Price optimisation is a well-defined problem with a clean answer, and almost nobody has the input it requires. The answer is the price where marginal revenue equals marginal cost. The input is a demand curve — a schedule of how many units you would sell at every price — which most businesses simply do not possess. This optimal price calculator is honest about that: it fits the simplest possible demand curve to two real observations and solves the maximisation exactly, while making clear that the curve, not the arithmetic, is doing all the work.
Arb Digital works on pricing and conversion for ecommerce and service businesses, and the most valuable thing this calculation usually produces is not the recommended price. It is the shape of the profit curve around it, which shows how much a pricing decision actually matters before anyone spends a quarter arguing about it.
What This Optimal Price Calculator Does
You supply two price points and the units sold at each, plus your variable cost per unit. The tool fits a linear demand curve through those two points, writes profit as a function of price, and solves for the maximum. It returns the profit-maximising price, the units that curve predicts at that price, the resulting profit after fixed costs, and how that compares to the profit at your first price point.
It also reports the price elasticity of demand at the optimum. That figure is a useful consistency check: at any profit-maximising price on a standard demand curve, elasticity must be greater than one in absolute terms. If the tool returns an elasticity below one, the curve is telling you that raising price would still increase revenue, which usually means one of the two observations is not measuring what you think it is.
How to Use It
- Enter two genuine price-and-volume observations. Ideally from a controlled test. Failing that, from two comparable periods where price was the only thing that changed meaningfully.
- Make sure the higher price sold fewer units. If volume rose with price, the periods differ in something other than price and the fit is meaningless.
- Enter variable cost per unit. Only per-unit costs. Rent, salaries and software subscriptions are fixed and belong in the separate field.
- Add fixed costs if you want profit stated after them. They shift the profit figure down by a constant and leave the optimal price completely unchanged.
- Compare the three contribution bars. If they are close together, price is not the lever worth pulling this quarter.
The Formula and How It Is Calculated
A linear demand curve takes the form Q = a − bP. Two points determine it exactly:
b = (Q₁ − Q₂) ÷ (P₂ − P₁) and a = Q₁ + b × P₁
Profit is (P − c) × Q where c is variable cost per unit, so π = (P − c)(a − bP). Differentiating with respect to price and setting the result to zero gives the standard solution:
P* = a ÷ (2b) + c ÷ 2
Working through the defaults: selling 1,200 units at 40 and 900 units at 50 gives b = (1,200 − 900) ÷ (50 − 40) = 30 and a = 1,200 + 30 × 40 = 2,400. With variable cost at 22, the optimal price is 2,400 ÷ 60 + 11 = 40 + 11 = 51. At that price the curve predicts 2,400 − 30 × 51 = 870 units, contribution of (51 − 22) × 870 = 25,230, and after 15,000 of fixed costs a profit of 10,230. At the original price of 40 the same curve gives contribution of 18 × 1,200 = 21,600 and profit of 6,600 — so the model estimates a 3,630 improvement.
Elasticity at the optimum is −b × P ÷ Q = −30 × 51 ÷ 870 = −1.76. Note the identity that follows: the margin ratio (51 − 22) ÷ 51 = 0.569 is exactly 1 ÷ 1.76. That relationship between margin and elasticity holds at every profit-maximising price, and it is the reason economists describe optimal pricing as a markup over marginal cost governed by elasticity. The underlying condition is the standard one set out in OpenStax's microeconomics treatment of how a profit-maximising firm chooses output and price: produce up to the quantity where marginal revenue equals marginal cost.
The Honest Limitation: You Probably Do Not Have a Demand Curve
Everything above is exact arithmetic on an assumed curve. The assumption is the weak point, and it is worth stating plainly rather than burying.
Two points define a straight line perfectly, which means the fit always succeeds and never tests itself. There is no residual, no goodness-of-fit statistic, no way to detect that demand is actually curved, kinked at a psychological threshold, or flat across a range and then collapsing. If real demand falls away sharply above 49.99 and your two observations sit at 40 and 50, a linear fit will happily recommend 51 and be badly wrong. OpenStax's discussion of polar cases of elasticity and constant elasticity shows how differently curves of different shapes behave — a constant-elasticity curve is not a straight line, and fitting the wrong family produces a confidently wrong optimum.
The second problem is that the two observations rarely differ only in price. Seasonality, a competitor's promotion, a stock-out, a change in ad spend, a press mention — any of these contaminates the volume difference and gets attributed to price by the fit. The output is only as good as the elasticity assumption underneath it, and that assumption deserves more scrutiny than the number it produces.
Getting Inputs Worth Trusting
The strongest input is a deliberate price test: two prices shown to comparable audiences at the same time, with everything else held constant, run long enough to accumulate a meaningful number of orders. That is a genuine experiment and its elasticity estimate is worth acting on. A geographic split or an alternating-week design both work when a true randomised split is not possible.
