Price elasticity calculator
If you change the price, how far does quantity fall, and what happens to revenue and profit? Calculate the price elasticity of demand from two price-quantity points or from a price history, then compare price scenarios under a constant-elasticity assumption.
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- Arc (midpoint) elasticity
- -1.34
- Point elasticity (at P1, Q1)
- -1.20
- Log elasticity (constant-elasticity curve)
- -1.341
- Price change
- +10%
- Quantity change
- -12%
- Revenue (P × Q)
- 100,000 → 96,800
- Revenue change
- -3,200 (-3.2%)
- Profit ((P − cost) × Q)
- 40,000 → 44,000
- Profit change
- 4,000
Elastic demand (|e| > 1)
Quantity changes faster than price: a price increase lowers revenue, a price cut raises revenue (profit also depends on cost).
Arc: e = (ΔQ / avg Q) / (ΔP / avg P) · Point: e = (ΔQ / Q1) / (ΔP / P1) · Log: e = ln(Q2/Q1) / ln(P2/P1)
- Observations
- Constant-elasticity curve
This is a preliminary estimate. Elasticity is often not constant; it changes with price, competition, season, promotions and stock. An elasticity found from observational data may not be causal; we recommend confirming it with price tests.
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How to use it
A
Choose the calculation type: two price-quantity points, a price history with many observations (regression), or a price scenario.
B
Enter or paste the price and quantity values; add the unit cost for profit analysis.
C
Read the elasticity, its interpretation and the demand chart; in the scenario tab see the effect of a price change on revenue and profit and the profit-maximising price.
02
What is elasticity, and which formula when?
Price elasticity of demand is the percentage change in quantity divided by the percentage change in price. If e = −2, a 1% price increase lowers quantity by about 2%. If |e| > 1 demand is elastic (a price increase lowers revenue); if |e| < 1 it is inelastic (a price increase raises revenue). Profit also depends on unit cost; with inelastic demand a price increase raises profit too, while with elastic demand the direction of profit depends on cost.
Between two points, arc (midpoint) elasticity divides the changes by the averages and gives the same result whether the price rises or falls. Point elasticity divides by the starting point, so for large changes it gives different results depending on direction. Log elasticity, ln(Q2/Q1) / ln(P2/P1), is the exponent of the constant-elasticity curve Q = k · P^e through the two points; the scenario tab uses this curve.
03
How to read the many-point (log-log) regression
In the log-log model the slope of the line ln Q = a + e · ln P gives the constant elasticity. The tool finds the slope by least squares and gives R² for the share of variation explained and a 95% confidence interval for e based on the t distribution (n − 2 degrees of freedom). With few observations the interval is wide; if it includes −1, the data cannot tell whether demand is elastic.
The biggest trap is non-price factors. Price often changes in high-demand seasons or together with campaigns; then the slope measures those factors rather than the effect of price and can even come out positive. Treat elasticity from observational data only as a starting hypothesis; price tests (A/B or regional) give causal evidence.
04
Scenarios and the profit-maximising price
The scenario tab assumes constant elasticity: Q = Q0 · (P / P0)^e. It varies the price from −20% to +20% and shows the change in quantity, revenue and (if a unit cost is entered) profit. Constant elasticity is a reasonable approximation only near the observed price range; at distant prices it departs from the real demand curve.
Profit is π = (P − c) · Q. Setting the derivative to zero under constant elasticity gives P* = c · e / (1 + e), which is equivalent to (P* − c) / P* = 1 / |e|. The solution exists only for e < −1: if |e| ≤ 1, profit keeps rising with price and the model gives no optimal price. The result ignores competitor reaction, capacity, cross-effects with other products and costs that are not constant.
FAQ
- Is the data I enter sent anywhere?
- No. All calculations run in code inside your browser; the data is neither transmitted to a server nor stored.
- Why is the elasticity negative?
- That is normal: quantity falls when price rises. Some sources report the absolute value; when interpreting, look at |e|. A positive value points to non-price factors or a data problem.
- Should I use arc or point elasticity?
- For large price changes arc (midpoint) elasticity is consistent because it does not depend on direction. Point elasticity suits small changes. With several observations log-log regression is more robust.
- How many observations do I need?
- Technically 2 observations give an elasticity and at least 3 are needed for a confidence interval. For a meaningful result, at least 8–12 observations in which the price changes noticeably and non-price factors can be held constant are good.
- Why was the profit-maximising price not calculated?
- The formula P* = c · e / (1 + e) is valid only for e < −1 and unit cost c > 0. If elasticity is −1 or higher, the constant-elasticity model has no optimal price; the scenario tab explains the details.
- Is the result enough for a pricing decision?
- Not on its own. Elasticity changes with competition, season, promotions and stock, and a value found from observational data may not be causal. Confirm it with price tests.
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