Maximum Revenue Calculator
Estimate the revenue-maximizing price, quantity, and revenue peak for a linear demand curve, then compare that midpoint with your current price, sales volume, and optional unit-cost context before testing a pricing change.
Revenue Inputs
Revenue-Maximizing Point
Maximum revenue
$25,000.00
Optimal price
$50.00
Optimal quantity
500
Elasticity at peak
-1
Calculation TrailShow details
Input substitution
Current inputs inserted into the formulas
Demand slope
b = a / Qmax
b = $100.00 / 1,000 = 0.1
Optimal quantity
Q* = a / 2b = Qmax / 2
Q* = 1,000 / 2 = 500 units
Optimal price
P* = a / 2
P* = $100.00 / 2 = $50.00
Maximum revenue
R* = P* x Q*
R* = $50.00 x 500 = $25,000.00
Profit at max revenue
Profit at max revenue = (P* - Unit cost) x Q*
Profit = ($50.00 - $20.00) x 500 = $15,000.00
Curve checkpoints
Demand-line and midpoint reference values
Maximum price (a)
$100.00
Highest price intercept used in the current line.
Maximum quantity
1,000
Zero-price quantity intercept used in the current line.
Demand slope (b)
0.1
Slope implied by the two intercepts.
Demand function
P = 100 - 0.1Q
Price as a function of quantity for the current line.
Revenue function
R = 100Q - 0.1Q^2
Total revenue after substituting the demand line.
Marginal revenue
MR = 100 - 0.2Q
Used to identify the midpoint revenue peak.
Break-even quantity at unit cost
800
Quantity where the current unit cost meets the same demand line.
Editorial & Review Information
Reviewed on: 2026-03-27
Published on: 2025-12-03
Author: LumoCalculator Editorial Team
What we checked: Formula math, midpoint logic, result labels, worked examples, boundary statements, and source accessibility.
Purpose and scope: This page supports pricing review, revenue-gap analysis, and linear-demand scenario planning. It is a business decision aid, not a full market-modeling or profit optimization platform.
How to use this review: Estimate one realistic demand line, compare the midpoint with your current setup, and then check cost, capacity, and market response before changing price.
Use Scenarios
Pricing review
Check the midpoint before moving price
Use the page when you already have a reasonable linear demand estimate and want a fast read on the revenue-maximizing price and quantity before changing list price.
Gap analysis
Compare current pricing with the target
Enter current price and quantity to see whether you are operating below the midpoint, above it, or already close to the top-line peak implied by the same curve.
Input handoff
Move from elasticity work into pricing
If you are still estimating how quantity responds to price, start with the Price Elasticity Calculator and then bring the cleaned demand assumption here to test the revenue-maximizing midpoint.
Formula Explanation
Step 1
Define one linear demand curve
P = a - bQ, where b = a / Qmax
The Maximum Revenue Calculator starts from two intercepts: the highest feasible price when quantity falls to zero and the highest feasible quantity at a zero price. Those intercepts are enough to define one straight demand line.
Step 2
Turn that line into a revenue function
R = P x Q = aQ - bQ^2
Once price is substituted into the revenue equation, revenue becomes a downward-opening quadratic. That shape is why this page can find a single midpoint revenue peak instead of brute-forcing every possible price.
Step 3
Locate the midpoint with marginal revenue
MR = a - 2bQ, so MR = 0 at the revenue peak
The same result can be read from marginal revenue. Setting marginal revenue to zero lands at the vertex of the revenue curve, which is the revenue-maximizing quantity under the same linear assumption.
Step 4
Separate revenue from profit before acting
P* = a / 2, Q* = Qmax / 2, but profit max usually needs MR = MC
This page is a revenue maximization calculator, not a final profit model. The midpoint is helpful for pricing direction, but once cost matters you still need to test whether the revenue peak is economically worth pursuing.
How to Read the Result
Headline metric
Maximum revenue is the top-line peak
The main revenue figure is the highest total revenue the entered line can produce under the same demand assumption. It is a top-line ceiling, not a promise that the market will behave that way after a live price change.
Midpoint metrics
Optimal price and quantity move together
The optimal price and optimal quantity are midpoint outputs, so they should be read together. A higher price target without its matching quantity adjustment is not the full recommendation.
Comparison read
The revenue gap shows distance, not certainty
When current inputs are present, the gap tells you how far the current setup sits from the midpoint on the same line. Use it as a scenario gap, not as guaranteed upside.
Decision filter
Cost and curve-fit checks come next
If unit cost is close to the midpoint price or the current point does not sit on the same curve, the result should stay a planning benchmark. Before acting, compare it with the Marginal Cost Calculator or your own contribution-margin work.
Example Cases
Worked example
Case 1: Subscription priced below the midpoint
Inputs
- Maximum price: $80.00
- Maximum quantity: 1,200
- Current price / quantity: $34.00 / 700
- Unit cost: $18.00
Computed Results
- Optimal price: $40.00
- Optimal quantity: 600
- Maximum revenue: $24,000.00
- Revenue gap to midpoint: +$200.00 (+0.84%)
Interpretation
The current price sits well below the midpoint, so the business is leaning on volume more than the estimated revenue peak requires.
Decision Hint
Test a measured price increase before spending more to chase extra volume, then confirm margin and churn risk before rolling it out broadly.
Worked example
Case 2: Workshop ticket priced above the midpoint
Inputs
- Maximum price: $220.00
- Maximum quantity: 300
- Current price / quantity: $150.00 / 120
- Unit cost: $65.00
Computed Results
- Optimal price: $110.00
- Optimal quantity: 150
- Maximum revenue: $16,500.00
- Revenue gap to midpoint: -$1,500.00 (-8.33%)
Interpretation
The current ticket is above the midpoint, which suggests a lower price could recover enough attendance to lift total revenue under the same line.
Decision Hint
Use the midpoint as a pricing test anchor, but check whether the added seats would still be profitable after delivery and support costs.
Worked example
Case 3: Low-cost digital plan with wide demand
Inputs
- Maximum price: $50.00
- Maximum quantity: 8,000
- Current price / quantity: $20.00 / 4,700
- Unit cost: $4.00
Computed Results
- Optimal price: $25.00
- Optimal quantity: 4,000
- Maximum revenue: $100,000.00
- Revenue gap to midpoint: +$6,000.00 (+6.38%)
Interpretation
Low unit cost makes the midpoint easier to experiment with, but the model still shows that current pricing is below the revenue-maximizing level.
Decision Hint
Compare the midpoint with activation, support, and retention constraints before treating top-line improvement as the only goal.
Boundary Conditions
Sources & References
- OpenStax - How a Profit-Maximizing Monopoly Chooses Output and Price - Used for the distinction between a total-revenue peak and a profit-maximizing price once cost and marginal analysis matter.
- Lumen Learning - The Relationship Between Price Elasticity and Total Revenue - Used for the unit-elastic interpretation of the revenue peak and for explaining how revenue shifts across elastic and inelastic ranges.
- Khan Academy - Total Revenue and Price Elasticity of Demand - Used as a plain-language reference for why revenue peaks around the unit-elastic midpoint on a linear demand curve.