Weaker but still usable is a natural experiment — a price change you already made, comparing the periods either side, with a check that traffic, marketing spend and product mix were stable. Weakest of all is a survey asking people what they would pay, because stated willingness to pay is a poor predictor of actual purchase behaviour and consistently overstates it. If you already have an elasticity estimate from a proper test, our price elasticity calculator computes it directly from your observations and is the right place to start before using this page.
The Profit Curve Is Flatter Than You Think
This is the most practically useful property of the maximisation, and it is invisible if you only read the recommended price. Because profit is quadratic in price around the optimum, the curve is flat at its peak: prices meaningfully either side of the optimum give profits very close to the maximum. In the worked example, pricing at 49 or 53 instead of 51 costs only a small fraction of the available profit.
Two conclusions follow. First, precision beyond the nearest sensible price point is false comfort — a model built on two noisy observations cannot distinguish 51.00 from 51.40, and you should round to whatever price point your market actually uses. Second, being roughly right matters far more than being exactly right. A business currently pricing at 40 when the optimum is near 51 is leaving real money on the table; a business debating 51 against 52 is not.
What the Model Leaves Out
Several things that matter commercially are absent from the arithmetic. Competitor response is not modelled at all: a price rise that triggers matching by a rival changes the demand curve itself, and the fitted curve assumes it stays put. Long-run effects are missing — a higher price may raise this quarter's profit while slowing customer acquisition and reducing lifetime value, which a single-period maximisation cannot see. Brand positioning and fairness perceptions are real and unmeasured here. Capacity limits are ignored, so the model can recommend a volume you cannot physically deliver.
Nor does it handle price discrimination, bundling, or tiering, all of which routinely beat any single optimal price by capturing different willingness to pay from different segments. Treat the output as one input to a pricing decision, alongside your contribution margin, your break-even volume and a clear view of what competitors are doing.
How This Differs From Cost-Plus Pricing
Cost-plus pricing sets price by applying a target margin or markup to cost, and never consults demand at all. It is fast, defensible internally, and structurally blind: it will produce the same price whether customers would have paid twice as much or half as much. Our product pricing calculator and markup calculator handle that approach, and it remains the right tool when you have no demand data whatsoever.
This page is the other approach: start from what customers actually did at two prices, and let the profit function pick the price. The two methods disagree constantly, and when they do, the disagreement is informative — a large gap between the cost-plus price and the demand-based optimum usually means your margin target was set by habit rather than by anything the market told you. Check the resulting figure against your profit margin calculator output to see what the recommended price does to the margin you report.
Arb Digital designs and runs pricing and conversion tests on ecommerce and service sites, and builds the tracking that makes the results trustworthy rather than anecdotal.
Web Growth Services Paid AdvertisingCommon Mistakes to Avoid
- Using two periods that differ in more than price — seasonality, promotions and stock-outs all get attributed to price by the fit.
- Including fixed costs in the per-unit cost field — this shifts the optimum upward artificially, when fixed costs should not affect the profit-maximising price at all.
- Extrapolating far beyond your observations — a curve fitted between 40 and 50 says very little about demand at 80.
- Reporting the optimum to the cent — the profit curve is flat near its peak and the inputs are noisy, so false precision is misleading.
- Treating the result as a decision rather than one input alongside competitor position, capacity and long-run customer value.
Related Free Tools From Arb Digital
Start with the price elasticity calculator to measure responsiveness directly, use the product pricing calculator and markup calculator for the cost-plus approach, and check the outcome with the contribution margin calculator, the break-even calculator and the profit margin calculator. The full free online tools hub has everything else.
Frequently Asked Questions
Fit a demand curve to observed price and quantity data, write profit as (price minus variable cost) times quantity, and find the price where that function peaks. For a linear curve Q = a − bP the answer is P = a ÷ (2b) + c ÷ 2.
No. Fixed costs subtract the same amount from profit at every price, so they shift the whole profit curve down without moving its peak. They affect whether you should sell the product at all, not what to charge.
Because a single observation tells you nothing about how demand responds to price. Two points are the minimum needed to estimate the slope of a demand curve, and more points from a proper test are considerably better.
An elasticity below one in absolute terms at the calculated optimum indicates an inconsistency, usually because the two observations differ in something other than price. Check the data before acting on the result.
Two points define a straight line exactly, so the fit always succeeds and never tests itself. It cannot detect that real demand is curved, kinked at a psychological price point, or shifting for reasons unrelated to price.
Cost-plus applies a target margin to cost and ignores demand entirely. This calculation starts from what customers did at two prices and lets the profit function choose. The two often disagree, and the size of the disagreement is useful information.
Round it to a sensible price point for your market. The profit curve is flat near its peak, so prices moderately either side of the optimum earn almost the same profit, and precision beyond that is not supported by the data.
This tool performs published pricing arithmetic on the figures you enter. The result depends entirely on the demand curve fitted to your two observations, and is an estimate rather than a recommendation. It does not account for competitor response, capacity, or long-run customer value.
