dB to gain ratio calculator
Twenty decibels is a voltage ratio of 10 but a power ratio of 100, so choosing the right kind matters. Enter the signed dB value, pick voltage or power, and get the linear multiplier labelled as gain, attenuation or unity. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Gain db
- 20
- Gain type
- Voltage
- Ratio
- 10
- Relationship
- gain
This dB to gain ratio calculator converts a signed amplifier or filter response from decibels back to its linear multiplier. Select voltage when the decibel figure describes an amplitude ratio, or power when it describes a power ratio. The calculator applies the correct inverse logarithmic formula, identifies the result as gain, attenuation, or unity, and returns a deterministic numeric ratio that can be used in design worksheets, response plots, laboratory checks, and automated analysis. Positive dB values produce ratios above one, negative values produce ratios below one, and zero dB produces exactly one.
Choose the inverse formula that matches the measured quantity
Decibels describe a ratio logarithmically, but the coefficient used to create the decibel value depends on the physical quantity. A voltage or other field-amplitude gain is normally written as twenty times the base-ten logarithm of the linear amplitude ratio. The distinction matters: twenty dB represents a voltage ratio of ten but a power ratio of one hundred.
Select voltage for amplifier voltage gain, filter magnitude expressed as an amplitude response, microphone sensitivity changes, or any specification explicitly based on twenty log ten. Select power for input-to-output wattage, RF power gain, insertion power loss, or a specification explicitly based on ten log ten. Do not choose by the unit label alone; consult the equation or datasheet convention behind the dB number.
Under equal impedances, squaring a voltage ratio produces the corresponding power ratio, which explains why the two decibel forms describe the same physical change while returning different linear ratios. This capability keeps the selection explicit so a plausible-looking number cannot silently come from the wrong convention.
Enter signed decibels and interpret the returned ratio
The default is voltage for convenient amplitude-response work. Positive decibels produce a linear ratio greater than one and the response labels the relationship as gain. Negative decibels produce a positive ratio below one and are labeled attenuation.
Zero decibels returns a ratio of exactly one and is labeled unity. For example, plus six point zero two decibels is approximately a two-to-one voltage ratio, while plus three point zero one decibels is approximately a two-to-one power ratio. A minus twenty dB voltage gain yields one tenth, meaning the output amplitude is ten percent of the input amplitude.
Ratios are dimensionless; they multiply a compatible input magnitude rather than carrying volts or watts themselves.
Apply linear ratios to amplifiers, filters, and response analysis
Linear ratios are useful whenever the next calculation needs multiplication instead of logarithmic addition. In an amplifier worksheet, multiply an input voltage by a returned voltage ratio to estimate output voltage while the circuit remains in its linear operating region. In a filter response analysis, convert sampled magnitude values from dB to amplitude ratios before comparing passband ripple directly, normalizing curves, or feeding data to software that expects linear magnitude.
Power ratios support transmitter chains, attenuator checks, and link-budget verification when you need to recover watts from a known reference power. Remember that a gain ratio does not model clipping, impedance mismatch, bandwidth limits, phase shift, noise, or component tolerances. It only reverses the stated logarithmic relationship.
When cascading stages, it is usually simpler to add their signed dB values first and convert the total once; multiplying individually converted ratios is mathematically equivalent but can accumulate extra rounding. Treat negative gain as attenuation rather than as a negative linear magnitude, because the returned ratio always remains positive and does not encode signal polarity or phase inversion.
What you can do with it
Amplifier gain worksheets
Convert a datasheet or measured voltage gain in dB into the multiplier needed to estimate output amplitude from an input signal.
Filter magnitude reconstruction
Turn frequency-response samples from dB into linear amplitude ratios for plots, normalization, tolerance comparisons, and numerical processing.
RF power and attenuation checks
Recover a power multiplier from signed dB gain or loss before applying it to a reference wattage in a link or test budget.
FAQ
What formula converts voltage gain in dB to a ratio?
For example, 20 dB becomes a voltage ratio of 10, while -20 dB becomes 0.1.
What formula converts power gain in dB to a ratio?
For example, 20 dB becomes a power ratio of 100, while -10 dB becomes 0.1.
Why do voltage and power use different divisors?
Power is proportional to amplitude squared under the relevant impedance assumptions. That square introduces the factor of two behind the twenty-log amplitude convention.
Does a negative dB value produce a negative ratio?
No. It produces a positive ratio below one and represents attenuation. A gain ratio alone does not describe polarity or a 180-degree phase inversion.
How do I know whether to choose voltage or power?
Check the equation or datasheet convention behind the dB figure, not the unit label. Amplitude figures such as amplifier voltage gain or filter magnitude use twenty log ten; wattage, RF power gain and insertion loss use ten log ten.
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/elec/gain-db-to-ratio \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"gain_db":20}'const res = await fetch("https://api.kit.forhosting.com/elec/gain-db-to-ratio", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"gain_db": 20
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/gain-db-to-ratio",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"gain_db": 20
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/gain-db-to-ratio", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"gain_db":20}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"gain_db":20}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/gain-db-to-ratio", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"gain_db": 20
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.gain_db_to_ratio",
"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
The browser calculation is free, while a successful API item costs $0.002.
Choose the inverse formula that matches the measured quantity
Reversing that equation gives ratio equals ten raised to gain_db divided by twenty. A power gain is written as ten times the base-ten logarithm of the power ratio, so its inverse is ratio equals ten raised to gain_db divided by ten.
Enter signed decibels and interpret the returned ratio
Provide gain_db as a finite signed number from minus three thousand through plus three thousand and choose gain_type as voltage or power. The result includes the original cleaned gain_db, the selected gain_type, the computed ratio, the relationship label, and the formula used. Numeric strings are accepted by the pure solver for common form and SDK inputs, but blank strings, NaN, Infinity, unsupported types, conflicting aliases, and values outside the stated range return invalid_input.
Apply linear ratios to amplifiers, filters, and response analysis
The implementation uses no network, randomness, clock, or stored state, so the same JSON input always produces the same response. Interactive browser use is free, and successful API requests cost $0.002 per item for scripts, regression suites, and batch engineering tools.
Technical questions
How much does the calculator cost?
The browser calculator runs free. Each successful API item costs $0.002; invalid input is rejected with an invalid_input error.