To calculate marginal revenue, divide the change in total revenue by the change in units sold: MR = (TR₂ − TR₁) ÷ (Q₂ − Q₁). If revenue rises from $3,600 to $4,200 while sales rise from 80 to 100 units, marginal revenue is $600 ÷ 20 = $30 per additional unit over that interval.
The calculation measures how revenue changes as sales volume changes. It does not deduct costs, and the answer can differ from the price charged for each item.
Key Takeaways
- Subtract the starting revenue and quantity from the ending figures, then divide the two changes.
- A result calculated across several extra units is the average revenue change per added unit over that interval.
- If a lower price applies to the whole volume, include the revenue lost on units that would otherwise sell at the higher price.
- More units sold can mean less total revenue. Positive marginal revenue also does not establish a profit.
The marginal revenue formula
Marginal revenue = Change in total revenue ÷ Change in quantity sold
When ΔQ is greater than one unit, this calculation gives the average revenue change per additional unit across that interval.
In the formula, TR means total revenue, Q means quantity, and Δ means “change in.” The subscripts 1 and 2 identify the starting and ending situations. Use the same subtraction order for both changes.
The result is money per unit, such as dollars per bottle. It is not a percentage. When quantity increases by exactly one unit, marginal revenue equals the dollar change in total revenue. If quantity increases by 20 units, the result describes the interval as a whole; it does not reveal the revenue change from the twentieth extra unit alone.
For retail calculations, count units sold, rather than items purchased for inventory. Buying another 100 units from a supplier does not itself create sales revenue.
How to calculate marginal revenue step by step
You need two quantities and their corresponding revenue totals. The following examples are hypothetical, use US dollars, and exclude tax, shipping charges, returns, and costs so the revenue arithmetic stays visible.
Suppose you are comparing two possible weekly sales outcomes for the same insulated bottle. At $45 per bottle, assume 80 units sell. At $42, assume 100 sell. These quantities are inputs to the example, not a forecast of customer demand.
| Input | Starting situation | Alternative situation |
|---|---|---|
| Units sold | 80 | 100 |
| Price per unit | $45 | $42 |
| Total revenue | $3,600 | $4,200 |
1. Calculate total revenue for each situation
When every unit in a situation sells for one price, multiply that price by quantity:
- Starting revenue: 80 × $45 = $3,600.
- Alternative revenue: 100 × $42 = $4,200.
If orders contain different discounts, add up the actual item revenue instead. Multiplying a displayed list price by all units would overstate revenue when some customers paid less. The distinction between list price and net item price helps you choose the right input.
2. Find the change in revenue
Subtract the starting total from the alternative total:
ΔTR = $4,200 − $3,600 = $600
This is the extra revenue across the entire comparison. It is not yet a per-unit result.
3. Find the change in units sold
ΔQ = 100 − 80 = 20 units
Use the additional 20 units as the denominator. Dividing by the full 100 units would answer a different question.
4. Divide and label the result
MR = $600 ÷ 20 = $30 per additional bottle
Across the move from 80 to 100 bottles, revenue increases by an average of $30 per added unit. Check the calculation by multiplying back: 20 × $30 = $600, which matches the change in total revenue.
Why marginal revenue can differ from selling price
Marginal revenue equals selling price when an extra sale adds that price to total revenue without changing revenue from other sales. For example, moving from 80 to 81 bottles at an unchanged $45 price raises revenue from $3,600 to $3,645. MR is $45.
In the textbook model of perfect competition, a price-taking firm faces an unchanged market price as it varies its own output, so MR equals price. That assumption does not describe every online retailer.
In the bottle comparison, the $42 alternative applies to all 100 bottles. The revenue change has two parts:
| Part of the change | Calculation | Revenue effect |
|---|---|---|
| Revenue from 20 additional bottles | 20 × $42 | +$840 |
| Lower revenue on the original 80-bottle volume | 80 × ($42 − $45) | −$240 |
| Combined change | $840 − $240 | +$600 |
Dividing $600 by 20 gives MR of $30, even though the alternative selling price is $42. The additional sales do not keep the whole $840 increase because the lower price also reduces revenue on the original volume.
These are two alternative outcomes for the same sales window. The comparison does not assume that completed $45 orders are refunded after a later price change.
