How much more do I need to sell to offer a discount?

People type this into search every day: how much more do I need to sell to offer a discount.

The cut comes out of contribution, the gap between the selling price and the variable cost of one unit. A 10% lower price leaves a thinner gap. You need enough extra units that the thinner gaps add back to the same total contribution.

The SBA break-even guide defines contribution margin as the difference between price and the cost to make the product. The SBA glossary of business financial terms describes break-even analysis as the sales volume that covers costs, using variable cost and profit. The discount break-even calculator asks a narrower question. It holds total contribution steady after the price cut.

New price = list price × (1 − discount)

Extra volume = original contribution ÷ new contribution − 1

Variable cost per unit stays the same in that formula. A bigger ad budget, or a cap on how many units you can make, sits outside it. These are labeled examples. They are a worksheet, and they are not business advice.

The contribution margin post starts from the same leftover. This page asks what happens to unit count when you give part of that leftover away.

Example 1. Ten percent off an $80 price

Calculator defaults:

• Selling price: $80
• Variable cost: $48
• Discount: 10%
• Current unit sales: 500

Original contribution: 80 − 48 = $32.00.

New price: 80 × (1 − 0.10) = $72.00.

New contribution: 72 − 48 = $24.00.

Extra volume: 32 ÷ 24 − 1 = 0.333… = 33.3%.

Extra units: 0.333… × 500 = 166.7 units.

Units after the discount: 500 + 166.7 = 666.7 units.

Contribution at the old volume: 32 × 500 = $16,000.00.

Contribution at 666.7 units: 24 × 666.666… = $16,000.00. The total matches. The unit count is one third higher.

SBA writes the contribution ratio as (price − variable cost) ÷ price. On the list price that is 32 ÷ 80 = 40%. After the cut it is 24 ÷ 72 = 33.3%. Markup on cost falls from 32 ÷ 48 = 66.7% to 24 ÷ 48 = 50%. The markup vs margin post builds the price from a target margin. This page starts after that price already exists.

Example 2. What if the discount is 5%?

Same $80 price, same $48 cost, same 500 units. Only the cut changes.

New price: 80 × 0.95 = $76.00.

New contribution: 76 − 48 = $28.00.

Extra volume: 32 ÷ 28 − 1 = 14.3%.

Extra units: 71.4 units. Units after the discount: 571.4 units.

A 5% cut needs 71.4 extra units. The 10% cut in example 1 needs 166.7. The first 5 points of discount add 71.4 units. The next 5 points add 166.7 − 71.4 = 95.3 units, because you are dividing by a smaller contribution.

Example 3. What if the discount is 20%?

New price: 80 × 0.80 = $64.00.

New contribution: 64 − 48 = $16.00.

Extra volume: 32 ÷ 16 − 1 = 100%.

Extra units: 500 units. Units after the discount: 1,000 units.

You sell twice as many units to keep $16,000 of contribution. Each unit now leaves half of what it left before.

Example 4. A 25% cut, then a 30% cut

Still $80, $48, and 500 units.

At 25% off, the new price is 80 × 0.75 = $60.00. Contribution is 60 − 48 = $12.00. Extra volume is 32 ÷ 12 − 1 = 166.7%. Extra units are 833.3. You need 1,333.3 units in total.

At 30% off, the new price is 80 × 0.70 = $56.00. Contribution is 56 − 48 = $8.00. Extra volume is 32 ÷ 8 − 1 = 300%. Extra units are 1,500. You need 2,000 units.

The 15% step on this chart is 32 ÷ 20 − 1 = 60%, because 80 × 0.85 = $68 and 68 − 48 = $20. That row is the bridge between example 1 and example 3.

Example 5. A thin contribution, 15% off

A different product:

• Price: $40
• Variable cost: $32
• Discount: 15%
• Current units: 200

Original contribution: 40 − 32 = $8.00. That is 8 ÷ 40 = 20% of the price.

