Law of Demand Calculator
The law of demand says that as price rises, quantity demanded falls, and as price falls, quantity demanded rises, other things equal. The useful question is always how much, and that is what this calculator measures three ways: find price elasticity of demand from two real price and quantity observations, forecast the new quantity a planned price change will produce at a known elasticity, or evaluate a linear demand function QD = a − bP at any price, including the maximum price where demand reaches zero.
Quick Answer
The three pre-filled examples give the shape of the whole topic. A product selling 100 units at $10 that drops to 80 units at $12 has a price elasticity of demand of -1.00, unit elastic. At an elasticity of -1.5, cutting that $10 price to $8 lifts demand from 1,000 to 1,300 units. And the demand function QD = 500 − 5P returns 300 units at $40, with demand reaching zero at the $100 maximum price.
- Quick Answer
- How to use the three modes
- The formulas, and the one this tool does not use
- Worked examples for all three modes
- Reading your result: elastic, inelastic and the revenue test
- The assumption under every number here: other things equal
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the three modes
Pick the mode that matches what you actually know: two observations, a known elasticity, or a demand equation. Each mode answers a different question, and feeding one mode’s inputs into another is the most common way students and pricing teams confuse themselves.
- Find elasticity is for learning from history. Enter the original price and quantity (P1, Q1) and the new price and quantity (P2, Q2) from a real price change. You get the elasticity, both percentage changes, and the elastic, inelastic or unit elastic classification.
- Forecast demand is for planning. Enter the current price and quantity, the price you are considering, and an elasticity you already trust, from your own data or published estimates for the category. You get the predicted new quantity before you commit to the price.
- Demand function is for working with an equation, the form most textbooks use. Enter the intercept a, the slope b and any price to evaluate QD = a − bP, and the tool also reports the maximum price a ÷ b where demand hits zero.
The Find elasticity mode is the single-good cousin of a broader family: a coefficient of elasticity calculator applies the same percentage-change logic when the second variable is income or the price of a related good rather than this good’s own price. Keep the periods consistent across every input: a week of sales against a month of sales manufactures an elasticity that does not exist.
The formulas, and the one this tool does not use
All three modes run on percentage changes measured from the starting value, the base-point method taught first in most courses, including the treatment in OpenStax Principles of Economics, section 5.1 on price elasticity. The formulas are:
- Price elasticity of demand: PED = %ΔQ ÷ %ΔP, where %ΔP = (P2 − P1) ÷ P1 and %ΔQ = (Q2 − Q1) ÷ Q1.
- Forecast: Q2 = Q1 × (1 + Ed × %ΔP). The elasticity multiplies the percentage price change to give the percentage quantity change, which is then applied to the starting quantity.
- Demand function: QD = a − (b × P), with maximum price Pmax = a ÷ b.
The honest limitation: this tool does not use the midpoint (arc) formula, which divides each change by the average of the two values instead of the starting value. The midpoint method gives the same answer whichever direction the change runs; the base-point method does not. On the worked example the difference is visible: the tool returns -1.00, while the midpoint calculation, (-20 ÷ 90) ÷ (2 ÷ 11), returns -1.22. For small price changes the two methods nearly agree. For large ones, record which method produced a number before you compare it with a textbook, a competitor or a colleague, because a -1.22 from a midpoint tool and a -1.00 from this tool describe the same market event.
Two further behaviours are worth knowing before you quote a forecast. The forecast applies the elasticity once, as a single straight-line step, so a predicted fall larger than 100% is clamped to zero units in the headline while the detail line still shows the raw percentage (a -300% prediction appears in the worked vectors for this tool). And elasticity along a linear demand curve is not constant: with QD = a − bP, point elasticity equals −b × P ÷ QD, so demand grows more elastic as price climbs toward the maximum, which is why a single elasticity is always local to the price range it was measured in.
Worked examples for all three modes
Each example below is pre-filled in its mode and reproduces exactly in the calculator. Together they cover the three questions this page exists to answer.
Elasticity, step by step: %ΔP = (12 − 10) ÷ 10 = +20.00%. %ΔQ = (80 − 100) ÷ 100 = -20.00%. PED = -20.00% ÷ +20.00% = -1.00, unit elastic: the percentage loss of quantity exactly matches the percentage gain in price. One subtlety the classification can hide: revenue moves from $10 × 100 = $1,000 to $12 × 80 = $960, a $40 slip. Unit elasticity holds revenue exactly constant only for small changes, or along a constant-elasticity curve; across a 20% jump the base-point method is an approximation, which is the same limitation behind the midpoint difference described in the formula section.
Forecast, step by step: %ΔP = (8 − 10) ÷ 10 = -20.00%. Predicted %ΔQ = -1.5 × -20.00% = +30.00%. New demand = 1,000 × 1.30 = 1,300.00 units. Demand function, step by step: QD = 500 − (5 × 40) = 300.00 units, and Pmax = 500 ÷ 5 = $100.00. The full demand schedule for that equation shows the law of demand as a table:
| Price | Quantity demanded (QD = 500 − 5P) | Share of maximum quantity |
|---|---|---|
| $0 | 500 units | |
| $20 | 400 units | |
| $40 | 300 units | |
| $60 | 200 units | |
| $80 | 100 units | |
| $100 | 0 units | None |
Reading your result: elastic, inelastic and the revenue test
The classification is the decision-relevant part of the elasticity number, because it predicts what a price change does to revenue. The badge in the results area applies the same bands as this table.
| Band | Meaning | Verified example in this tool |
|---|---|---|
| Elastic, |PED| above 1 | Quantity moves more than price; a price rise cuts revenue | $20 to $22, 200 to 150 units: PED -2.50, revenue $4,000 to $3,300 |
| Unit elastic, |PED| = 1 | Quantity and price move by the same percentage | $10 to $12, 100 to 80 units: PED -1.00 |
| Inelastic, |PED| below 1 | Quantity moves less than price; a price rise grows revenue | $5 to $6, 1,000 to 950 units: PED -0.25, revenue $5,000 to $5,700 |
What pushes a product toward the elastic end is substitutes: the more easily buyers can switch, wait or do without, the harder a price rise bites. Necessities with no close substitute sit at the inelastic end, and every product grows more elastic given time, as buyers find the alternatives a short-run measurement cannot see. Note also what elasticity is not: it describes movement along one demand curve when this good’s own price changes. When income, tastes or the price of related goods change, the whole curve shifts instead, which is the distinction the change in aggregate demand calculator works with at the whole-economy level.
