Percentage of a percentage calculator
20% of 50% is 10%, because (20 × 50) / 100 = 10. Enter two percentages to get the compound rate they form together, for a cut of a discount, a tax on a taxable share or a subset of a subset. Free in your browser.
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- Your data stays on your device
Run — free
Worked example
- Percent
- 20
- Of percent
- 50
- Result percent
- 10
- Result decimal
- 0.1
- Expression
- 20% of 50% = 10%
A percentage of a percentage is the compound rate you get when one percent is taken of another percent, not of a raw amount. People search this when a commission is itself a cut of a discount, when a tax applies only to a taxable share, or when a survey reports a subset of a subset. Twenty percent of fifty percent is ten percent, because (20 × 50) / 100 equals 10. The same identity works above one hundred percent, for zeros, and for signed rates.
What a percentage of a percentage actually computes
A percentage already names a hundredths-scale rate: twenty percent is the fraction twenty over one hundred. Taking a percentage of another percentage therefore means multiplying those two fractions and scaling the product back to percent so the answer stays in the same units as the inputs. Twenty percent of fifty percent is ten percent because 0.20 times 0.50 equals 0.10, and 0.10 times one hundred is ten.
The same identity is what people mean when they say a cut of a cut, a share of a share, or a rate applied to a rate. Values above one hundred percent are allowed because a rate can exceed a whole, so one hundred fifty percent of forty percent is sixty percent. Zero is allowed and yields zero.
Negative rates are allowed and preserve sign, which is how a signed rebate of a signed discount stays a signed compound rate. The operation is commutative: A percent of B percent equals B percent of A percent, because multiplication of the two fractions commutes. Use this page when both numbers are already percentages and you need the single compound percentage they form together.
Where a percentage of a percentage comes up
Retail and marketplace teams use a percentage of a percentage calculator when a seller commission is taken on an already discounted slice of list price, or when a coupon applies only to a promotional share of a basket. Survey and analytics notebooks reduce nested shares the same way: if thirty percent of respondents saw an ad and twenty percent of those converted, the joint share of the whole sample is six percent, which is exactly this product.
Tax and payroll scripts apply a levy to a taxable fraction of a wage, then need the levy expressed again as a percent of the original base. Classrooms and tutoring platforms let learners check the classic trap that twenty percent of fifty percent is ten percent, not seventy, against a deterministic oracle instead of a spreadsheet cell that might have added the two rates.
Keep requests small, pin the rounded fields in tests, and you get a reproducible compound rate without standing up a spreadsheet or a computer-algebra library for two multiplications.
What you can do with it
Stacked retail rates and commissions
Turn a seller cut of an already discounted slice into one compound percentage of list price, without mixing dollars and percents.
Nested survey and conversion shares
Combine a reach percent with a conversion percent of that reach to report the joint share of the whole sample.
FAQ
How do I compute a percentage of a percentage?
Example: 20 and 50 yield 10, because 20% of 50% is 10%.
Why is 20% of 50% equal to 10% and not 70%?
Addition would give 70, but a percentage of a percentage multiplies the two rates as fractions: 0.20 × 0.50 = 0.10, which is 10%. This calculator never adds the two inputs.
Can I use values above 100% or negative percentages?
Yes. Rates above one hundred and signed rates are finite numbers, so 150% of 40% is 60% and a negative rate keeps its sign in the product.
What happens if a value is missing or not a finite number?
NaN, Infinity, empty strings, and non-numeric values are rejected and are not billed.
How do I combine two nested shares, such as a group within a group?
Multiply the two percentages and divide by 100. If 30% of respondents saw an ad and 20% of those bought something, the buyers are 6% of the whole sample, not 50%.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/math/percentage-of-percentage \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"percent":20,"of_percent":50}'const res = await fetch("https://api.kit.forhosting.com/math/percentage-of-percentage", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"percent": 20,
"of_percent": 50
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/percentage-of-percentage",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"percent": 20,
"of_percent": 50
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/percentage-of-percentage", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"percent":20,"of_percent":50}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"percent":20,"of_percent":50}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/percentage-of-percentage", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"percent": 20,
"of_percent": 50
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.percentage_of_percentage",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
This calculator accepts two finite percentage values — percent and of_percent — multiplies them as fractions, and returns the resulting percentage. Non-finite inputs fail with invalid_input and are not billed.
What a percentage of a percentage actually computes
Algebraically the identity is result_percent equals (percent times of_percent) divided by one hundred, which is the same as converting each input to a decimal, multiplying, and converting the product back. It is not addition: twenty percent plus fifty percent is seventy percent, a different question that this endpoint does not answer. It is also not twenty percent of a fifty-dollar amount, which would be ten dollars; here both operands are already percentages and the result is a percentage.
Input contract, formula, and how errors are reported
Results are rounded to twelve decimal places so goldens and clients compare stably across runtimes. There is no domain clamp at zero or one hundred: a stacked markup, a sample weight, or a signed adjustment can sit outside that interval and still be a well-defined product of two rates. Failed validation is not billed. POST a JSON body with two required finite numbers: percent, the first rate (the X in X percent of Y percent), and of_percent, the second rate (the Y). Each field may arrive as a JSON number or as a numeric string; missing fields, empty strings, booleans, arrays, objects, NaN, and Infinity fail with invalid_input naming the field. On success the body echoes both inputs, returns result_percent as the compound percentage, returns result_decimal as that same rate written as a fraction of one, and includes a short expression string plus the formula result_percent = (percent × of_percent) / 100 so you can display the identity next to the answer. Example: percent equals twenty and of_percent equals fifty yields result_percent ten, result_decimal one tenth, and the expression 20% of 50% = 10%. If the product overflows IEEE floating point and is no longer finite, the task fails instead of returning Infinity. Pair the numeric fields with your own copy if you need step-by-step classroom prose; this endpoint computes the compound percentage and does not emit worked solutions beyond the formula and expression strings.
Integration use cases
Classroom checks of the classic trap
Let students verify that 20% of 50% is 10%, not 70%, against a deterministic API instead of a handwritten product.
Technical questions
What does the percentage of a percentage calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.