The formulas
Write both percentages as decimals (40% is 0.4), then:
markup = margin ÷ (1 − margin)
margin = markup ÷ (1 + markup)
A 0.4 margin becomes 0.4 ÷ 0.6 = 0.667, a 66.7% markup. A 0.5 markup becomes 0.5 ÷ 1.5 = 0.333, a 33.3% margin.
Conversion table
| Margin | Markup | Multiply cost by |
|---|---|---|
| 5% | 5.3% | 1.053 |
| 10% | 11.1% | 1.111 |
| 15% | 17.6% | 1.176 |
| 20% | 25% | 1.25 |
| 25% | 33.3% | 1.333 |
| 30% | 42.9% | 1.429 |
| 35% | 53.8% | 1.538 |
| 40% | 66.7% | 1.667 |
| 45% | 81.8% | 1.818 |
| 50% | 100% | 2 |
| 60% | 150% | 2.5 |
| 70% | 233.3% | 3.333 |
| 80% | 400% | 5 |
The gap widens fast. Up to about 20% the two numbers are close, past 50% markup runs away from margin, and near 100% margin it heads for infinity.