45% Margin to Markup: a 45% margin needs a 81.8% markup
At a 45% margin the price is cost ÷ (1 − 45/100), which is a 81.8% markup on cost. Everything on this page follows from that division.
Price any cost at a 45% margin
Prefilled with this page's numbers. Change either field; results update instantly and nothing is sent anywhere.
The formula
45 ÷ 55 × 100 = 81.8%
price = cost ÷ (1 − 45/100) = cost ÷ 0.55
A 45% margin and a 81.8% markup are the same price. The margin figure is what appears on a profit and loss statement; the markup figure is what you type into a price list. Keep both in the spreadsheet and label them honestly.
Price table at 45% margin
Each price is the cost divided by 0.55. The markup column stays at 81.8% on every line; only the amounts scale.
| Cost | Price at 45% margin | Gross profit | Markup |
|---|---|---|---|
| $5.00 | $9.09 | $4.09 | 81.8% |
| $10.00 | $18.18 | $8.18 | 81.8% |
| $25.00 | $45.45 | $20.45 | 81.8% |
| $50.00 | $90.91 | $40.91 | 81.8% |
| $100.00 | $181.82 | $81.82 | 81.8% |
| $250.00 | $454.55 | $204.55 | 81.8% |
| $500.00 | $909.09 | $409.09 | 81.8% |
| $1,000.00 | $1,818.18 | $818.18 | 81.8% |
| $2,500.00 | $4,545.45 | $2,045.45 | 81.8% |
| $10,000.00 | $18,181.82 | $8,181.82 | 81.8% |
Margins near 45%
Between 35% and 55% margin the markup needed runs from 53.8% to 122.2%: it climbs faster than the margin because the cost share of the price keeps shrinking. The multiplier column turns a cost list into prices at that margin in one step.
Worked example
Take a $12.50 item. To keep 45% of the price, divide by 0.55: $22.73. The profit is $10.23, which is 45% of the price and 81.8% of the cost. Adding 45% to cost instead would have given $18.12, a margin of only 31%.
The margin-as-markup trap
The classic error is adding 45% to cost and calling it a 45% margin. That gives a margin of only 31%, and on a full year of sales the shortfall is 14 points of gross margin that the business planned to spend.
When a margin target is the right tool
Set prices from a margin target when the business is judged on gross margin: an online store, a wholesaler with published margin bands, or any company preparing accounts for a lender. A 45% margin target converts to a 81.8% markup for the person entering prices.
Coming from the other direction: a 45% markup, the number people often type by mistake, produces only a 31% margin. The 45% margin on this page needs the full 81.8% markup.
Mirror page: what margin a 45% markup produces.