Common logarithm calculator
The common logarithm of 1000 is 3, because ten cubed is 1000: enter any positive number and get the power of ten behind it, negative for values between 0 and 1. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Value
- 1,000
- Logarithm
- 3
- Base
- 10
- Expression
- log10(1000)
The common logarithm calculator finds the exponent to which ten must be raised to produce a positive number. Enter 1000 and the result is 3 because ten cubed equals 1000; enter a value between zero and one and the result is negative. Zero and negative real arguments are outside the common logarithm domain and are rejected clearly instead of producing a misleading value.
What a common logarithm means
A common logarithm is a logarithm with base ten. The notation log10(x) asks a precise inverse question: what exponent y makes ten raised to y equal x? For familiar powers of ten, the relationship is immediate.
The common logarithm of 100 is 2 because ten squared is 100, and the common logarithm of 0.01 is negative 2 because ten raised to negative 2 is one hundredth. Values do not need to be exact powers of ten. For example, log10(2) is approximately 0.301029995664, locating 2 between ten to the zero and ten to the one.
This calculator accepts one positive finite number and evaluates that relationship directly. The result is rounded to twelve significant digits to suppress insignificant floating-point noise while retaining useful precision. It does not calculate natural logarithms, arbitrary-base logarithms, complex logarithms, or symbolic expressions; those are distinct operations with different input contracts.
Use this focused tool when the intended question is specifically the real base-ten logarithm of a numeric value.
Enter a valid value and interpret the result
Positive integers, positive decimals, and very small or large positive finite numbers are valid. A result of zero means the input was 1, since ten to the zero equals 1. A positive result means the argument is greater than 1, while a negative result means the argument lies strictly between zero and 1.
The integer part also describes decimal scale: a logarithm between 3 and 4 corresponds to a number between 1000 and 10000. Missing values, blank strings, nonnumeric text, NaN, and Infinity are rejected because they cannot produce a finite real calculation. Zero is rejected because no finite exponent of ten equals zero.
Correct the value and retry rather than treating an invalid request as a numerical answer.
What you can do with it
Check powers of ten
Confirm the exponent represented by a positive power of ten while teaching or reviewing exponential notation.
Normalize positive measurements
Transform a positive value onto a base-ten logarithmic scale before charting or statistical analysis.
FAQ
What is a common logarithm?
It is a logarithm with base 10: log10(x) is the exponent y for which 10 raised to y equals x.
Can I calculate the logarithm of zero?
No. No finite power of 10 equals zero, so zero is outside the real common-logarithm domain and is rejected.
Are negative numbers accepted?
No. This capability returns real values only, and the real common logarithm is undefined for negative arguments.
Why is the result negative for a positive input?
Positive inputs between zero and one have negative common logarithms because they equal negative powers of ten.
What does the whole-number part of a logarithm tell me?
It shows the decimal scale of the number. A common logarithm between 3 and 4 belongs to a number between 1000 and 10000, so the whole part gives you the order of magnitude at a glance.
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/algebra/common-log \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"value":1000}'const res = await fetch("https://api.kit.forhosting.com/algebra/common-log", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"value": 1000
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/algebra/common-log",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"value": 1000
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/algebra/common-log", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"value":1000}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"value":1000}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/algebra/common-log", 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": 1000
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "algebra.common_log",
"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 calculation is deterministic, requires no network lookup, and returns structured JSON suitable for lessons, spreadsheets, scientific utilities, and automated checks. Browser calculations are free, while each successful API request costs $0.002.
What a common logarithm means
Its response echoes the normalized value, reports the logarithm, identifies the base as 10, and includes a compact expression for display.
Enter a valid value and interpret the result
Send the required value field as a JSON number or a conventional decimal or scientific-notation string. Negative arguments are rejected because a real-valued common logarithm is not defined there; supporting complex values would require a branch convention and a different response shape. Validation errors use the invalid_input code so calling software can distinguish a domain or formatting problem from an infrastructure failure. Every successful response is deterministic: the same supported input produces the same JSON without network calls, randomness, stored state, or time-dependent behavior.
Use the result in calculations and automation
Common logarithms appear whenever quantities are compared by orders of magnitude. Scientists use them to reason about scales that span many powers of ten; engineers use them inside decibel formulas; analysts use them to compress skewed positive measurements; and educators use them to connect exponent rules with inverse functions. Keep full awareness of units in downstream work: taking a logarithm of a dimensional measurement normally assumes comparison with an agreed reference quantity. Because the implementation performs constant-time validation and one native mathematical operation, it is suited to lightweight repeated calls, although batching and application-specific transformations should remain in the caller when many related values are already available together. Remember that this endpoint returns log10(value) itself, not a decibel conversion, pH calculation, digit count, or rounded order-of-magnitude category. Those applications may multiply, negate, floor, or otherwise transform the logarithm according to their own definitions. For server automation, submit the same value field and budget $0.002 for each successful item.
Integration use cases
Build reproducible test fixtures
Generate stable common-log values for calculators, worksheets, scientific utilities, and automated regression tests.
Technical questions
What does an API calculation cost?
Each successful API item costs $0.002. You can also use the browser calculator for free.