Price Elasticity of Demand Calculator

Calculate price elasticity of demand (PED), classify demand as elastic, inelastic, or unit elastic, and see how a change in price affects total revenue. This student-friendly calculator supports the midpoint method, simple percentage method, direct % changes, and point elasticity from a linear demand function.

Background

Price elasticity of demand measures how strongly quantity demanded responds to a change in price. It is one of the most important ideas in Microeconomics because it connects demand behavior with revenue, pricing decisions, and graph interpretation. This calculator is built to help students do more than get a number — it explains what the answer means in plain English and connects it back to the course.

Enter values

Choose calculation mode

Midpoint method — best for most textbook and exam questions Simple percentage method — uses the initial value as the base From % changes directly — fast for MCQs and conceptual practice Point elasticity / demand function — use Q = a − bP at a specific price

Tip: Midpoint mode is the best default for most Microeconomics homework and exams.

What this calculator can show

Depending on the mode, this calculator can show % change in quantity demanded, % change in price, PED, elasticity classification, total revenue before and after, a plain-English explanation, a cleaner demand-curve visual with arrows and labels, common-mistake warnings, point-elasticity region guidance, and step-by-step work.

Midpoint method inputs

Prices

Enter the original and new price.

Price data

Initial price

New price

Quantities demanded

Enter the original and new quantity demanded.

Quantity data

Initial quantity demanded

New quantity demanded

This mode uses the midpoint formula, which avoids the direction problem that occurs with the simple percentage method.

Simple percentage method inputs

Initial price

New price

Initial quantity demanded

New quantity demanded

This method uses the initial values as the base. It is common in early lessons, but it can produce different answers depending on direction.

Direct % change inputs

Percentage changes

Enter the percentage change in quantity demanded and the percentage change in price.

Fast mode

% change in quantity demanded

Enter as a percent, not a decimal. Example: -22.22 for -22.22%.

% change in price

Optional revenue check

Add revenue data if you want to compare before and after total revenue.

Optional

Initial total revenue (optional)

New total revenue (optional)

Point elasticity / demand function inputs

Linear demand function

Use a function of the form Q = a − bP.

Demand function

a (intercept)

b (slope coefficient)

Price at the point

This mode uses the point elasticity formula PED = (dQ/dP)(P/Q). For Q = a − bP, the derivative is dQ/dP = -b.

Options

Show PED as positive magnitude (economics style)

Show step-by-step

Show plain-English explanation

Show revenue analysis

Show elasticity meter and demand visual

Display rounding

Quick picks

Chips prefill and calculate immediately.

Result

No results yet. Enter values and click Calculate. A great starting example is price 10 → 12 and quantity 100 → 80.

How to use this calculator

Choose one of the 4 modes: Midpoint Method, Simple Percentage Method, From % Changes Directly, or Point Elasticity / Demand Function.
For the first two modes, enter the original and new price and quantity demanded.
For direct % changes mode, enter the percentage change in quantity demanded and the percentage change in price.
For point elasticity mode, enter a linear demand function of the form Q = a − bP and the price at the point.
Choose whether you want the answer shown as a positive magnitude or with the negative sign kept.
Click Calculate to see PED, elasticity type, revenue effect, interpretation, and step-by-step work.

How this calculator works

Price elasticity of demand measures how responsive quantity demanded is to a change in price.
PED = (% change in quantity demanded) / (% change in price)
In the midpoint method, percentage changes are based on the average of the old and new values.
In the simple percentage method, percentage changes are based on the initial value.
For a linear demand function, point elasticity uses PED = (dQ/dP)(P/Q).
If |PED| > 1, demand is elastic. If |PED| = 1, demand is unit elastic. If |PED| < 1, demand is inelastic.
The calculator also compares total revenue before and after, which helps students connect elasticity to pricing outcomes.

Formula & Equations Used

Midpoint method

P E D = \frac{(Q_{2} - Q_{1}) / (Q_{1} + Q_{2}) / 2}{(P_{2} - P_{1}) / (P_{1} + P_{2}) / 2}

This is the most common textbook formula because it uses averages and avoids the direction problem.

Simple percentage method

P E D = \frac{(Q_{2} - Q_{1}) / Q_{1}}{(P_{2} - P_{1}) / P_{1}}

This version uses the initial values as the base, so reversing the direction can change the numerical answer.

Point elasticity

P E D = (\frac{d Q}{d P}) (\frac{P}{Q})

Use this when you are given a demand function and need elasticity at one specific price-quantity point.

Linear demand function

Q = a - b P

\frac{d Q}{d P} = - b

For a linear demand curve, the derivative is constant, so point elasticity changes because the price-to-quantity ratio changes from point to point.

Total revenue

T R = P \times Q

The calculator compares total revenue before and after the price change so students can connect elasticity to pricing outcomes.

Example Problem & Step-by-Step Solution

Example 1 - Midpoint method

Suppose price rises from \$10 to \$12, and quantity demanded falls from 100 to 80.

Step 1 — Find the change in quantity demanded

Δ Q = 80 - 100 = - 20

Step 2 — Find the average quantity

Average Q = \frac{100 + 80}{2} = 90

Step 3 — Compute % change in quantity demanded

% Δ Q = \frac{- 20}{90} = - 0.2222 = - 22.22 %

Step 4 — Find the change in price

Δ P = 12 - 10 = 2

Step 5 — Find the average price

Average P = \frac{10 + 12}{2} = 11

Step 6 — Compute % change in price

% Δ P = \frac{2}{11} = 0.1818 = 18.18 %

Step 7 — Compute PED

P E D = \frac{- 22.22 %}{18.18 %} = - 1.22

Step 8 — Interpret the answer

The magnitude is 1.22, so demand is elastic.

Step 9 — Compare total revenue

T_{R} 1 = 10 \times 100 = 1000

T_{R} 2 = 12 \times 80 = 960

Total revenue falls from \$1,000 to \$960, which is consistent with elastic demand when price rises.

Example 2 - Point elasticity from a demand function

Let the demand function be Q = 100 − 2P, and let P = 20.

Step 1 — Find quantity at the chosen price

Q = 100 - 2 (20) = 60

Step 2 — Find the derivative

\frac{d Q}{d P} = - 2

Step 3 — Apply the point elasticity formula

P E D = (- 2) (\frac{20}{60}) = - 0.667

Step 4 — Interpret the answer

The magnitude is less than 1, so demand is inelastic at that point.

Step 5 — Connect it to the linear demand curve

On a linear demand curve, points above the midpoint price are elastic, the midpoint is unit elastic, and points below the midpoint price are inelastic. This point falls in the inelastic region.

Frequently Asked Questions

Q: What is price elasticity of demand?

It measures how strongly quantity demanded responds to a change in price.

Q: Why is PED often shown as a positive number in economics?

Because demand usually slopes downward, PED is often negative in math terms. Many economics classes report the magnitude as a positive number for easier interpretation.

Q: What does elastic demand mean?

Elastic demand means quantity demanded changes by a larger percentage than price, so |PED| > 1.

Q: How does elasticity relate to total revenue?

When demand is elastic, price and total revenue move in opposite directions. When demand is inelastic, price and total revenue move in the same direction.

Q: When should I use midpoint instead of simple percentage?

Use midpoint when you want a direction-neutral answer. It is usually the safer and more standard method for textbook and exam work.