Coefficient Of Elasticity Calculator
Raise a price by 20% and watch sales fall, but by how much? The coefficient of elasticity turns that question into one number: the percentage change in one value divided by the percentage change in the variable that moved it.
Enter the starting and ending figures for both, and this calculator returns the coefficient with its sign kept, both percentage changes shown, and a plain reading of whether the response is elastic, inelastic, or exactly proportional.
How it was calculated
This calculator uses the endpoint method: percentage changes are measured from the initial values, which is the textbook starting point. The midpoint method gives a different number for the same data; the article below shows both so you can see the gap.
Quick Answer
Key takeaways
- Elasticity is a ratio of percentage changes, so it has no units and can be compared across products, currencies, and time periods.
- The sign carries information: negative for ordinary price elasticity of demand, positive for supply, and either sign for income and cross-price elasticity depending on the good.
- Size decides the label: absolute value above 1 is elastic, below 1 is inelastic, exactly 1 is unit elastic, and 0 is perfectly inelastic.
- This calculator uses the endpoint method, measured from the initial values. The midpoint method gives a different answer for the same data, and honest work says which one it used.
- Quick Answer
- How to use the coefficient of elasticity calculator
- The formula: percentage change divided by percentage change
- Worked example: a 20% price rise that cuts volume by 20%
- Reading the result: sign first, then size
- One formula, four different elasticities
- The endpoint trap: direction changes the answer
- What competing calculators miss
- What the coefficient does to revenue
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
How to use the coefficient of elasticity calculator
Put the responding quantity in the value fields and the thing that changed in the variable fields. For price elasticity of demand, the value is quantity demanded and the variable is price. For income elasticity, the variable is income instead. For cross-price elasticity, the variable is the price of a different good. Press Calculate and the tool shows both percentage changes before the ratio, so you can check the arithmetic instead of trusting a bare number.
The order matters. Swapping initial and final values does not just flip the sign: because the endpoint method divides by the starting values, running the same change backwards gives a different coefficient. The section on the endpoint trap below shows that with real numbers. If you are checking a percentage change on its own first, the change percent calculator isolates that single step.
The formula: percentage change divided by percentage change
The coefficient is the percentage change in the value divided by the percentage change in the variable, with each percentage change measured from its starting point.
Dividing one percentage change by another is what makes elasticity useful. A slope depends on units: sell in cases instead of units and the slope changes twelvefold while nothing real has moved. Elasticity is unit-free, which is why economists can compare the price sensitivity of gasoline with the price sensitivity of restaurant meals on the same scale. OpenStax defines it the same way in its price elasticity of demand and supply section: a ratio of percentage changes, grouped into elastic, inelastic, and unitary cases.
Worked example: a 20% price rise that cuts volume by 20%
The calculator is pre-filled with this case, and every figure below is what it returns.
| Step | Calculation | Result |
|---|---|---|
| Percentage change in quantity | (80 - 100) / 100 | -20.00% |
| Percentage change in price | (12 - 10) / 10 | +20.00% |
| Coefficient of elasticity | -20.00% / +20.00% | -1.0000 |
| Reading | Absolute value exactly 1 | Unit elastic |
Unit elastic is the revenue dividing line. At exactly this responsiveness, a price rise loses just enough volume to cancel itself out, so revenue stays roughly flat. More elastic than this and a price rise cuts revenue; less elastic and it raises revenue, which is why sellers care about which side of 1 they sit on before touching a price.
Reading the result: sign first, then size
Read the sign before the size. A negative coefficient for price elasticity of demand is normal: price and quantity move in opposite directions. A positive cross-price coefficient says the two goods are substitutes, a negative one says complements, and a negative income coefficient marks an inferior good. Dropping the sign, as some tools do, throws away exactly that information.
| Absolute value | Label | What it means |
|---|---|---|
| 0 | Perfectly inelastic | No response Quantity does not move at all |
| Between 0 and 1 | Inelastic | Weak response Quantity moves less than proportionally |
| Exactly 1 | Unit elastic | Proportional Quantity moves in the same percentage |
| Above 1 | Elastic | Strong response Quantity moves more than proportionally |
| Toward infinity | Perfectly elastic | Extreme Any price rise kills demand at that price |
Published estimates put most everyday goods well inside the inelastic band. The selected elasticities collected in the elasticity and pricing chapter of OpenStax Principles of Economics include housing at 0.12, electricity at 0.20, and gasoline at 0.35, with restaurant meals at 2.27 on the elastic side. Necessities cluster near zero because buyers have no substitute and no real choice; discretionary spending sits above 1 because skipping it is easy.
One formula, four different elasticities
The same four boxes serve four standard measures. Only the pairing of value and variable changes.
Price elasticity of demand
- Value: quantity demanded
- Variable: own price
- Usually negative: price up, quantity down
Price elasticity of supply
- Value: quantity supplied
- Variable: own price
- Usually positive: price up, supply up
Income elasticity of demand
- Value: quantity demanded
- Variable: consumer income
- Positive for normal goods, negative for inferior goods
Cross-price elasticity
- Value: quantity demanded of good A
- Variable: price of good B
- Positive for substitutes, negative for complements
Context decides which one you are looking at. A demand shift driven by income or by a rival's price is a different story from movement along your own demand curve, and the change in aggregate demand calculator covers the economy-wide version of those shifts.
