Stock beta calculator
Stock returns of 0.10, 0.20 and 0.30 against market returns of 0.05, 0.10 and 0.15 give a beta of 2: the stock moved twice as far as the index. Paste your own pairs to get the same slope a spreadsheet would. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Stock beta measures how a security's period returns move with the market. In the capital-asset pricing model it is the slope of an ordinary-least-squares regression of the stock's historical returns on the matching benchmark returns, which is the same as the covariance of the two series divided by the variance of the market. A coefficient of one tracks the index; above one the name is more aggressive than the market; between zero and one it is defensive; a negative beta moves against the benchmark.
What stock beta is and how the coefficient falls out of paired returns
Beta is the number that answers a simple question: when the market moves by one unit of return, how many units does this stock tend to move? In the capital-asset pricing model that number is the slope of the line that best fits the cloud of period observations, stock return against market return. Algebraically the slope is the covariance of the two series divided by the variance of the market, which is identical to the ordinary-least-squares coefficient of the stock on the benchmark.
Write each observation as a pair of decimals for the same window—two percent is 0.02, not 2—and the identities never change. A beta of one means the name tracked the index over the sample; a beta of two means it tended to move twice as far in the same direction; a beta of one half means it was defensive; a negative beta means it tended to rise when the market fell.
Sample covariance and sample variance both divide by n minus one, so the n versus n minus one choice cancels in the ratio and the published beta equals the OLS slope you would get from a spreadsheet SLOPE of stock on market. Two pairs that lie on a straight line through a non-constant market series recover that slope exactly: stock returns 0.10, 0.20, 0.30 against market returns 0.05, 0.10, 0.15 yield beta two.
The calculator does not download prices, does not subtract a risk-free rate, does not annualize a monthly series, and does not lever or unlever the coefficient.
Where a stock beta calculator earns its keep
Portfolio construction and risk memos need a reproducible coefficient so an aggressive name with beta one point four is not confused with a defensive utility near zero point six, and so two analysts working from the same monthly pairs do not publish two different slopes because one used population covariance and the other used a spreadsheet SLOPE.
Cost-of-equity work in the capital-asset pricing model starts from this beta; this landing is the search for a stock beta calculator, not a full CAPM engine that also wants the risk-free rate and the equity risk premium, not a Bloomberg download, and not a realized-volatility calculator that ignores the market. Failed validation does not consume balance. Keep requests small, pin the rounded beta in tests, and you get stable OLS arithmetic for widgets, notebooks, and edge workers without standing up a full statistics library of your own.
What you can do with it
CAPM cost of equity and risk memos
Turn a window of paired stock and index returns into a single OLS beta so a cost-of-equity note and a risk memo share the same slope instead of two ad-hoc regressions.
Aggressive versus defensive screening
Flag names with beta above one as more volatile than the benchmark and names below one as defensive, using the same paired history your attribution already stores.
FAQ
How is stock beta calculated from historical returns?
Beta is Cov(R_stock, R_market) / Var(R_market), the OLS slope of the stock's period returns on the matching benchmark returns. Send at least two {stock, market} pairs as decimals for the same windows.
Why do I need at least two return pairs?
Variance and covariance are undefined on a single observation. Two or more pairs with a non-constant market series produce a finite beta.
What does a beta of 1, above 1, or below 0 mean?
One means the stock tracked the market over the sample. Above one it was more aggressive; between zero and one it was defensive; a negative beta tended to move against the benchmark.
What if every market return is the same?
Market variance is then zero and beta is undefined.
Should I enter returns as percentages or decimals?
As decimals for the same window: a two percent return is 0.02, not 2. Keep the stock series and the market series in the same form, period by period, before you paste the pairs.
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/fin/beta-stock \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"pairs":[{"stock":0.1,"market":0.05},{"stock":0.2,"market":0.1},{"stock":0.3,"market":0.15}]}'const res = await fetch("https://api.kit.forhosting.com/fin/beta-stock", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"pairs": [
{
"stock": 0.1,
"market": 0.05
},
{
"stock": 0.2,
"market": 0.1
},
{
"stock": 0.3,
"market": 0.15
}
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/fin/beta-stock",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"pairs": [
{
"stock": 0.1,
"market": 0.05
},
{
"stock": 0.2,
"market": 0.1
},
{
"stock": 0.3,
"market": 0.15
}
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/fin/beta-stock", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"pairs":[{"stock":0.1,"market":0.05},{"stock":0.2,"market":0.1},{"stock":0.3,"market":0.15}]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"pairs":[{"stock":0.1,"market":0.05},{"stock":0.2,"market":0.1},{"stock":0.3,"market":0.15}]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/fin/beta-stock", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"pairs": [
{
"stock": 0.1,
"market": 0.05
},
{
"stock": 0.2,
"market": 0.1
},
{
"stock": 0.3,
"market": 0.15
}
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "fin.beta_stock",
"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.
Limits
max_items | 10000 |
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 stock beta calculator takes paired historical returns, computes that OLS coefficient, and rejects the request when fewer than two return pairs are provided or when the market series has zero variance. Successful calls cost $0.002; invalid input is not billed.
Input contract, response shape, and validation
Each object carries stock and market as finite decimals for the same period. Fewer than two return pairs cannot define a variance, and a flat market series would make the denominator zero, so both are hard failures rather than Infinity. Example: three pairs with stock 0.10, 0.20, 0.30 and market 0.05, 0.10, 0.15 yield beta two. Prefer decimal fractions, not percents labeled as 10 for ten percent. POST a JSON body with one required array, pairs, of at least two objects. Aliases returns, observations, data, and rows are accepted so a quote export does not need a rename step. Parallel arrays stock_returns and market_returns of equal length are also accepted when you already have two columns. Values may arrive as JSON numbers or as numeric strings. At most ten thousand pairs are read; each return must stay within an absolute value of one million so products remain finite IEEE doubles on the Worker and in the browser. Missing pairs, a single pair, empty strings, non-numeric tokens, mismatched parallel lengths, NaN, Infinity, and a market series in which every return is the same fail with invalid_input naming the problem and are not billed. On success the body returns beta, the observation count n, stock_mean, market_mean, the sample covariance, the sample market_variance, a formula string you can print next to the number, a short English message, and ordered substitution steps. Pricing for a successful item is a flat $0.002.
Where a stock beta calculator earns its keep
Classroom and CFA-style drills need an oracle that treats three collinear pairs as beta two, rejects a single pair as invalid_input, and refuses a constant market series instead of returning Infinity. Engineers writing factor and screening tests pin known-good pairs—perfect slope two, a short mixed series with a non-integer slope, and a one-row payload as a hard failure—so a helper cannot quietly drop a period or treat percents as decimals. This landing is not a total-return price feed, not an alpha calculator, and not a correlation-only tool; those are different searches.
Integration use cases
Homework, CFA drills, and regression tests
Pin a known slope (three collinear pairs → beta 2) and reject fewer than two return pairs with invalid_input so classroom oracles and pricing helpers share one contract.
Technical questions
What does the stock beta calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.