Percentage of a Percentage Calculator

How to Use

1. Enter the first percentage (X): This is the percentage you want to take of the second percentage. For example, an additional 20% discount.
2. Enter the second percentage (Y): This is the base percentage. For example, 70% (the remaining fraction after a 30% discount).
3. Read the results: See X% of Y%, the effective single percentage, and what 100 becomes after applying both.

What You'll Discover

• X% of Y% — the headline result, (X × Y) ÷ 100, as a percentage. 20% of 70% is 14%.
• Applied to 100 — what you get if you start with 100, take Y% of it, then take X% of that. With 20 and 70, 100 becomes 70, then 14. Because the base is 100, this number always matches the headline percentage, which makes it easy to scale: for a $250 base, multiply by 2.5.
• Effective single percentage — the one-step percentage that has the same effect as applying both percentages in turn. Use it when you want to replace two steps with one.
• vs. simple addition (X + Y) — the sum of the two inputs, shown only for contrast. Adding percentages is the most common mistake with stacked rates, and seeing the two numbers side by side makes the gap obvious.

To find a final price after stacked discounts, enter the percentages you keep: 80 for 20% off and 70 for 30% off. The result, 56%, is what you pay, so the total discount is 100% − 56% = 44%.

Formula

To find X% of Y%, multiply them and divide by 100:

Result = (X × Y) / 100

For stacked discounts, the effective discount on the original price is:

Effective discount = 100 − ((100 − X) × (100 − Y) / 100)

The Critical Insight: Stacked Discounts Are Not Additive

A common mistake is adding percentages when they are applied sequentially. Consider: a 30% discount, then an additional 20% off.

• Wrong: 30% + 20% = 50% total discount
• Correct: After 30% off, you pay 70%. Then 20% off 70% = 14% off the original. Total discount = 30% + 14% = 44%.

The formula: 100 − (70 × 80 / 100) = 100 − 56 = 44% effective discount.

Examples

Example 1 — Stacked retail discounts

An item is 25% off, then an extra 10% off at checkout. The effective discount: 100 − (75 × 90 / 100) = 100 − 67.5 = 32.5% total discount, not 35%.

Example 2 — Tax on a sale price

A 15% tax is applied to an item already discounted by 40%. The customer pays 60% of the original price, then 15% tax on that. Effective total: (60 × 115) / 100 = 69% of the original price.

Example 3 — Commission on discounted revenue

A 5% sales commission is earned on a product sold at 80% of list price. Commission as a percentage of list price: (5 × 80) / 100 = 4% of list price.

Percent of a Percent vs Stacked Discounts vs Percentage Points

Three different calculations all involve "two percentages", and they give very different answers. Before you calculate, decide which question you are asking.

Percent of a percent answers "what share of the whole is this share of a share?" If 20% of a company's staff work in sales, and 10% of the sales team are managers, then sales managers are 2% of all staff.

Stacked discounts answer "how much do I save in total?" After 20% off you pay 80%. Another 10% off leaves 90% of that, so you pay 80 × 90 ÷ 100 = 72% and save 28%. Enter 80 and 90 in the calculator to see the 72%.

Percentage points answer "how far apart are two rates?" A rate that moves from 10% to 20% has risen by 10 percentage points, which is a 100% relative increase. Mixing up percent and percentage points is a common error in news reports.

The base always changes

The key to all of these is the base. In "X% of Y%", the X applies to the Y group, not to the whole. The result is then re-expressed as a share of the whole. Keep track of which total each percentage refers to and the right formula becomes clear.

Share of a Share: Subgroups, Commissions and Probabilities

Outside of shopping, a percentage of a percentage usually describes a subgroup of a subgroup. The same multiplication works in each case.

Subgroups in surveys and data

If 30% of survey respondents are students and 50% of those students commute by bike, then 30% × 50% ÷ 100 = 15% of all respondents are student cyclists. This is how you turn a figure about part of a group into a figure about everyone.

Commission splits and royalties

A real estate commission of 5% that is split 50/50 between two agents gives each agent 2.5% of the sale price. On a $300,000 home, that is $7,500 each. Royalties work the same way: a 15% royalty on a product with a 40% share of sales is 6% of total sales.

Joint probabilities

If two events are independent, the chance that both happen is the product of their probabilities. A 30% chance of rain and a 50% chance your train is late give a 15% chance of both, but only if the two are unrelated. If one makes the other more likely, the simple product is wrong.

