Find the profit-maximizing price from a linear demand curve and unit cost.
Please do not make financial decisions based on these results.
What is the Optimal Price Calculator?
Find the profit-maximizing price from a linear demand curve and unit cost. To use the Optimal Price Calculator, enter demand intercept, demand slope, unit cost; it returns optimal price, quantity sold, maximum profit, and shows them instantly as you type.
Where the Optimal Price Calculator fits
Find the profit-maximizing price from a linear demand curve and unit cost. The main figure it returns is the Optimal price, worked out from the values you enter.
It belongs with the other accounting & microeconomics tools. If you are comparing options or checking a result from another angle, try the Consumer Surplus Calculator, Price Elasticity of Demand Calculator or the Cross Price Elasticity Calculator.
How to use the Optimal Price Calculator
- Enter your numbers. The inputs are Demand intercept (a), Demand slope (b), Unit cost ($). Use numbers from the same accounting period so the ratios are comparable. Fields marked optional can stay at zero.
- Read the result. The highlighted box gives the Optimal price, and the cards below show Quantity sold, Maximum profit. Tables and charts break it down further.
- Test other scenarios. Results update as you type. Change one value at a time to see what drives the answer, and press Reset to go back to the defaults.
Formula and how it works
Example with real numbers
Here is the Optimal Price Calculator using the default values shown in the calculator above:
Inputs
| Demand intercept (a) | 5,000 |
|---|---|
| Demand slope (b) | 40 |
| Unit cost ($) | 30 |
Results
| Optimal price | $77.50 |
|---|---|
| Quantity sold | 1,900 |
| Maximum profit | $90,250.00 |
With these inputs the calculator returns Optimal price: $77.50. Change any value in the calculator to see how the result moves.
What if you change one input?
Sensitivity check: raising Demand intercept (a) from 5,000 to 6,000 (about 20% higher) and leaving everything else as in the example above changes the results like this:
| Result | Example | After the change | Change |
|---|---|---|---|
| Optimal price | $77.50 | $90.00 | +16.1% |
| Quantity sold | 1,900 | 2,400 | +26.3% |
| Maximum profit | $90,250.00 | $144,000.00 | +59.6% |
The input that moves the result most is the one to check twice. Change it in the calculator above to test your own case.
What the results tell you
The results panel of the Optimal Price Calculator reports Optimal price, quantity sold and maximum profit. Compare these figures while changing one input at a time, and use the related calculators below to look at the same situation from another angle.
Method and limits. This calculator applies the formula in the section above to your inputs, in your browser; nothing you enter is stored on our servers. The result is only as accurate as the numbers you enter and the formula shown above. It is for information, not financial, tax or legal advice.
Frequently asked questions
What does the optimal price depend on?
The size of demand, how sensitive it is to price and unit cost.
Why use average balances?
Ratios that compare a flow (sales, income) with a balance (assets, equity) are fairer when the balance is averaged over the period.
What is the cash conversion cycle?
It is DIO plus DSO minus DPO: the days between paying suppliers and collecting from customers.
Are the results guaranteed?
No. Results depend entirely on the numbers you enter and the formulas shown on this page. Please do not make financial decisions based on them alone; confirm important figures with a licensed professional.
Related accounting & microeconomics calculators
- Consumer Surplus Calculator
- Price Elasticity of Demand Calculator
- Cross Price Elasticity Calculator
- Marginal Cost Calculator
- Marginal Revenue Calculator
- Accounting Profit Calculator
- Economic Profit Calculator
- Average Variable Cost Calculator
- Revenue Calculator
- Working Capital Calculator
- Net Debt Calculator
- EOQ Calculator (Economic Order Quantity)
All Accounting & Microeconomics calculators →