Complement probability calculator
An event with a probability of 0.35 has a complement of 0.65, the chance it does not happen. Enter any probability from 0 to 1 to get both sides as decimals and percentages, with the formula to show beside your answer. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Probability
- 0.35
- Complement
- 0.65
- Percentage
- 35
- Complement percentage
- 65
The complement rule is one of the first identities every probability student memorizes: if A is an event, the probability that A does not occur is one minus the probability that A does occur. This complement probability calculator takes a single number P(A) in the closed unit interval from zero to one and returns the complement P(A′) equals one minus P(A), together with percentage forms of both sides and a short formula string you can show next to the answer. Boundary cases are first-class: when the event is certain (probability one) the complement is zero; when the event is impossible (probability zero) the complement is one.
What the complement rule means and what you get
In a probability space the sample space is exhaustive: for any event A, either A occurs or its complement A-prime occurs, and the two outcomes are mutually exclusive. Kolmogorov’s axioms therefore force the sum of their probabilities to equal one, which rearranges into the one-line identity P(A-prime) equals one minus P(A). That identity is the entire mathematical core of this calculator.
You send a finite probability for the event, and the engine subtracts it from one, rounds the floating-point result to a stable display precision, and echoes both the original probability and the complement. Nothing else is invented: there is no independence assumption, no Bayesian update, and no distribution family. Classic textbook checks include a rain probability of zero point three, which yields a complement of zero point seven, and a fair-coin heads probability of one half, which yields a complement of one half.
Certainty and impossibility are valid successes, not errors: probability one maps to complement zero, and probability zero maps to complement one.
Where complement probability shows up in real work
Product analytics teams convert a conversion rate into the probability that a visitor does not convert so funnel reports can quote both sides without re-deriving one minus p in every dashboard. Quality and reliability engineers turn a defect probability into a non-defect complement when communicating process capability to non-statisticians. Risk and compliance summaries often need the chance that an adverse event does not occur given a modeled hit rate.
Keep requests small, pin the rounded complement in tests, and you get reproducible answers for homework, LMS plugins, and edge workers without standing up a statistics library of your own. If you later need binomial CDFs, conditional probability, or odds conversion, treat those as separate search intents and landings rather than overloading this complement calculator page.
What you can do with it
Classroom and homework complement drills
Let students submit P(A) and verify P(not A) equals one minus the value, including the certainty and impossibility edge cases.
Analytics and funnel non-conversion rates
Turn a conversion or click-through probability into the complementary non-event rate for dashboards without hand-written one-minus formulas.
FAQ
What happens if the probability is outside 0 to 1?
Values strictly below 0 or above 1 are not valid probabilities and are not charged.
Can I send the value as p or percent-style 35?
A raw percentage such as 35 is rejected because it is greater than 1; send 0.35 instead.
What about probability 0 or 1?
Both are valid. Probability 0 yields complement 1 (impossible event), and probability 1 yields complement 0 (certain event).
What does it cost?
The browser tool is free and runs locally.
Does the complement rule need independent events?
No. It only relies on the fact that an event either happens or does not, so the two probabilities add up to one. No independence assumption, update with new evidence or distribution family is involved.
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/stat/complement-probability \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"probability":0.35}'const res = await fetch("https://api.kit.forhosting.com/stat/complement-probability", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"probability": 0.35
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/stat/complement-probability",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"probability": 0.35
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/stat/complement-probability", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"probability":0.35}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"probability":0.35}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/stat/complement-probability", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"probability": 0.35
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "stat.complement_probability",
"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
Values outside the unit interval are rejected with invalid_input instead of a silent clamp, so bad spreadsheet cells and off-by-percent mistakes never become a fake probability. Successful API calls are priced at the published base of $0.002 per item; validation failures are not charged.
What the complement rule means and what the response contains
The response also multiplies each side by one hundred so callers who think in percentages can read percentage and complement_percentage without a second conversion step. A formula field restates the identity as P(A-prime) equals one minus P(A) for teaching widgets and API documentation side panels.
Input contract, aliases, and error behaviour
Provide exactly one of those names so a client does not accidentally send two conflicting numbers. After parsing, the engine enforces the closed unit interval: any number strictly less than zero or strictly greater than one fails with a clear message that probability must lie between zero and one inclusive. That check is intentional and strict. Many real-world mistakes come from sending a percentage such as thirty-five instead of zero point three five, or from residual likelihood scores that slightly overshoot one after floating-point work elsewhere. Clamping those mistakes would hide bugs in upstream code; rejecting them keeps the contract honest and leaves the caller free to fix the scale. POST a JSON body with a single required field named probability, or use one of the classroom and form aliases p, prob, or chance. The value may arrive as a JSON number or as a numeric string; empty strings, missing fields, non-numeric text, NaN, and Infinity fail with invalid_input naming the field. On success the body includes the cleaned probability, the complement, percentage and complement_percentage, and the formula string. Example: probability zero point three five yields complement zero point six five, percentage thirty-five, and complement_percentage sixty-five. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance and return the same invalid_input code the rest of the KIT catalog uses for client-side mistakes.
Where complement probability shows up in real work
Secondary-school and college probability units constantly assign complement drills, mutual-exclusivity checks, and “probability of not” word problems; a single trusted oracle that returns cleaned JSON speeds grading, demo setup, and interactive lesson design. Curriculum authors building browser widgets want the same JSON shape free on the page and paid through the API so offline worksheets and online auto-graders stay aligned. Because this capability is a pure parse engine, every successful call costs the published $0.002 base price with no model tokens and no outbound network, and failed validation does not consume balance.
Integration use cases
Grading fixtures and simulation checks
Generate deterministic expected non-event probabilities for unit tests, LMS auto-graders, and Monte Carlo validation harnesses.
Technical questions
What is the complement probability formula?
P(A′) = 1 − P(A). Send a probability in [0, 1] and the API returns the complement, plus percentage forms of both sides.