Now change the assumption: keep the original 80 sales at $45 and sell only the extra 20 bottles at $42. Revenue becomes $3,600 + $840 = $4,440, so MR is $840 ÷ 20 = $42. The calculation changes because the price reduction affects a different set of units.
How to find marginal revenue from a table
Calculate the change between each pair of adjacent rows, then divide by the quantity change. Use both columns: a revenue difference alone is sufficient only when quantity changes by one unit.
The table below is an assumed demand schedule for teaching, with one uniform price applying to all units in each row. It is not measured store data, an estimated demand curve, or evidence that a retailer is a monopolist. Each row represents an alternative outcome for an equal sales window.
| Units sold | Price per unit | Total revenue | MR from the previous row |
|---|---|---|---|
| 80 | $45 | $3,600 | — |
| 100 | $42 | $4,200 | $30 |
| 120 | $35 | $4,200 | $0 |
| 140 | $28 | $3,920 | −$14 |
For the move from 100 to 120 units:
MR = ($4,200 − $4,200) ÷ (120 − 100) = $0
The extra volume exactly offsets the lower price. Revenue stays unchanged.
For the move from 120 to 140 units:
MR = ($3,920 − $4,200) ÷ (140 − 120) = −$14
Twenty more bottles sell, but total revenue falls by $280. Negative MR here does not mean any bottle has a negative selling price. It means the additional volume fails to offset the revenue lost through the lower price on the whole volume.
The first row has no MR because no preceding comparison is supplied. You could calculate from zero sales if you explicitly added that baseline, but it would describe the full zero-to-80 interval.
Marginal revenue vs. average revenue vs. total revenue
Total revenue measures the whole sales amount. Average revenue divides that amount across all units sold. Marginal revenue measures the change between two sales quantities.
Using the original move from 80 bottles at $45 to 100 bottles at $42:
| Measure | Calculation | Result |
|---|---|---|
| Total revenue at 100 units | 100 × $42 | $4,200 |
| Average revenue at 100 units | $4,200 ÷ 100 | $42 per unit |
| Marginal revenue from 80 to 100 units | ($4,200 − $3,600) ÷ (100 − 80) | $30 per added unit |
Average revenue equals the selling price when every unit sells at that price. With several actual selling prices, it is the unit-weighted average. Neither result tells you marginal revenue unless you also know how total revenue changes with quantity.
Contribution margin subtracts variable costs from revenue. MR contains no cost deduction. A price index compares prices with a reference; it does not measure the extra revenue associated with additional units sold.
Calculate marginal revenue in a spreadsheet
Put quantity in column A and total revenue in column B. Enter the starting values in row 2 and the alternative values in row 3:
| Row | A: Units sold | B: Total revenue | C: Marginal revenue |
|---|---|---|---|
| 2 | 80 | 3600 | Leave blank |
| 3 | 100 | 4200 | Enter the formula below |
In C3, use:
=IF(A3=A2,"N/A",(B3-B2)/(A3-A2))
The result is 30, meaning $30 per additional unit over the interval. Format numeric results as currency. Copying the formula down compares each row with the row immediately above it, so each pair must represent a meaningful comparison.
The guard returns “N/A” when quantity is unchanged. If revenue changes while both rows still show 100 units, ΔQ is zero and this MR calculation is undefined. Returning zero would incorrectly suggest that additional units produced no extra revenue.
Use comparable sales data before interpreting the result
For real store records, start with one SKU or a clearly defined set of comparable units. Check these inputs before using the result in a pricing decision:
- Sales window: Compare periods of equal length and record differences in traffic, availability, and seasonality.
- Revenue basis: Use the same currency and treatment of discounts, returns, taxes, and shipping in both totals.
- Quantity basis: Count the same type of unit in both rows. Keep treatment of returned units consistent with the revenue adjustment, and avoid mixing individual items with multipacks.
- Product mix: A shift toward higher-priced products can change revenue per unit without showing what happened to demand for any one product.
An observed before-and-after ratio is descriptive. If sales rise after a price cut while traffic also rises or stock becomes available again, the calculation alone cannot isolate the price effect. Two observed rows also do not establish a demand curve you can extend to untested prices.
Finally, keep the $600 revenue gain in the example separate from earnings. If obtaining the extra sales adds $700 in total costs, profit changes by $600 − $700 = −$100, assuming everything else is unchanged. Use MR to explain the revenue change, then evaluate the relevant cost change separately before deciding whether the extra volume is worthwhile.
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