Price Elasticity of Demand Calculator - Arc PED
Measure the signed response of quantity demanded to a price change.
Enter the initial and new price together with the initial and new quantity demanded.
About the Price Elasticity of Demand Calculator
Price elasticity of demand measures how quantity demanded responds when price changes. The price elasticity of demand calculator uses the midpoint, or arc, formula so the result does not depend on which observation you call the start. Percentage changes are taken from the average of the two prices and the average of the two quantities. The sign is preserved: a price increase paired with a quantity decrease produces a negative elasticity, which is the usual slope of a demand curve. A positive result means price and quantity moved in the same direction, which is atypical for ordinary demand and may signal a data error or a Giffen-like case. Formula: PED = [(Q2 − Q1) / ((Q1 + Q2) / 2)] ÷ [(P2 − P1) / ((P1 + P2) / 2)]. Quantity change % = (Q2 / Q1 − 1) × 100 and price change % = (P2 / P1 − 1) × 100 use the starting observation as the base, so they are not midpoint percentages. Because PED is a ratio of midpoint percentages, its absolute value can differ from the simple percent-change ratio. An absolute value above 1 is elastic demand; below 1 is inelastic; equal to 1 is unit elastic. All four inputs must be positive; a zero price or quantity would make the midpoint undefined or misleading. Arc elasticity is the right tool when the price change is large enough that a point derivative would be sensitive to direction. It is still only a two-point summary. Income, substitutes, seasonality, and stockouts can move quantity independently of price. Use the same unit for both quantities and the same currency for both prices. Mixing weekly unit sales with monthly prices will not produce a meaningful elasticity. Retailers use PED to judge whether a promotion will raise revenue: elastic demand means a price cut can increase quantity enough to lift sales, while inelastic demand means a price increase may raise revenue. That revenue test uses the sign-aware elasticity together with the percent changes shown beside it. The result is an analytical measure, not a forecast of future demand and not a recommendation to change price. Recompute whenever you have a cleaner pair of comparable observations.
Price elasticity of demand examples
Arc PED values with the sign preserved.
| Inputs | Output | Note |
|---|---|---|
| Price $10 to $12; quantity 100 to 80 | PED -1.2222; quantity -20.00%; price 20.00% | A modest price rise with an elastic quantity response. |
| Price $10 to $20; quantity 100 to 50 | PED -1; quantity -50.00%; price 100.00% | Midpoint percentages are equal in size, so arc PED is unit elastic. |
| Price $5 to $6; quantity 200 to 190 | PED -0.2821; quantity -5.00%; price 20.00% | Quantity barely falls, so demand looks inelastic over this range. |
How to calculate price elasticity of demand
- Gather two comparable observations of price and quantity demanded.
- Enter the initial and new price and the initial and new quantity.
- Select Calculate to review signed arc PED plus the simple percent changes.
- Interpret |PED| against 1 to classify elastic, inelastic, or unit-elastic demand.
Price elasticity of demand FAQ
Why is the elasticity negative?
Demand usually slopes down, so price and quantity move in opposite directions. The calculator keeps that sign instead of taking an absolute value.
Is this the midpoint formula?
Yes. Both the quantity change and the price change in the PED ratio use the average of the two observations. The separate percentage-change outputs still use the initial value as the base.
What does unit elastic mean here?
Arc PED equals −1 when the midpoint percent changes are equal in size and opposite in sign. Revenue is locally unchanged for a small move around that pair of points, holding other factors fixed.
Can I enter a price cut?
Yes. Set the new price below the initial price. If quantity rises, PED remains negative. Percent-change outputs will then show a negative price change and a positive quantity change.
Is elasticity a forecast?
No. It summarizes two historical or hypothetical points. Competing products, income, and availability can change the relationship before the next price move.