Price Elasticity of Demand Calculator

What is a price elasticity of demand calculator?

A price elasticity of demand calculator is a free online tool that tells you how strongly the quantity people buy reacts when a price moves. You enter the price and quantity before the change and the price and quantity after it, and the calculator returns the price elasticity of demand (PED) along with the percentage change in quantity, the percentage change in price, and a plain-language verdict on whether demand is elastic, unit elastic, or inelastic. It is a quick way to gauge how a price decision is likely to affect sales volume and revenue.

Why elasticity matters

Elasticity is one of the most practical numbers in pricing. When demand is elastic, a small price cut can win a disproportionately large jump in volume, so lowering the price can actually raise total revenue. When demand is inelastic, buyers keep purchasing roughly the same amount regardless of price, so a price increase tends to lift revenue. Knowing where a product sits on this spectrum helps you set prices, plan promotions, and forecast how a competitor’s move or a tax change might ripple through your sales.

How does the calculator work?

You supply four numbers:

• Initial price (P₁) and new price (P₂) — the price before and after the change.
• Initial quantity (Q₁) and new quantity (Q₂) — the quantity demanded before and after the change.

The calculator uses the midpoint, or arc, method. Instead of dividing each change by its starting value, it divides by the average of the start and end values. This makes the result symmetric: you get the same elasticity whether the price rises from P₁ to P₂ or falls from P₂ back to P₁. The raw PED is usually negative, because price and quantity move in opposite directions, so the calculator reports its absolute value and uses that to classify demand. If the price does not change, the percentage change in price is zero and elasticity is undefined, so the tool returns no result rather than dividing by zero.

Formula

The midpoint (arc) price elasticity of demand is the percentage change in quantity divided by the percentage change in price, where each percentage change is measured against the average of the two values:

$PED = \frac{\dfrac{Q_2 - Q_1}{(Q_1 + Q_2) / 2}}{\dfrac{P_2 - P_1}{(P_1 + P_2) / 2}}$

The two percentage changes are:

$\%\,\Delta Q = \frac{Q_2 - Q_1}{(Q_1 + Q_2) / 2} \times 100$

$\%\,\Delta P = \frac{P_2 - P_1}{(P_1 + P_2) / 2} \times 100$

Where:

• $P_1$ and $P_2$ are the initial and new prices.
• $Q_1$ and $Q_2$ are the initial and new quantities demanded.

Demand is classified by the absolute value of the elasticity:

• $|PED| > 1$ — elastic.
• $|PED| = 1$ — unit elastic.
• $|PED| < 1$ — inelastic.

Worked examples

1. A store drops the price of a TV from $800 to $700 and weekly sales rise from 200 to 250 units: $\%\,\Delta Q = \frac{250 - 200}{(200 + 250) / 2} \times 100 = 22.22\%$ $\%\,\Delta P = \frac{700 - 800}{(800 + 700) / 2} \times 100 = -13.33\%$ $|PED| = \left| \frac{22.22}{-13.33} \right| = 1.67$ Because $|PED| > 1$, demand is elastic — the price cut wins a large volume gain.

2. A coffee shop raises a drink from $10 to $12 and sales slip from 100 to 95 cups: $\%\,\Delta Q = \frac{95 - 100}{(100 + 95) / 2} \times 100 = -5.13\%$ $\%\,\Delta P = \frac{12 - 10}{(10 + 12) / 2} \times 100 = 18.18\%$ $|PED| = \left| \frac{-5.13}{18.18} \right| = 0.28$ Because $|PED| < 1$, demand is inelastic — buyers barely cut back, so the price rise lifts revenue.

3. A product moves from $9 to $11 while quantity falls from 110 to 90: $\%\,\Delta Q = \frac{90 - 110}{(110 + 90) / 2} \times 100 = -20\%$ $\%\,\Delta P = \frac{11 - 9}{(9 + 11) / 2} \times 100 = 20\%$ $|PED| = \left| \frac{-20}{20} \right| = 1$ Because $|PED| = 1$, demand is unit elastic — revenue stays roughly unchanged.

Practical notes

The midpoint method is the standard choice for arc elasticity because it removes the bias you get from picking one endpoint as the base. Keep in mind that elasticity is rarely constant: a product can be inelastic over a small price range and elastic over a larger one, so the figure you compute applies to the specific move you measured. Necessities, items with few substitutes, and small-ticket purchases tend toward inelastic demand, while luxuries, easily substituted goods, and big-ticket items tend toward elastic demand.

FAQs

Why is the elasticity usually shown as a positive number?

The raw ratio is negative because price and quantity normally move in opposite directions. By convention the result is reported as an absolute value so it is easier to compare and to classify; the sign simply confirms the inverse relationship.

Why use the midpoint method instead of a simple percentage change?

A simple percentage change gives a different answer depending on whether you treat the start or the end as the base, so the elasticity from A to B would not match the elasticity from B to A. The midpoint method divides by the average of the two values, producing one consistent figure for the whole interval.

What does it mean for revenue when demand is elastic or inelastic?

When demand is elastic, cutting the price tends to raise total revenue because the gain in volume outweighs the lower price. When demand is inelastic, raising the price tends to raise revenue because volume barely falls. At unit elasticity, revenue is roughly unchanged by a small price move.