New price: 40 × 0.85 = $34.00.

New contribution: 34 − 32 = $2.00.

Extra volume: 8 ÷ 2 − 1 = 300%.

Extra units: 3 × 200 = 600 units. Units after the discount: 800 units.

Old contribution total: 8 × 200 = $1,600.00. New total at 800 units: 2 × 800 = $1,600.00.

The discount is 15%, the same rate as the middle bar in the chart above. The lift is 300%, the same lift the $80 product needed at a 30% discount. The rate on the sticker is the smaller part of the story. The contribution you have left is the part that sets the unit count.

Example 6. A wide contribution, same 15% off

• Price: $120
• Variable cost: $30
• Discount: 15%
• Current units: 200

Original contribution: 120 − 30 = $90.00. That is 90 ÷ 120 = 75% of the price.

New price: 120 × 0.85 = $102.00.

New contribution: 102 − 30 = $72.00.

Extra volume: 90 ÷ 72 − 1 = 25%.

Extra units: 0.25 × 200 = 50 units. Units after the discount: 250 units.

Old contribution total: 90 × 200 = $18,000.00. New total: 72 × 250 = $18,000.00.

Same discount rate as example 5, and the same starting unit count. One product needs 600 extra units. The other needs 50. I would price the sale from the contribution line, then check whether the kitchen or the warehouse can make the extra units.

Example 7. Same percent, two shop sizes

Back to $80, $48, and a 10% discount. The extra-volume percent stays 33.3%. The unit count scales with the base.

A shop that sells 40 units needs 13.3 extra units, 53.3 units in total. Contribution to hold: 32 × 40 = $1,280.00.

A shop that sells 2,000 units needs 666.7 extra units, 2,666.7 units in total. Contribution to hold: 32 × 2,000 = $64,000.00.

The percent answers “how hard is this discount.” The unit line answers “can we ship it.” A 33.3% lift on 40 units might be a busy Saturday. The same lift on 2,000 units is 667 more units to make, pack, and collect.

Example 8. The 10% mistake, worked on the default shop

Two shortcuts show up in pricing meetings. Both use the example 1 inputs. Old contribution is $16,000. Old revenue is 80 × 500 = $40,000.00.

Shortcut A says a 10% discount means you sell 10% more units. That is 550 units at $72.

Contribution: 24 × 550 = $13,200.00.

You are $2,800.00 short of $16,000. Revenue at those 550 units is 72 × 550 = $39,600.00, which is also under the old $40,000.

Shortcut B replaces the revenue you gave away. Ten percent of $40,000 is $4,000, so the target revenue is $44,000. At $72 that is 44,000 ÷ 72 = 611.1 units.

Contribution: 24 × (44,000 ÷ 72) = $14,666.67.

You are still $1,333.33 short of $16,000. Revenue can be restored while contribution is not, because each new unit carries $48 of variable cost.

The volume that holds contribution is 666.7 units, from example 1.

Example 9. The sale also costs $4 more per unit

Keep the list economics from example 1: $32 of contribution, 500 units, $16,000 to hold. The discounted price is still $72. Packaging, a free insert, or a per-unit ad cost adds $4 only on the sale units. Contribution on a sale unit is 72 − 48 − 4 = $20.00.

Units that hold $16,000: 16,000 ÷ 20 = 800 units.

Extra units: 800 − 500 = 300 units. Extra volume: 300 ÷ 500 = 60%.

The calculator has one variable-cost field, used on both the old price and the new price. If you type $52 as that cost, it treats $52 as the cost at the list price too. Original contribution becomes 80 − 52 = $28, new contribution is 72 − 52 = $20, and the printed extra volume is 28 ÷ 20 − 1 = 40% (200 extra units, 700 units in total). Use that row when the higher cost is permanent. Use the 800-unit hand count when the extra $4 exists only while the discount is on.

