Price Elasticity of Demand Calculator

What price elasticity of demand measures

The price elasticity of demand is the percentage change in the quantity demanded divided by the percentage change in the price. It answers one question: when the price moves, how hard do buyers push back? OpenStax Principles of Economics 3e, section 5.1 gives the same definition and the same formula, and it is the standard classroom treatment of the topic.

The USDA Economic Research Service food demand analysis page frames the measure as responsiveness. Its worked illustration is an own-price elasticity for apples of -0.58, which means a 1 percent increase in the price of apples cuts demand for apples by 0.58 percent. Multiply that number by a planned price change and you have a quick forecast of what sales will do.

Because elasticity is a ratio of two percentages, the units cancel. The answer carries no currency and no product, and that is what makes it comparable: the elasticity of a fuel purchase can be set beside the elasticity of concert tickets without converting anything first. The calculator also reports what the change does to revenue, since a price decision is usually a revenue decision.

Why the midpoint method comes first

Elasticity needs a base for each percentage change, and the choice of base changes the answer. The midpoint method divides each change by the average of the starting and ending values rather than by the starting value alone, and that is the method this calculator puts first.

Consider a price move from 4 dollars to 6 dollars. Using the starting value as the base, the rise looks like 50 percent. Using the midpoint of 5 dollars, it looks like 40 percent. The midpoint version also reads 40 percent when the price travels back from 6 dollars to 4 dollars, so the answer no longer depends on which direction you write the change in. The lecture notes for ECON 323 at Texas A&M (2025) set the point formula and the midpoint formula side by side, and OpenStax calls the same approach the Midpoint Method for Elasticity.

Because the base sits in the middle of the move, the midpoint method is the right choice whenever you have two observed price and quantity pairs, which is the situation most businesses face when they look at last quarter and this quarter. The calculator keeps the starting point version on screen as well, so you can see how much the base matters on your own numbers.

Worked example: a price rise that costs revenue

A streaming service lifts its monthly price from 10 dollars to 12 dollars, and subscriptions fall from 100,000 to 80,000. Run the same move on 100 subscriptions priced at 10 dollars, then 80 at 12 dollars, and the arithmetic is identical.

Step 1, quantity change on the midpoint base: (80 - 100) divided by the average of 100 and 80, which is 90, gives -20 divided by 90, or -22.22 percent.
Step 2, price change on the midpoint base: (12 - 10) divided by the average of 10 and 12, which is 11, gives 2 divided by 11, or 18.18 percent.
Step 3, elasticity: -22.22 divided by 18.18 gives -1.22.
Step 4, revenue: 10 x 100 gives 1,000 before, and 12 x 80 gives 960 after, a change of -4.00 percent.

The magnitude of 1.22 is above 1, so demand is elastic here, and the revenue test agrees with that label: a price rise on elastic demand lowers revenue, which is what the 1,000 to 960 line shows. Enter those four numbers in the calculator and it returns the same four results, an elasticity of -1.22, the label elastic, revenue moving from 1,000 to 960, and a starting point elasticity of -1.00 for comparison.

Worked example: a price cut that pays for itself

A cafe cuts the price of a large coffee from 4.50 dollars to 4.00 dollars and daily sales rise from 200 cups to 230 cups.

Step 1, quantity change on the midpoint base: (230 - 200) divided by the average of 200 and 230, which is 215, gives 30 divided by 215, or 13.95 percent.
Step 2, price change on the midpoint base: (4.00 - 4.50) divided by the average of 4.50 and 4.00, which is 4.25, gives -0.50 divided by 4.25, or -11.76 percent.
Step 3, elasticity: 13.95 divided by -11.76 gives -1.19.
Step 4, revenue: 4.50 x 200 gives 900 before, and 4.00 x 230 gives 920 after, a change of +2.22 percent.

An elasticity of -1.19 says buyers respond more than proportionally to the cut, so revenue rises by 2.22 percent. Watch the sign handling here: the quantity change is positive and the price change is negative, so the ratio comes out negative. Most reporting drops the sign and keeps the magnitude, so the figure is normally quoted as 1.19.

Worked example: an inelastic necessity

Now take a fuel station whose price goes from 3.00 dollars to 3.60 dollars while weekly sales slip from 1,000 gallons to 980 gallons. These are worked figures chosen to show the shape of an inelastic demand curve, not a published estimate for any real market.

Step 1, quantity change on the midpoint base: (980 - 1,000) divided by the average of 1,000 and 980, which is 990, gives -20 divided by 990, or -2.02 percent.
Step 2, price change on the midpoint base: (3.60 - 3.00) divided by the average of 3.00 and 3.60, which is 3.30, gives 0.60 divided by 3.30, or 18.18 percent.
Step 3, elasticity: -2.02 divided by 18.18 gives -0.11.
Step 4, revenue: 3.00 x 1,000 gives 3,000 before, and 3.60 x 980 gives 3,528 after, a change of +17.60 percent.

A magnitude of 0.11 sits far below 1, so demand is inelastic, and the revenue test agrees: the price rise lifts revenue. A small elasticity number does not mean a small market. It means buyers do not change their minds much when the price moves, which is why staples such as fuel or a basic grocery basket can carry a price rise without losing volume.

The three ranges and the revenue test

Elasticity is normally quoted as a magnitude, and the magnitude sorts demand into three ranges. The table shows what each range means for a price cut and for a price rise.

Elasticity depends on the product and on the horizon, not on the arithmetic. Plenty of close substitutes push a price rise into a larger quantity drop. A product that eats a large slice of the household budget behaves the same way, because a move in price hits the wallet harder. Luxury goods with many alternatives tend to sit above 1, while staple goods with few alternatives tend to sit below it. Over a longer window buyers find replacements, so measured elasticity usually grows in absolute value as the period widens, and a value measured over one week is not a value for one year.

One more line of reasoning belongs next to the table. Elasticity describes how quantity responds to price along a demand curve. It does not tell you where you sit on that curve, so it cannot forecast a price change on its own. It tells you what a given price move is likely to do to volume once you already know the starting point.

What the calculator reports

The widget takes four numbers: a starting price P1, the quantity demanded at that price, a new price P2, and the quantity demanded at the new price. From those it returns eight result lines, each rounded to two decimals so that two runs on the same inputs match line for line.

Prices and quantities have to be positive, and the two prices cannot be equal, because a percentage change in price of zero has no elasticity to divide into. Units are yours to choose: enter dollars and units of output, or cents and units, and the ratio lands on the same number either way. Revenue lines carry whatever unit you typed for price multiplied by whatever unit you typed for quantity.

Five mistakes that skew the result

First, mixing bases. Run the streaming example through the starting point base and you get -1.00 rather than -1.22, and the label moves from elastic to unit elastic on identical data. Second, dropping the sign without saying so. The sign carries the direction of the law of demand, so removing it is a reporting convention rather than a change in the math.

Third, treating an elasticity as a promise. A magnitude of 1.22 does not mean that every 1 percent price cut lifts revenue by 1.22 percent. It is a response measured around the point you observed, and the response can differ at another price. Fourth, confusing revenue with profit. Revenue ignores cost, so a price cut can lift revenue and still cut profit when unit costs do not move with it.

And fifth, dropping the quantity side of the ratio. Elasticity built from price alone is a different number, and one that has no meaning on its own.