +18.18%, elasticity -1.222
- Coming back: quantity +22.22%, price -18.18%, elasticity -1.222
- One answer both ways, which is why textbooks use it between two points
Worked example: a $10 to $12 price rise
A shop raises a product from $10 to $12 and weekly sales fall from 100 units to 80. Here is the full calculation the calculator performs.
The revenue check confirms the verdict. At $10 the shop took $1,000 a week; at $12 it takes $960. When demand is elastic, a price rise loses more in volume than it gains per unit, so revenue falls. Had the same price rise produced an elasticity of -0.538, like a staple moving from $5.00 to $5.50 while quantity eased from 1,000 to 950, revenue would have risen instead, because buyers barely adjusted. That link between elasticity and revenue is also why the size of a price move shows up in wider measures such as a change in aggregate demand estimate at market level.
Reading the result: elasticity bands and revenue
Judge the result by its absolute value. The bands below are the standard textbook set, set out in the OpenStax section on polar cases of elasticity, with the revenue consequence that follows for a price rise.
| Absolute value | Reading | Price rise does what to revenue? |
|---|---|---|
| Above 1: elastic | Quantity responds more than price changes. Typical for luxuries and goods with close substitutes. | Revenue falls: volume loss beats the higher price. |
| Exactly 1: unit elastic | Quantity and price change by the same midpoint percentage. | Revenue is at its peak for that demand curve. |
| Below 1: inelastic | Quantity responds less than price changes. Typical for necessities with few substitutes. | Revenue rises: buyers keep buying at the higher price. |
| 0: perfectly inelastic | Quantity did not change at all between the two prices. | Revenue rises by the full price increase. |
Two limits worth knowing. First, this is arc elasticity between two observed points: it describes the move you measured, not the whole demand curve, and a bigger jump to a third price can give a different figure. Second, the two quantities must differ only because of price. If a competitor launched, the season turned or incomes shifted between the two observations, the result mixes those effects into the elasticity. The Lumen Learning macroeconomics chapter on elasticity works through the same midpoint arithmetic for supply, and the method transfers directly: put quantities supplied in place of quantities demanded and the sign comes out positive, because supply rises with price.
Not the geometry midpoint: read this before you calculate
Midpoint means two unrelated things in maths and economics, and search results mix them freely. The geometry midpoint is the point halfway between two coordinates on a line, found by averaging the x values and the y values. This page has no coordinates and finds no point: it is the economics midpoint method, where averaging the two prices and the two quantities is simply the base for two percentage changes. If your homework question gives two prices and two quantities and asks for elasticity, you are in the right place. If it gives coordinate pairs and asks for the point between them, you need the geometry tool instead.
What competing calculators miss
- Direction dependence, hidden: many elasticity tools quietly use the simple percentage method, so swapping old and new values changes the answer. This one uses averages as the base, and the worked example proves the same -1.222 comes back in reverse.
- A number with no reading: returning -1.222 alone leaves students and sellers to guess what it means. The verdict badge and bands table classify it and state the revenue consequence in the same view.
- The no-change trap: when the price does not change, elasticity is undefined, not zero and not infinity. This calculator says so plainly instead of printing a broken number, a case most tools leave as NaN.
- Geometry confusion: pages titled midpoint calculator often blend the coordinate formula with the elasticity formula. This page separates them in its own section so the two intents never contaminate each other.
Frequently asked questions
It is a way of calculating elasticity between two points that divides the change in quantity by the average quantity, and the change in price by the average price, then divides the first percentage by the second. Using averages as the base means the result is the same whether price rose or fell between the two points.
Because ordinary percentages use the starting value as the base, so the answer depends on direction. In the worked example the simple method gives -1.00 for the price rise and -1.50 for the return move over the same two points. The midpoint method gives -1.222 both ways, which is why it is also called arc elasticity.
Both conventions exist. The calculator keeps the true signed result, which is negative for normal demand because price and quantity move in opposite directions. When classifying demand as elastic, unit elastic or inelastic, compare the absolute value with 1, and say which convention you are using in written work.
Yes. Enter quantities supplied at the old and new prices in place of quantities demanded. The calculation is identical and the result is normally positive, because quantity supplied rises when price rises. The bands read the same way: above 1 is elastic supply, below 1 is inelastic supply.
Elasticity is undefined, because the percentage change in price is zero and the formula divides by it. This calculator reports Undefined rather than a number. In practice a zero price change tells you nothing about responsiveness, so you need a different pair of observations.
Point elasticity measures responsiveness at a single point on a demand curve and uses the slope of the curve, which needs calculus or a demand equation. Midpoint, or arc, elasticity measures responsiveness across the stretch between two observed points, which is all you have when your data is two prices and two quantities from real sales.
No. The geometry midpoint averages two coordinates to locate the point halfway between them. The economics midpoint method averages two prices and two quantities only to build percentage changes for elasticity. Same word, different job: if your problem has no prices or quantities, this is not the tool for it.
Demand is unit elastic: the percentage change in quantity matches the percentage change in price, so the two effects cancel and total revenue stays the same across the move. On a typical demand curve, revenue is highest near the unit elastic point, which is why sellers test prices around it.
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References
- OpenStax. Price Elasticity of Demand and Price Elasticity of Supply, Principles of Economics 3e. Accessed October 21, 2026.
- OpenStax. Polar Cases of Elasticity and Constant Elasticity, Principles of Economics 3e. Accessed October 21, 2026.
- Lumen Learning. Price Elasticity of Demand and Price Elasticity of Supply, Macroeconomics. Accessed October 21, 2026.
- TutorChase. Calculating Price Elasticity of Demand, AP Microeconomics Notes. Accessed October 21, 2026.
- LibreTexts. Reading: Calculating Price Elasticities. Accessed October 21, 2026.