Price Elasticity of Demand Calculator

Point and arc elasticity of demand from a linear demand curve.

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About this tool

Enter a linear demand curve and a price to get the point elasticity of demand and whether demand is elastic, inelastic or unit elastic. Add a second price to get the arc elasticity between the two points.

How to use

1
Step 1
Enter the demand intercept a and slope b.
2
Step 2
Enter the price point.
3
Step 3
Optionally enter a second price for arc elasticity, then compute.

How it works

Point elasticity at price P is −b × P ÷ Q. It measures the percentage change in quantity for a 1% price change. Its size matters: above 1 is elastic, below 1 inelastic, exactly 1 unit elastic. On a straight demand line elasticity changes along the curve, high at high prices and low at low prices. Arc elasticity compares two points using midpoints, so the answer is the same in either direction.

point: E = −b × P ÷ Q(P)      arc: E = [(Q₂ − Q₁) ÷ average Q] ÷ [(P₂ − P₁) ÷ average P]

Worked example

Qd = 120 − 3P

Input
a 120; b 3; price 30, then 10, then arc from 20 to 30
Output
P = 30: −3 (elastic). P = 10: −0.3333 (inelastic). Arc 20 to 30: −1.6667
Walkthrough
At 30, quantity is 120 − 90 = 30, so E = −3 × 30 ÷ 30 = −3. At 10, quantity is 90, so E = −3 × 10 ÷ 90 = −0.3333. At 20 quantity is 60 and E = −1, unit elastic. Arc from 20 to 30: quantity 60 to 30, ΔQ = −30 over average 45, ΔP = 10 over average 25, giving −0.6667 ÷ 0.4 = −1.6667.

Limitations

  • Linear demand only.
  • Undefined when quantity demanded is zero at the chosen price.
  • Supply parameters are not used here.

Questions

How do I calculate price elasticity of demand?
For a linear demand curve, E = −b × P ÷ Q at that price. At P = 30 with Qd = 120 − 3P, E = −3 × 30 ÷ 30 = −3.
What does an elasticity of −3 mean?
A 1% price rise cuts quantity demanded by about 3%, so demand is elastic.
What is the difference between point and arc elasticity?
Point elasticity is at one price. Arc elasticity is the average over a price range between two points, using midpoints.
Why does elasticity change along a straight line?
Because the percentage changes depend on the starting price and quantity, which both change as you move along the curve.

Features

  • Point and arc elasticity
  • Elastic or inelastic label
  • Runs in your browser

Related resources

Guides and videos from around the web—opens on YouTube or the publisher’s site.

  • Market equilibrium

    Khan Academy

    How P* and Q* arise before surplus shading.

    Watch on YouTube

  • Taxes and deadweight loss

    Khan Academy

    Tax wedges and DWL behind the incidence calculator.

    Watch on YouTube

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