Optimal Price Calculator

Background.

Every price is a trade. Raise it and each sale earns more, but fewer people buy; cut it and volume rises while the margin on each unit shrinks. Somewhere between giving the product away and pricing everyone out sits the price that leaves the most profit, and when demand falls along a straight line there is a tidy formula for it.

Write demand as Q = a − bP. The intercept a is how many units would go at a price of zero; the slope b is how many sales you lose for each extra dollar. Dividing one by the other gives the choke price, a/b, where demand dries up completely. Add a constant cost c for each unit you make or buy, and the profit-maximising price lands exactly halfway between that cost and the choke price. With demand of 1,000 − 10P and a $20 unit cost, the choke price is $100 and the best price is $60.

Two consequences tend to surprise people. Only half of any change in unit cost belongs in the price: a $10 rise in cost lifts the best price by $5. And the profit curve is flat near its peak. In that example, pricing at $50 or $70 instead of $60 gives up just $1,000 of $16,000, so getting close matters more than being exact.

The setting is the textbook monopoly: one seller, one product, one price, and a demand curve that does not shift when rivals react. Fixed costs have no bearing on the best price, only on whether the product is worth selling at all. Capacity limits, different prices for different customer groups and charm prices such as $59.99 are outside the model, and the answer is only as good as your estimates of a and b.

What is optimal price calculator?

The optimal price here is the single price that maximises profit, meaning revenue minus variable cost, for a seller facing the linear demand curve Q = a − bP with a constant marginal cost c per unit. It is the price at which marginal revenue, the extra revenue from selling one more unit, equals marginal cost. With linear demand the marginal revenue line falls twice as steeply as the demand line, and that is what places the best price midway between cost and the choke price.

How to use this calculator.

1. 01Estimate the demand line from two prices you have tried. If 500 units sold at $50 and 300 at $70, b is the drop in units divided by the rise in price, 200 ÷ 20 = 10, and a is 500 + 10 × 50 = 1,000. Use quantities for the same period each time, such as units per month.
2. 02Enter a as the linear demand intercept and b as the positive demand slope. The minus sign is already built into Q = a − bP, so b goes in as a positive number.
3. 03Enter the constant marginal cost: what one more unit costs you in materials, packaging, shipping, payment fees and other per-unit spending. Leave out rent, salaries and other costs that do not change with volume.
4. 04Read the price and the quantity demanded at that price. A quantity of 0 means your unit cost is at or above the choke price a/b, so no price on this demand line covers it.

The formula.

Profit = (P − c) × (a − bP). Setting its derivative with respect to price to zero gives a − 2bP + bc = 0, so P* = (a + bc) ÷ (2b). The same expression can be written (a/b + c) ÷ 2, the average of the choke price and marginal cost. The quantity sold is then Q* = a − bP*, which simplifies to (a − bc) ÷ 2: half of what would sell if price were set equal to cost. When c is at or above a/b the quantity is shown as 0 instead of a negative number, and the price figure then lies at or above the point where anyone buys, so it has no practical use. A quick check on any answer is the price elasticity of demand at P*, which is −bP*/Q*. At the profit-maximising price the markup (P* − c)/P* always equals 1 divided by the size of that elasticity, the condition economists call the Lerner rule.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Principles of Finance, 2022. Chapters 6–10. Retrieved 2026-08-06.
2. [2]U.S. Internal Revenue Service. Tax guidance current 2026. Official forms, instructions and tax topics. Retrieved 2026-08-06.
3. [3]U.S. Securities and Exchange Commission. Investor.gov current 2026. Investment products and risk. Retrieved 2026-08-06.