# Optimal Price Calculator

Created by Bogna Szyk and Wei Bin Loo
Reviewed by Steven Wooding
Based on research by
Alireza Ardalan A comparative analysis of approaches for determining optimal price and order quantity when a sale increases demand European Journal of Operational Research (July 1995)
Last updated: Jun 05, 2023

Welcome to the optimal price calculator! Whether your business provides customers with physical products, intangible goods, or a service, your main goal is always the same: maximum profit. This optimal price calculator will help you maximize your profit by analyzing the patterns of the price vs. demand relationship.

In this article, we will explain how to find the optimal price and accompanying quantity of units sold. Once you get a result, you can immediately use it to adjust the prices and enjoy maximized total profit!

🙋 When running a business, you may find our margin calculator helpful on a daily basis.

## What is the optimal price?

By definition, optimal price is the price per unit at which the overall profit (calculated as quantity multiplied by unit price) is maximized. Our unit price calculator will help you evaluate it.

Let's consider two shops selling notebooks on two sides of the same street. One of them sells high-quality notebooks for $15 per unit. The other one sells very basic notebooks at$3 per unit.

As you can expect, the shop with luxury notebooks will sell fewer notebooks per month. Still, their revenue per unit is high enough to allow for selling only a small quantity. On the other hand, the second shop needs to sell a lot of notebooks to make a profit. Low price causes more customers to buy in their shop.

Each of the two shops makes a certain profit. The question they both could be asking – and that gets answered by our calculator – is:

At what price should I sell my product to optimize the profit?

## How to find the optimal price

If you want to use this maximum profit calculator to determine the optimal price, you need to provide it with the following values:

1. Marginal cost: this is the cost of producing one additional unit of your product. Typically, this cost is lowered with every item produced.

2. Marginal revenue: revenue generated by selling one additional unit. For an optimal price, the marginal revenue is equal to the marginal cost.

3. Initial price and quantity: the initial behavior of the sales process – the price at which you sold the product and the amount that you managed to sell.

4. Final price and quantity: the product's price after a price change and the corresponding demand.

Based on this input, our optimal price calculator will determine these results:

1. Price elasticity of demand: the optimal price is highly dependent on the elasticity of demand. In short, this value describes the relationship between price and demand for a particular product. You can estimate the exact deal with Omni's price elasticity of demand calculator

2. Optimal price: the price at which you should sell your product. We can calculate it with the following formula:

OP = MC × (PED / (PED + 1))

where OP is the optimal price, MC is the marginal cost, and PED stands for price elasticity of demand.

3. Optimal quantity: the actual number of units you will be able to sell at the optimal price.

4. Profit at initial and final price: the profit generated when selling your product at the initial or final price.

5. Profit at optimal price: the profit generated when selling your product at the optimal price. We can calculate it with the use of the following equation:

profit = (OP - MC) × OQ

where OP is the optimal price, MC is the marginal cost, and OQ is the optimal quantity.

Remember that the profit calculation does not show you the actual profit, as it assumes that every unit is produced at the same cost. If you want to analyze your profit in more detail, check the markup calculator.

Bogna Szyk and Wei Bin Loo
Marginal costs
$Marginal revenue$
Price elasticity of demand
Initial price
$Initial quantity Final price$
Final quantity
Price elasticity of demand
Optimum
Optimal price
$Optimal quantity Total profit figures Profit at initial price$
Profit at final price
$Profit at optimal price$
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