The assumption under every number here: other things equal
Every mode assumes ceteris paribus, that nothing else moved while the price changed. Real sales data rarely cooperates: if your price rose during a holiday peak, the measured elasticity blends the price effect with the seasonal one, and the tool has no way to separate them.
Treat measured elasticity as evidence with a margin of error, not a constant of nature. Prefer observations where the price change was the only obvious event, average several episodes when you have them, and distrust any elasticity measured across a period when a competitor launched, a substitute went on sale or incomes shifted. Forecast mode inherits all of this: it is a disciplined way to ask “if elasticity is about -1.5, what does an $8 price do?”, not a promise that 1,300 units will sell. Operations teams planning stock from a forecast usually convert the period total into a daily planning figure, which is the job of an average daily demand calculator, and they plan a range around it rather than the single number.
What competing calculators miss
Elasticity calculators are easy to find; complete ones are not. The pattern across the top results:
- CalculatorSpot’s PED calculator: correct base-point formula, but it reports elasticity as an absolute value by construction, throwing away the sign that tells you whether the data even obeyed the law of demand.
- MadeCalculators’ elasticity tools: PED only, in two near-identical versions, with an honest limitations note about linearity but no forecast mode, no demand function and no revenue readout.
- ActiveCalculator’s PED calculator: the strongest rival, because it adds a revenue breakdown showing whether the price change paid. It still stops at the single measurement: no forecasting from a known elasticity and no demand equation.
- EDUCBA’s formula calculator: a worked example and an Excel-style table that takes percentage changes as inputs rather than computing them from prices and quantities, so the actual measurement work is left to the reader.
- The gap this page fills: measure, forecast and evaluate the equation in one tool, with the sign preserved, the classification spelled out, the base-point method and its midpoint difference disclosed with numbers, and copy and share on every result.
Frequently asked questions
Price elasticity of demand measures how strongly quantity demanded reacts to a price change: PED = % change in quantity demanded divided by % change in price. It is usually negative, because price and quantity demanded move in opposite directions under the law of demand, and economists often discuss its absolute value when the direction is not in question.
Elastic demand, with |PED| above 1, means quantity moves by a bigger percentage than price, as with restaurant meals or branded snacks that have close substitutes. Inelastic demand, with |PED| below 1, means quantity barely moves, as with insulin or gasoline in the short run. An |PED| of exactly 1 is unit elastic, where the two percentage changes match.
For a normal good, no: a price rise that increases quantity demanded would break the law of demand. The rare exceptions are Giffen goods, where a staple’s price rise squeezes household budgets toward more of the staple, and Veblen goods, where a higher price itself adds status. This calculator reports the sign exactly as computed, so a positive result is a prompt to check your data before believing either exception applies.
They are two views of the same relationship. The demand function gives the exact quantity at any single price, while elasticity summarizes how sensitive quantity is between two prices. On a linear demand curve elasticity is not constant: it grows in absolute value as price rises toward the maximum price a divided by b, which the Demand function mode reports with every result.
In the linear model each extra $1 of price removes b units of quantity. Once price reaches a divided by b, the removals have used up the whole intercept a, and past that point the equation would return a negative quantity, which cannot happen in a market. The calculator reports No demand instead of a negative number, and it does the same exactly at the maximum price, where quantity is zero.
Use Forecast demand when you already have a credible elasticity, from your own past price changes or published estimates for the product category, and want to test a price before committing to it. Use Find elasticity when you have two real observations and need to learn the elasticity itself. A forecast is only as good as the elasticity fed into it, and it assumes that elasticity stays constant across the price change.
Because the starting-value, or base-point, method is the version most courses and pricing teams reach for first, and it keeps the direction of the change visible. The midpoint method divides by the average of the two prices and quantities instead, which gives the same answer whichever direction you travel: for the worked example it returns -1.22 against this tool’s -1.00. For small price changes the two methods nearly agree; for large ones, state which method a number came from before comparing it with anyone else’s.
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References
- OpenStax, Rice University. Principles of Economics 3e, 5.1: Price Elasticity of Demand and Price Elasticity of Supply. Accessed October 22, 2026.
- OpenStax, Rice University. Principles of Microeconomics 2e, Chapter 3 Key Concepts: demand schedules, the law of demand and equilibrium. Accessed October 22, 2026.
- LibreTexts, Social Sciences. Principles of Microeconomics 3e, 5.7: Key Concepts and Summary for Elasticity. Accessed October 22, 2026.
- LibreTexts, Social Sciences. Principles of Microeconomics 3e, Chapter 3: Demand and Supply. Accessed October 22, 2026.
- University of Minnesota Libraries. Principles of Economics, Chapter 5: Elasticity, A Measure of Response. Accessed October 22, 2026.
- Khan Academy. Lesson Summary: Demand and the Determinants of Demand. Accessed October 22, 2026.
- LibreTexts, Social Sciences. Principles of Macroeconomics 3e, 3.8: Key Concepts and Summary for Demand and Supply. Accessed October 22, 2026.