The endpoint trap: direction changes the answer
The endpoint method measures percentage changes from the starting values, and that choice has a cost you should know about. Run the pre-filled example backwards, a price cut from $12 to $10 with quantity recovering from 80 to 100, and the same calculator returns (100 - 80) / 80 divided by (10 - 12) / 12, which is 25.00% / -16.67% = -1.5000. Same two points on the same demand curve, two different coefficients, purely because the base changed.
The midpoint (arc) method fixes that by dividing each change by the average of the two endpoints. For the pre-filled example it gives (-20 / 90) / (2 / 11) = -1.2222, and it returns the same -1.2222 in both directions. Neither answer is a mistake; they are different conventions. The trap is a tool that never tells you which convention it used, so its number cannot be compared with anyone else's.
What competing calculators miss
The price elasticity tools reviewed for this page split into two silent camps, and neither camp labels itself.
Miss 1: the method is never named. Some of the top-ranking tools use the midpoint formula, others the endpoint formula, and the pages rarely say which. For identical data the two methods returned -1.0000 and -1.2222 in our test case, a gap big enough to flip a pricing decision. This page names its method in the calculator, shows both percentage changes, and prints the midpoint figure for the worked example so the difference is visible.
Miss 2: the sign is stripped. At least one top tool applies an absolute value and reports elasticity as a positive number. That is convenient for demand and wrong for everything else: it erases the substitute-versus-complement signal in cross-price elasticity and the inferior-good signal in income elasticity. This calculator keeps the sign and explains what it means.
Miss 3: price and demand only. Most rival tools hard-label their fields as price and quantity demanded, so supply, income, and cross-price work means pretending your income figures are prices. The generic value and variable fields here accept any pairing, and the four-box guide above shows how to set each one up.
One honest limit: two points give one coefficient for one range of one curve. Elasticity changes along a demand curve and over time, so a coefficient measured last quarter is an estimate for next quarter, not a law.
What the coefficient does to revenue
Revenue is price times quantity, so the coefficient predicts the direction of a price change before you make it. With elastic demand, the percentage loss in quantity beats the percentage gain in price and revenue falls. With inelastic demand, quantity barely moves and revenue rises. At unit elasticity the two cancel. Sellers working through a price rise usually check the margin side of the same move as well, for example with the 20 percent margin calculator, because revenue and profit do not always move together.
Taxes follow the same logic. A tax lands mostly on whichever side of the market is less elastic, because that side cannot walk away. Fuel taxes fall on drivers (elasticity near 0.35) rather than on stations, which is a policy conclusion drawn straight from the coefficient.
Frequently Asked Questions
It is the percentage change in one value divided by the percentage change in another: how strongly quantity, sales, or supply responds when price, income, or a related price moves. Because it is a ratio of percentages it has no units, so coefficients can be compared across products and markets.
Because price and quantity demanded move in opposite directions: price rises and quantity falls, so one percentage change is positive and the other is negative. Many textbooks report the absolute value, but the negative sign is the honest result and this calculator keeps it.
It means the percentage change in the value exactly equals the percentage change in the variable, a coefficient of 1 in absolute value. For pricing it is the dividing line: at unit elasticity a price change leaves revenue roughly unchanged, because the volume gained or lost exactly offsets the price move.
The endpoint method: each percentage change is divided by its initial value. It is the standard textbook starting point and the easiest to audit by hand. Be aware it is direction-sensitive: the same change run backwards gives a different coefficient, while the midpoint method gives one answer both ways.
Yes. The fields are deliberately generic. For income elasticity, enter quantity demanded as the value and income as the variable. For cross-price elasticity, enter the quantity of one good as the value and the price of the other good as the variable. A positive cross-price result means substitutes; negative means complements.
Slope measures the absolute change in one variable per unit change in another, so it depends on the units you measure in. Elasticity measures percentage change against percentage change, so it is unit-free. The same demand curve has many slopes in different units but a comparable elasticity at each point.
Elasticity is undefined, because the formula would divide by a zero percentage change. In plain terms, if the price never moved, the data contains no information about how quantity responds to price. The calculator flags this instead of printing an infinite or meaningless result.
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References
- OpenStax, "Price Elasticity of Demand and Price Elasticity of Supply," Principles of Economics 3e, Section 5.1: the definition of elasticity as a ratio of percentage changes and the elastic, inelastic, and unitary categories. OpenStax: Price Elasticity of Demand and Price Elasticity of Supply. Accessed October 2026.
- OpenStax, "Elasticity and Pricing," Principles of Economics 2e, Section 5.3: how elasticity determines whether a price change raises or lowers revenue, with a table of selected demand elasticities (housing 0.12, gasoline 0.35, restaurant meals 2.27). OpenStax: Elasticity and Pricing. Accessed October 2026.
- OpenStax via LibreTexts, "Price Elasticity of Demand and Price Elasticity of Supply," Principles of Macroeconomics 3e, Section 5.2: worked calculation of price elasticity from percentage changes. LibreTexts: Price Elasticity of Demand and Price Elasticity of Supply. Accessed October 2026.
- OpenStax via LibreTexts, "Elasticity and Pricing," Principles of Microeconomics 3e, Section 5.4: elasticity, total revenue, and tax incidence. LibreTexts: Elasticity and Pricing. Accessed October 2026.
- James Cook University, "Price Elasticity of Demand and Price Elasticity of Supply," Principles of Economics (Pressbooks): an open-text treatment of the same formula and categories, adapted from OpenStax. JCU Pressbooks: Price Elasticity of Demand and Price Elasticity of Supply. Accessed October 2026.