Example 10. Monthly break-even after the same idea of a cut

The business break-even calculator divides fixed costs by contribution per unit. Defaults:

• Monthly fixed costs: $18,000
• Price: $120
• Variable cost: $48
• Target monthly profit: $10,000

Contribution: 120 − 48 = $72.00.

Break-even units: 18,000 ÷ 72 = 250 units. The calculator prints 250 units. Break-even revenue: 250 × 120 = $30,000.00.

Units for the $10,000 profit target: (18,000 + 10,000) ÷ 72 = 388.888…, which the calculator rounds up to 389.

A 10% discount moves the price to $108. Contribution is 108 − 48 = $60.00.

Break-even units: 18,000 ÷ 60 = 300 units. Revenue: 300 × 108 = $32,400.00.

Target-profit units: 28,000 ÷ 60 = 466.666…, printed as 467.

The unit lift to hold the break-even contribution total is 72 ÷ 60 − 1 = 20%. That is the same extra-volume formula as the discount page, applied to the fixed-cost pile. Revenue at break-even rises from $30,000 to $32,400 because each dollar of price now carries less contribution.

A 20% discount moves the price to $96. Contribution is 96 − 48 = $48.00. Break-even units: 18,000 ÷ 48 = 375 units. Revenue: 375 × 96 = $36,000.00. Target-profit units: 28,000 ÷ 48 = 583.333…, printed as 584.

Example 11. The $80 price was a 40% margin, and a project quote

The markup vs margin calculator solves price = cost ÷ (1 − margin). A $48 cost and a 40% margin:

48 ÷ 0.60 = $80.00.

Markup on cost: 32 ÷ 48 = 66.7%. Gross profit on 100 units: $3,200.00.

That $80 is the list price in example 1. After the 10% discount the selling price is $72, profit per unit is $24, and the margin on price is 24 ÷ 72 = 33.3%. You aimed the list at 40% of price. The sale lands at 33.3% of price.

A project has the same shape when the price falls and the costs do not. The project profit calculator defaults are a $12,000 price, 120 hours at $45, $2,600 of materials, and $500 of other costs.

Cost: 120 × 45 + 2,600 + 500 = $8,500.00.

Profit: 12,000 − 8,500 = $3,500.00. Margin: 3,500 ÷ 12,000 = 29.2%. Profit per hour: $29.17.

A 10% discount sets the price to $10,800. Cost stays $8,500. Profit is 10,800 − 8,500 = $2,300.00. Margin is 2,300 ÷ 10,800 = 21.3%. Profit per hour is $19.17.

Projects needed to hold one full-price profit: 3,500 ÷ 2,300 − 1 = 52.2% more projects. Ten full-price projects make 10 × 3,500 = $35,000. At $2,300 each you need 35,000 ÷ 2,300 = 15.2 projects. Fifteen discounted projects make $34,500, which is $500 short of $35,000.

A 15% discount sets the price to $10,200. Profit is 10,200 − 8,500 = $1,700.00. Margin is 16.7%. Profit per hour is $14.17. Replacing one full-price profit takes 3,500 ÷ 1,700 = 2.06 discounted projects, which is 105.9% more projects.

Example 12. The discount that lands on cost

Price $80, variable cost $48, discount 40%, 500 units.

New price: 80 × 0.60 = $48.00.

New contribution: 48 − 48 = $0.00.

The calculator stops and prints Discount wipes out contribution. Selling more units at a $0 contribution keeps the total at $0. It does not climb back to $16,000.

A 50% discount prices the unit at 80 × 0.50 = $40.00, which is $8 under the $48 cost. Each extra unit widens the hole. The same stop applies. The formula needs a new contribution above zero.

Twelve discount cases side by side

Open the discount break-even calculator with your price, your variable cost, and the cut you are considering. If the question is the units that cover a monthly fixed bill, use the business break-even calculator. If the question is what you earned on the money you spent to run the promotion, the return on investment page is the next worksheet.