Fees on taxes and charges

A fee charged on a tax, rather than on the price, is a percentage of a percentage. A 5% fee on a 10% tax is 0.5% of the original price, not 5%. On a $1,000 purchase, the tax is $100 and the fee is $5.

Results Over 100% and Other Edge Cases

The formula works for any numbers, but a few patterns are worth knowing so the results do not surprise you.

• Order does not matter. Multiplication is commutative, so 15% of 40% and 40% of 15% are both 6%.
• Two inputs between 0% and 100% give a smaller result. The answer is never larger than either input. 90% of 90% is 81%.
• Inputs over 100% can give results over 100%. 150% of 80% is 120%. But an input over 100% does not guarantee it: 150% of 10% is 15%.
• Halving both inputs quarters the result. 40% of 60% is 24%, while 20% of 30% is 6%. This is why stacked small rates shrink quickly.
• Zero gives zero. 0% of anything is 0%.
• Negative inputs follow the usual sign rules. A negative times a positive is negative. In most real problems, though, a decrease is better entered as the percentage kept (90 for a 10% fall).

For a rise followed by a fall of the same size, the result is always below where you started. A 10% rise then a 10% fall is 110 × 90 ÷ 100 = 99%, a 1% net loss.

What Is X% of Y% If...

What is 20% of 50%?

20% of 50% is 10%. Multiply the two and divide by 100: 20 × 50 ÷ 100 = 10. In decimals, 0.2 × 0.5 = 0.1, which is 10%.

What is 50% of 50%?

50% of 50% is 25%. Half of a half is a quarter: 50 × 50 ÷ 100 = 25%.

What is 25% of 60%?

25% of 60% is 15%. 25 × 60 = 1,500, and 1,500 ÷ 100 = 15%. A quarter of 60 is 15.

What is 10% of 10%?

10% of 10% is 1%. 0.1 × 0.1 = 0.01, which is 1%. Small percentages of small percentages shrink fast.

What is 150% of 80%?

150% of 80% is 120%. 150 × 80 ÷ 100 = 120%. When one input is above 100%, the result can be larger than the other input.

What is my total discount if I get 20% off and then 10% off?

The total discount is 28%, not 30%. You pay 80% after the first discount and 90% of that after the second: 80 × 90 ÷ 100 = 72%. So you save 100% − 72% = 28%. On an $80 item you pay $57.60.

What is my total discount if I get 40% off and then an extra 25% off?

The total discount is 55%, not 65%. You keep 60% and then 75% of that: 60 × 75 ÷ 100 = 45%. You pay 45% of the original price and save 55%.

What is the net change if a price rises 10% and then falls 10%?

The price ends 1% lower than it started. 110% × 90% ÷ 100 = 99%. The fall is taken from the higher price, so it removes more than the rise added.

What do I pay if an item is 25% off and then taxed at 8%?

You pay 81% of the original price. 75 × 108 ÷ 100 = 81%. On a $200 item, that is $150 after the discount and $162 after tax.

What share does each agent get if a 5% commission is split 50/50?

Each agent gets 2.5% of the sale price. 5 × 50 ÷ 100 = 2.5%. On a $300,000 sale, that is $7,500 per agent.

People Also Search For

How to calculate a percentage of a percentage by hand

Convert both percentages to decimals, multiply them, then multiply by 100. For 25% of 80%: 0.25 × 0.80 = 0.20, and 0.20 × 100 = 20%. The shortcut X × Y ÷ 100 gives the same answer in one step.

How to calculate stacked discounts

Multiply the percentages you pay, not the percentages you save. For 30% off then 20% off, multiply 70% by 80% to get 56%. You pay 56% of the original price, which is a 44% total discount.

How to combine two percentage increases

Multiply the growth factors and subtract 1. A 10% rise followed by a 15% rise is 1.10 × 1.15 = 1.265, a 26.5% total increase. Simply adding gives 25%, which is too low.

Percentage of a percentage in Excel

Multiply the two cells: =A1*B1. If A1 holds 20% and B1 holds 50%, Excel stores them as 0.2 and 0.5, so the product is 0.1. Format the result cell as a percentage to display 10%.

Percent vs percentage points

A percentage point is the plain difference between two percentages; a percent change is relative. Moving from 10% to 12% is a rise of 2 percentage points, but a 20% increase in the rate. Use percentage points when comparing rates directly.

How to find a subgroup's share of the whole

Multiply the group's share by the subgroup's share within it, then divide by 100. If 20% of students join a club and 10% of club members enter a contest, then 20 × 10 ÷ 100 = 2% of all students entered.

Frequently Asked Questions