Price elasticity of demand calculator

How to read this graph

• The blue line is demand. In point mode you can drag it; in midpoint mode it is the straight line through your two points, A and B.
• The shading splits the line in two. Above the halfway price (the dot marked E 1) demand is elastic: buyers are sensitive to price. Below it, demand is inelastic.
• The small rings show the elasticity at other prices. A quarter of the way down the price scale it is 3, at the halfway point 1, and three quarters of the way down 0.33. The slope never changes, but elasticity does.
• In the chips underneath you will find the signed elasticity, the percentage changes behind it, the revenue before and after, and the point elasticity at each end of your two points.

How it works

midpoint (arc) method, between (P₁, Q₁) and (P₂, Q₂):
%ΔQ = (Q₂ − Q₁) ÷ ((Q₂ + Q₁) ÷ 2)
%ΔP = (P₂ − P₁) ÷ ((P₂ + P₁) ÷ 2)
E = %ΔQ ÷ %ΔP
point method, on the straight line P = a − b × Q, at price P:
Q = (a − P) ÷ b
E = (dQ/dP) × (P ÷ Q) = −(1 ÷ b) × P ÷ Q = −P ÷ (a − P)

• a is where demand meets the price axis and b is the slope. A book that writes demand as Qd = 100 − 10P needs turning round first: P = 10 − 0.1Q, so a = 10 and b = 0.1.
• The point formula needs only the price and the intercept. The slope cancels out, which is why a steeper line is not the same as less elastic.
• Demand is unit elastic at P = a ÷ 2. Above it |E| is over 1, below it under 1. At that price total revenue (price × quantity) is at its largest.
• Perfectly inelastic means the quantity does not change when the price does (E = 0); perfectly elastic means the price did not change but the quantity did. The calculator says so instead of printing a number.
• Price and quantity carry no units. Dollars and units, euros and tonnes, all give the same elasticity.

Worked example

OpenStax’s demand example: the price falls from $70 (point B) to $60 (point A) and the quantity rises from 2,800 to 3,000. Open it in the calculator.

• Quantity: (3,000 − 2,800) ÷ 2,900 = 200 ÷ 2,900 = 6.9%.
• Price: (60 − 70) ÷ 65 = −10 ÷ 65 = −15.4%.
• Elasticity: 6.9 ÷ −15.4 ≈ −0.45, or 0.45 without the sign. It is under 1, so demand is inelastic here. A 10% price rise would cut the quantity by only about 4.5%.
• Revenue fell from 70 × 2,800 = 196,000 to 60 × 3,000 = 180,000, which is what inelastic demand predicts when the price drops.

More to try:

• OpenStax, G to H: $120 to $130 and 1,800 to 1,600 gives 1.47, elastic. Same slope, higher on the line.
• UW–Madison hot chocolate: Qd = 100 − 10P at P = 7 gives 30 units and an elasticity of 7/3, about 2.33.
• The calculus text’s ribbon winders: p = 300 − 0.02q at $70 gives 11,500 units and an elasticity of about 0.3.

Tips

• Mind the order of the inputs. The quantity typed under each price must be the quantity bought at that price. Swap them and you will get a positive (upward-sloping) result, which the calculator flags.
• Bigger steps, bigger gaps. The midpoint answer is an average over the stretch. Shrink the price change and it approaches the point elasticity at that price.
• Check against the graph. If your line sits mostly above the E 1 dot, expect an elastic answer; mostly below, an inelastic one.
• The straight-line model is a simplification. Real demand curves bend. The point method on a line is exact only for that line, and a real market’s elasticity at a price can only be estimated from data.
• Supply elasticity uses the same midpoint formula with supply’s price and quantity. The Supply & Demand Studio shows both elasticities at the equilibrium.

FAQ

Sources

1. 5.1 Price Elasticity of Demand and Price Elasticity of Supply, OpenStax, Principles of Economics 3e (Rice University). The midpoint formula, the $70 to $60 (0.45) and $120 to $130 (1.47) demand examples, the rent example for supply (3.53), and the reminder that elasticity is not slope.
2. ECON 101 Spring 2015, Homework #3 (answers), question 1c and 1f, University of Wisconsin–Madison, Economics 101 (Emily Kelly). Point elasticity on Qd = 100 − 10P and Qs = 5P − 5 at P = 7 (demand 7/3, supply 7/6) and after demand shifts (2.2 and 1.1).
3. Section 2.10: Elasticity of Demand, Business Calculus, David Lippman and Shana Calaway (Open Textbook Store). The point formula E = |(p/q)(dq/dp)| and the ribbon-winder demand p = 300 − 0.02q, where elasticity at $70 is about 0.3.

Formula and sources last checked September 30, 2026. How we test formulas.

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