When two percentages are applied one after the other, the result is not their sum but their product. A 40% cut followed by a 90% cut leaves 36% of the original — not 130% and not 50%. This calculator computes that combined percentage and shows its step-by-step effect on any starting value.
How to Use This Calculator
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1
Enter the first percentage in the "1st percentage" field.
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2
Enter the second percentage in the "2nd percentage" field.
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3
Read the cumulative percentage — the single equivalent percentage for both steps.
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4
Optionally enter an original value to see the result after each percentage is applied.
How to Calculate a Percentage of a Percentage
A percentage is a fraction with 100 in the denominator. Multiplying two percentages together requires converting each to its decimal form first. The product is then a decimal representing the cumulative proportion, which you multiply by 100 to get back to a percentage.
The rule: the result of applying p1% and then p2% to any value is the same as applying (p1 × p2 / 100)% once. The two percentages compound — each one acts on the result of the previous step.
Percentage of a Percentage Formula
Multiply the two percentages and divide by 100. Equivalently, multiply their decimal forms and convert back.
cumulative = p1 × p2 / 100
Worked Example — 40% of 90%
Suppose the first percentage is 40% and the second is 90%. What is the cumulative percentage?
Step 1 — convert to decimals: 40% = 0.4 and 90% = 0.9
Step 2 — multiply: 0.4 × 0.9 = 0.36
Step 3 — convert back: 0.36 × 100 = 36%
Now apply to a starting value of 10. After the first percentage: 10 × 40% = 4. After the second: 4 × 90% = 3.6. Shortcut: 10 × 36% = 3.6. Both methods give the same final value.
Common Percentage of Percentage Results
| 1st % | 2nd % | Cumulative % | Note |
|---|---|---|---|
| 10% | 10% | 1% | 10% of 10% |
| 20% | 20% | 4% | 20% of 20% |
| 25% | 50% | 12.5% | quarter of a half |
| 30% | 80% | 24% | 30% of 80% |
| 40% | 90% | 36% | 40% of 90% |
| 50% | 50% | 25% | half of a half |
| 75% | 75% | 56.25% | 75% of 75% |
| 100% | 50% | 50% | all of a half |
| 150% | 80% | 120% | can exceed 100% |
Real-Life Applications
Budget allocation: a company allocates 40% of its budget to marketing, and the marketing team spends 30% of their share on social media. Social media receives 40% × 30% / 100 = 12% of the total company budget.
Commission: a distributor earns 15% of the retailer's margin, and the retailer's margin is 40% of the sale price. The distributor earns 15% × 40% / 100 = 6% of the sale price.
Probability: if there is a 70% chance of rain and each rainy day has a 40% chance of flooding, the probability of a flood on any given day is 70% × 40% / 100 = 28%.
Sequential discounts: a product discounted by 20% and then by an additional 10% does not end up at a 30% discount. The cumulative discount is 100% − (80% × 90% / 100) = 100% − 72% = 28% off.
Sequential Discounts — Why the Order Does Not Matter
Multiplying two percentages is commutative — the order of application does not change the final result. Applying 40% first and then 90% gives the same cumulative as applying 90% first and then 40%:
40% × 90% / 100 = 36% and 90% × 40% / 100 = 36%
This is why a shop offering two sequential discounts of different sizes always produces the same final price regardless of which discount is applied first.
The percentage of a percentage calculator finds the combined effect of two percentages applied in sequence. Enter any two percentages to see the single equivalent percentage that achieves the same result.