Chain Percentages: When Percentages Stack
A chain percentage — also called a percentage of a percentage — applies multiple percentage steps in sequence, where each step operates on the result of the previous one. The key word is of: "30% of 20% of 500" means you take 20% of 500 first, then take 30% of that result.
This comes up constantly in the real world: nested discounts during sales, tax calculated on a commission, royalty percentages on a revenue share, or compound deductions on a paycheck. Treating each step independently — rather than adding percentages together — is what separates correct from incorrect answers.
How the Math Works
Each percentage in the chain acts as a multiplier. You can either apply them one at a time, or combine them upfront:
Result = Base × (P1/100) × (P2/100) × (P3/100) …
The combined multiplier is the product of all decimal forms. For 30% and 20%, that's 0.3 × 0.2 = 0.06, meaning the chain is equivalent to taking just 6% of the base in one step.
Worked Examples
Double discount at checkout
A jacket is ₹4,000. A store offers 20% off, and your member card gives a further 10% off. What do you pay?
Step 1: 20% of 4,000 = 800 → price after first discount = 3,200
Step 2: 10% of 3,200 = 320 → final price = ₹2,880
Note: 20% + 10% = 30% off would give ₹2,800. Chained discounts always yield less saving than their sum suggests.
Commission on a percentage of revenue
A salesperson earns 8% commission on 60% of a ₹1,50,000 deal (the portion after overhead). What's the commission?
60% of 1,50,000 = 90,000
8% of 90,000 = ₹7,200
Combined multiplier: 0.6 × 0.08 = 0.048 → 4.8% of the full deal.
Why You Cannot Add Chained Percentages
Two 10% discounts feel like 20% off. They're not — they're 19% off.
Start with ₹100
After 10% off → ₹90
After another 10% off ₹90 → ₹81
Actual saving: ₹19 = 19%, not 20%
The gap widens as percentages get larger. Two 50% discounts yield 75% off total, not 100%. This is why retailers love stacking discounts — the math sounds better than it is.
The Effective Percentage Shortcut
To find the single equivalent percentage for a chain, multiply the decimal forms and convert back:
25% of 40% of 80% = 0.25 × 0.40 × 0.80 = 0.08 → 8%
This means the three-step chain is always equal to taking just 8% of the base in a single step.
Common Questions
Does the order of percentages in a chain matter?▼
No — multiplication is commutative. 30% of 20% of 500 gives the same final answer as 20% of 30% of 500. The order of steps doesn't affect the result.
What if one of the percentages is over 100%?▼
The formula still works. 150% of 50% of 200 = 1.5 × 0.5 × 200 = 150. A percentage over 100% means that step produces a value larger than its input.
Is chaining the same as compounding?▼
They're related. Compound interest applies the same percentage repeatedly over time — which is a special case of chaining where all the percentages are identical. The chain calculator generalises this to any combination of percentages.
