Antilog calculator
The antilog of 2 in base 10 is 100, and the antilog of 3 in base 2 is 8. Enter the value and any positive base to turn a logarithm back into the real quantity. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Value
- 2
- Base
- 10
- Antilog
- 100
An antilogarithm answers the inverse question of a logarithm: if log base b of some unknown number equals y, then that number is b raised to the power y. Students meet antilogs when undoing common logs in chemistry pH work, recovering a quantity from a log table, or solving exponential equations that were linearized with logarithms. Engineers use the same identity when converting decibel readings back into power ratios or when a growth rate measured in log units must be turned back into a real multiplier.
What an antilogarithm is and why it undoes a logarithm
By definition, y equals log base b of x exactly when b raised to y equals x. The antilogarithm is that second direction: given the exponent y and the base b, recover the original quantity x as b to the power y. This is why antilogs appear wherever logarithms were used to compress a scale.
In classical log tables you looked up a logarithm to multiply numbers by adding; to finish the calculation you took the antilog of the sum. In chemistry, pH is the negative common logarithm of hydrogen ion concentration, so converting a pH reading back into a concentration is an antilog computation: ten raised to minus the pH. In acoustics and electronics, a decibel difference is ten times the common log of a power ratio, so recovering the ratio means raising ten to the decibel value over ten.
The same identity drives half-life and compound-growth models solved with logarithms: once you have solved for the exponent, the antilog returns the actual amount. Any positive base is valid, including bases below one, and base one is allowed too since one raised to any power is simply one. The value may be negative, zero, or fractional; a negative value yields the reciprocal, zero yields exactly one, and fractional values yield roots of the base.
Practical use, pricing, limits, and delivery
Use the browser tool when you need an immediate antilogarithm while checking homework, preparing a lecture slide, or converting a log-scale reading back into a real quantity without installing a computer-algebra system. There is no language model, no external math service, and no randomness, so the capability is safe to pin in continuous-integration checks and reproducible lesson materials. Results are fully deterministic: the same value and base always yield the same antilog.
Prefer this calculator when you need an arbitrary positive base; for the common case of base ten you simply pass ten, and for natural-log work you pass e. Source inputs and outputs follow the same retention rules as other KIT parse items, and a failed task is never charged after validation.
What you can do with it
Homework and tutoring verification
Students and graders confirm antilogarithms for any positive base, including domain errors that correctly fail, without a local CAS install.
Log-scale conversion in pipelines
Scripts that convert decibel ratios, pH values, or log-compressed measurements back into linear quantities call a deterministic antilog oracle instead of reimplementing exponent checks in every language.
FAQ
What happens if the base is not positive?
The antilogarithm is only well-defined for a positive base when the exponent can be any real number.
Can the value be negative or fractional?
Yes. A negative value returns the reciprocal (base^-2 = 1/base^2), zero returns exactly 1, and fractional values return roots of the base.
Is the antilog calculator free?
The browser tool runs free on your device.
How do I turn a pH reading back into a concentration?
pH is the negative common logarithm of the hydrogen ion concentration, so take the antilog in base 10 of minus the pH. The result is the concentration that the pH reading came from.
How do I convert decibels back into a power ratio?
A decibel difference is ten times the common logarithm of a power ratio. Divide the decibel value by 10 and take the antilog of that number in base 10 to recover the ratio.
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/antilog \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"value":2,"base":10}'const res = await fetch("https://api.kit.forhosting.com/math/antilog", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"value": 2,
"base": 10
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/antilog",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"value": 2,
"base": 10
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/antilog", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"value":2,"base":10}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"value":2,"base":10}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/antilog", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"value": 2,
"base": 10
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.antilog",
"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 capability computes the antilogarithm of any finite value for any positive base with a single deterministic exponentiation, antilog_b(value) equals base^value. The base must be a positive finite number; otherwise the request fails with invalid_input instead of returning NaN.
How to call the calculator and read the response
The base must be strictly greater than zero, because a non-positive base does not give a well-defined real exponential for arbitrary exponents. Numeric dust near zero is cleaned so goldens and human-readable demos stay stable, while ordinary non-integer results keep full double precision. Typical classroom checks include antilog base ten of two equals one hundred, antilog base two of three equals eight, and antilog of zero for any positive base equals one. Send a JSON body with the two required numbers: value, the exponent you want to undo, and base, the base of the original logarithm. Both may be given as JSON numbers or as plain numeric strings, including scientific notation, which the parser normalizes before computing. The engine validates that both are finite numbers; missing fields, empty strings, non-numeric strings, and NaN or Infinity fail immediately with invalid_input and are not charged. On success the response echoes the cleaned value and base, returns antilog as base raised to the value, and includes a short formula string documenting the identity used. If the combination overflows the finite floating-point range, the request fails with invalid_input rather than returning Infinity.
Practical use, pricing, limits, and delivery
Each successful request is one billable item at $0.002; failed validation and domain errors do not consume balance. Keep exponent magnitudes within the ordinary floating-point range so the result stays finite; the engine rejects overflows instead of emitting Infinity, which keeps downstream JSON consumers safe.
Integration use cases
Teaching inverse operations
Lesson pages can pair a logarithm and its antilog so learners see that log_b(x) and b^x undo each other with concrete numeric checks.
Technical questions
How do I compute an antilogarithm with this API?
Send JSON with a finite number value and a positive number base. The response returns antilog as base raised to the value, plus the echoed inputs and the formula string.
Does it compute logarithms too?
No. This capability evaluates antilogarithms (base^value). Computing log_b(x) for a given x and base is a separate capability.