Binary to decimal converter
1010 in binary is 10 in decimal: enter any run of zeros and ones and get the base-ten number, with each place worth a power of two. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Binary
- 1010
- Decimal
- 10
- Decimal string
- 10
- Bit length
- 4
- Base from
- 2
This binary to decimal converter takes a string of binary digits—only zeros and ones—and returns the equivalent decimal integer in base ten. Binary is the language of digital systems: each bit is a power of two, so the rightmost bit is 2 to the power of zero, the next is 2 to the power of one, and so on. Classic checks you already know include one-zero-one-zero equaling ten, eight ones equaling two hundred fifty-five, and a single one equaling one. The engine is fully deterministic: it scans left to right with the Horner rule value equals two times value plus the next bit, never calls the network, never samples randomness, and never depends on the clock.
What binary to decimal means and what you get
A binary number is a positional numeral written only with the digits zero and one. Each position multiplies its digit by a power of two: reading from the right, the least significant bit contributes zero or one times two to the power of zero, the next bit multiplies by two to the power of one, then four, eight, sixteen, and so on. Converting to decimal simply adds those weighted contributions to produce a single base-ten integer that people, spreadsheets, and most APIs expect.
There is no floating-point path, no approximate rounding of fractional bits, and no silent coercion of invalid characters into zeros.
How the binary field is read and how the decimal stays reproducible
Outer whitespace is trimmed; an optional 0b or 0B prefix is stripped so JavaScript-style literals such as 0b1101 work the same as bare 1101. After that strip, every remaining character must be the digit zero or the digit one—no spaces between bits, no commas, no underscores, and no other radices. A bare number that looks like one-zero-one-zero is accepted only when it is a non-negative integer whose decimal digit characters are exclusively zero and one; values like one thousand twenty-three fail because the digit two is not binary.
Conversion uses the classic left-to-right Horner accumulation: start at zero, then for each bit multiply the running total by two and add the bit. That is algebraically identical to summing each digit times two raised to its place index, but needs only integer multiply-and-add and never builds large intermediate powers.
Where binary-to-decimal conversion fits in study, engineering, and software
Students meet binary when a textbook introduces place value beyond base ten, when a computer-architecture course maps machine words to human-readable quantities, or when a coding interview asks for a mental convert of a short bit string. Teachers can pre-generate answer keys for modest bit lengths without trusting opaque calculator apps that silently drop leading zeros or accept hex digits by mistake. Embedded and firmware engineers check bit masks, register dumps, and LED patterns against the decimal values their documentation tables list.
Developers call the same contract from scripts to seed deterministic test vectors for parsers, to validate user-entered bit strings in configuration UIs, or to satisfy programming-challenge statements that demand a base-ten integer rather than a hand-waved sketch. Product and education tools use the conversion when a learner types a binary literal and the UI must show the decimal equivalent immediately. Pair it with related format or number tools when you are building a small lab of free, deterministic converters for base systems and digital literacy.
What you can do with it
Homework and exam checks
Convert textbook binary strings to base-10 integers and verify place-value work before submitting answers.
Firmware and bit-mask review
Map short register dumps and flag bit strings to the decimal values listed in hardware documentation.
FAQ
What does the binary to decimal converter cost?
It is free in your browser on this page.
Which characters are allowed in the binary field?
Only the digits 0 and 1 after an optional 0b or 0B prefix.
Does this tool convert decimal numbers back to binary?
No. It only maps a binary digit string to a non-negative decimal integer. Use a dedicated decimal-to-binary tool for the reverse direction.
What is 1010 in decimal?
1010 in binary is 10 in decimal. Reading from the right, the places are worth one, two, four and eight, and the two ones sit in the eight and two places, which add up to ten.
What do eight ones in binary equal?
Eight ones in a row equal 255 in decimal, because every place from one up to one hundred twenty-eight is filled and all of those values are added together.
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/fmt/binary-decimal \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"binary":"1010"}'const res = await fetch("https://api.kit.forhosting.com/fmt/binary-decimal", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"binary": "1010"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/fmt/binary-decimal",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"binary": "1010"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/fmt/binary-decimal", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"binary":"1010"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"binary":"1010"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/fmt/binary-decimal", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"binary": "1010"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "fmt.binary_decimal",
"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_bits | 53 |
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
What binary-to-decimal conversion means and what the response contains
This calculator returns the normalized binary string without a prefix, the decimal integer as a safe JavaScript number, the same value as a decimal_string for copy-paste, the bit_length of the digit string, a method tag binary_to_decimal, a short formula reminder of the summation and Horner forms, and the bases two and ten for documentation. The engine either builds an exact non-negative integer inside the supported bit length or rejects the input with invalid_input. Rejected cases include a missing binary field, an empty string after trimming, a 0b prefix with no digits, any character outside zero and one such as two, A, a space in the middle, a sign, or an underscore, and any string longer than the documented maximum of fifty-three bits so the result always stays within Number.MAX_SAFE_INTEGER.
How the binary field is read and how the decimal stays reproducible
The preferred field is binary, but aliases bin, value, text, input, and bits are accepted so query strings, spreadsheets, and typed forms can reuse the same contract without renaming columns. Length is capped at fifty-three bits so the result is always a safe integer in JavaScript and JSON goldens compare without BigInt serialization quirks. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing base conversion yourself.
Where binary-to-decimal conversion fits in study, engineering, and software
On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split—free interactive exploration and a priced, identical API—matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.
Integration use cases
Deterministic test fixtures
Generate reproducible decimal results for unit tests, property checks, and CI assertions on binary parsers.
Technical questions
What is the maximum binary length?
Fifty-three bits. That keeps the decimal result inside JavaScript Number.MAX_SAFE_INTEGER so goldens and JSON stay exact.
How is the decimal value computed?
With the Horner rule: start at 0, then for each bit left-to-right set value = 2·value + bit. That equals the sum of each digit times its power of two.