Price Elasticity of Demand Calculator
Enter two price-quantity pairs to calculate the price elasticity of demand (PED) using the midpoint formula. Switch modes to enter percentage changes directly or to evaluate point elasticity from a linear demand function. Results include the PED coefficient, elasticity classification, revenue before and after, and the revenue impact of the price change.
What is price elasticity of demand?
Price elasticity of demand (PED) measures how responsive the quantity demanded of a good is to a change in its price. A value of -2 means that a 1% rise in price leads to a 2% fall in quantity demanded. The negative sign is expected because of the law of demand: price and quantity move in opposite directions for normal goods. Economists often report the absolute value |PED| and classify goods as elastic (|PED| > 1), inelastic (|PED| < 1), or unitary elastic (|PED| = 1). Knowing where a product sits on this spectrum is one of the most actionable pieces of pricing intelligence a business can have, because it directly determines how a price change will affect total revenue.
The midpoint formula and why it matters
The simple percentage formula divides the % change in quantity by the % change in price, using the initial values as the base. This produces different answers depending on whether the price went up or down, which is known as the end-point bias. The midpoint formula solves this by using the average of the initial and final values as the denominator, giving a single consistent number regardless of direction. Most economics textbooks use the midpoint formula as the standard, and it is the default method in this calculator. For small price changes the difference between the two methods is negligible, but for large swings it can be significant. The formula is: PED = [(Q1 - Q0) / ((Q1 + Q0) / 2)] divided by [(P1 - P0) / ((P1 + P0) / 2)].
Point elasticity and linear demand functions
When you have a specific demand equation of the form Q = a - bP (a linear demand curve), you can calculate elasticity at any single point on the curve. Point elasticity is defined as (dQ/dP) x (P/Q). For the linear demand equation, the slope dQ/dP is simply -b (the coefficient is always negative because a higher price means lower quantity), so point elasticity becomes -b x (P/Q). Importantly, elasticity varies along a linear demand curve even though the slope is constant: demand is elastic in the upper half of the curve (high price, low quantity), unitary elastic at the midpoint, and inelastic in the lower half (low price, high quantity). The point elasticity mode in this calculator lets you visualize the entire demand and revenue curve for your equation.
Revenue and pricing strategy
The relationship between PED and total revenue is one of the most useful results in basic economics. If demand is elastic (|PED| > 1), raising price reduces revenue because the drop in volume more than offsets the higher per-unit margin. If demand is inelastic (|PED| < 1), raising price increases revenue because buyers barely reduce their purchases. If demand is unitary elastic (|PED| = 1), price changes have no effect on total revenue. These rules assume everything else is held constant. In practice, elasticity is not fixed: it can change with income levels, the availability of substitutes, brand strength, and the time horizon over which buyers can adjust. A product that is inelastic in the short run (no easy substitute today) can become elastic over months as buyers find alternatives or change habits.
Price elasticity of demand: classification guide
| |PED| | Classification | Buyer sensitivity | Revenue if price rises |
|---|---|---|---|
| = 0 | Perfectly inelastic | None - quantity never changes | Always rises |
| 0 to 1 | Inelastic | Low - quantity changes less than price | Rises |
| = 1 | Unitary elastic | Equal - quantity changes proportionally | Unchanged |
| > 1 | Elastic | High - quantity changes more than price | Falls |
| = Infinity | Perfectly elastic | Infinite - any price rise kills demand | Falls to zero |
How |PED| maps to elasticity type, what it means for buyers, and the revenue rule when raising price.
Frequently asked questions
Why is price elasticity of demand negative?
By the law of demand, price and quantity demanded move in opposite directions: when price rises, quantity falls, and vice versa. Because the numerator (% change in quantity) and denominator (% change in price) have opposite signs, their ratio is negative. Some textbooks and tools report the absolute value |PED| to make comparison easier, but the underlying formula always yields a negative number for normal goods.
What is the difference between the midpoint and simple percentage methods?
The simple percentage method uses the initial price and quantity as the base for the percentage calculation. This means you get a different answer depending on whether the price increased or decreased between the same two points, a problem called end-point bias. The midpoint method uses the average of the two prices and the average of the two quantities as the base, so the result is symmetric: you get the same |PED| whether you measure the change going up or going down. The midpoint method is the standard in most economics courses.
What PED value maximises revenue?
A firm maximises total revenue when PED = -1 (unitary elastic). At that point, the percentage drop in quantity exactly cancels the percentage rise in price, leaving revenue flat at a local peak. If |PED| > 1 (elastic), lowering price raises revenue. If |PED| < 1 (inelastic), raising price raises revenue. Revenue is maximised at the midpoint of a linear demand curve, where elasticity crosses through -1.
What factors make demand more elastic or inelastic?
Demand tends to be more elastic (buyers more sensitive) when: there are many close substitutes; the good is a luxury rather than a necessity; it takes a large share of the consumer budget; there is a longer time horizon for buyers to adjust. Demand tends to be more inelastic when: there are few or no substitutes (insulin, for example); the good is a necessity; spending on it is a small fraction of income; the time horizon is short and buyers cannot easily switch.
How do I interpret a PED of -0.5?
A PED of -0.5 means that a 10% increase in price leads to a 5% fall in quantity demanded. Because |PED| = 0.5, which is less than 1, demand is inelastic. A price increase will raise total revenue: you sell fewer units but the higher margin more than compensates. For every 1% price rise, revenue grows by approximately (1 - |PED|) = 0.5%.
Can PED be positive?
Yes, for two special categories: Giffen goods, where a price rise leads to more consumption because the good is a low-quality staple that people buy more of as their real income falls; and Veblen goods (luxury prestige items), where a higher price increases perceived status and thus demand. These cases are rare and the calculator flags them if your inputs produce a positive PED.
What is point elasticity versus arc elasticity?
Arc elasticity (including the midpoint method) measures the average elasticity between two distinct price-quantity points. It is useful when you have observed actual price and quantity data. Point elasticity measures the elasticity at a single exact price on a demand curve, using calculus (the derivative dQ/dP). It requires you to know the demand function. For small price changes, arc and point elasticity give very similar results.