Modulo order of operations calculator
Evaluate an expression with +, −, ×, ÷ and the % remainder in the standard order: 2 + 3 * 4 % 5 is 4, because 3 * 4 % 5 is worked out first, left to right. Parentheses change the order. Free in your browser.
- Free
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- Your data stays on your device
Run — free
Worked example
- Expression
- 2 + 3 * 4 % 5
- Result
- 4
An arithmetic expression that mixes addition, subtraction, multiplication, division, and modulo is easy to misread if every operator is treated as equal. Standard order of operations — often taught as PEMDAS or BODMAS — gives multiplication, division, and remainder the same rank, higher than addition and subtraction, and evaluates same-rank operators from left to right. Parentheses override that ranking. This modulo order of operations calculator accepts a single expression string, parses it with a deterministic recursive-descent grammar, and returns the numeric result.
What + − × ÷ % mean and how precedence actually binds
Order of operations is a reading convention, not a physical law. Without it, the string 2 + 3 * 4 % 5 could mean several different numbers depending on whether you add first, multiply first, or take remainder first.
The convention used in school algebra, programming languages such as C, Java, JavaScript, and Python, and this calculator is the same: parentheses group first; unary plus and minus attach next; then multiplication, division, and modulo share one rank and associate left to right; then addition and subtraction share a lower rank and also associate left to right. There is no extra rank that puts modulo above multiplication.
So 3 * 4 % 5 is (3 * 4) % 5, which is twelve remainder five, which is two, and 2 + that product-remainder is four — not 2 + 3 first, and not 4 % 5 first. Likewise 8 % 3 * 4 is (8 % 3) * 4, which is two times four, which is eight. Division is ordinary real division, not integer truncation: 7 / 2 is 3.5.
Parentheses change the walk: (2 + 3) * 4 % 5 is twenty remainder five, which is zero. This calculator implements that walk exactly. It does not invent exponentiation, factorial, implicit multiplication such as 2(3+4), or named functions.
A missing operand, an unmatched parenthesis, a stray letter, or a trailing operator is a malformed expression, not a guess.
What you can type, and what gets refused
The value is an arithmetic string of decimal numbers, the five operators plus, minus, asterisk, slash, and percent, parentheses, optional unary signs, and whitespace. Scientific notation such as 1e-3 is accepted as a number token. After trim, the string may contain at most 500 characters; that limit is declared and enforced so a pasted wall of operators cannot exhaust the isolate.
Division by a remainder-zero divisor fails with the message Division by zero; a zero modulus fails with Modulo by zero. Those failures are not billed. On success the body echoes the trimmed expression, returns result as a finite number rounded to twelve decimal places so goldens compare byte for byte across runtimes, and includes a formula string that restates the same-rank left-to-right rule.
Example: expression 2 + 3 * 4 % 5 yields result 4 because multiplication and modulo bind before addition.
Where a modulo order of operations calculator earns its keep
Classrooms and tutoring platforms use a modulo order of operations calculator so learners can check mixed expressions that include remainder without flipping PEMDAS by treating percent as weaker than times. Exam-prep generators and learning-management graders need a deterministic oracle that marks left-to-right same-rank walks correctly and that rejects division by zero instead of returning Infinity that a buggy grader might treat as success.
Programming courses that introduce % next to * and / can pin the same contract the language will use later, rather than a handheld calculator that has no remainder key or that evaluates strictly left to right. Failed validation does not consume balance. Keep expressions inside the published character limit, pin the rounded result in tests, and you get a reproducible mixed-arithmetic answer for worksheets, LMS plugins, and edge workers without standing up an expression service of your own.
What you can do with it
Classroom PEMDAS checks with remainder
Let students submit mixed + − × ÷ % expressions and verify the left-to-right same-rank walk against the textbook method, including parentheses.
Exam and LMS auto-grading
Mark order-of-operations items with a deterministic oracle that rejects division by zero and never evaluates left-to-right across all five operators.
Scripts that mix remainder with offsets
Evaluate wrap-around indexes and stride remainders that also add or scale, without importing a computer-algebra library.
FAQ
How is 2 + 3 * 4 % 5 evaluated?
Multiplication and modulo share precedence and bind left to right, above addition. So the walk is (3 * 4) % 5 first: 12 % 5 is 2, then 2 + 2 is 4.
Does modulo have the same precedence as multiplication?
Yes. *, /, and % share one rank and associate left to right. 8 % 3 * 4 is (8 % 3) * 4 = 8, not 8 % 12.
What happens on division by zero?
A zero modulus fails as Modulo by zero. Neither case is billed.
Are parentheses and unary minus supported?
Yes. Parentheses override rank, and unary plus or minus attaches tighter than * / %. The calculator does not accept exponentiation, factorial, or implicit multiplication.
Does division round to a whole number?
No. Division is ordinary division, so 7 / 2 gives 3.5, not 3. Only the percent sign takes a remainder, and it shares its rank with multiplication and division.
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/modulo-order-of-operations \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"expression":"2 + 3 * 4 % 5"}'const res = await fetch("https://api.kit.forhosting.com/math/modulo-order-of-operations", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"expression": "2 + 3 * 4 % 5"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/modulo-order-of-operations",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"expression": "2 + 3 * 4 % 5"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/modulo-order-of-operations", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"expression":"2 + 3 * 4 % 5"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"expression":"2 + 3 * 4 % 5"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/modulo-order-of-operations", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"expression": "2 + 3 * 4 % 5"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.modulo_order_of_operations",
"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_chars | 500 |
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
Division by zero and malformed input fail with invalid_input and are not billed.
What + − × ÷ % mean and how precedence actually binds
Remainder follows the JavaScript and IEEE remainder rule: the result has the sign of the dividend.
Input contract, response shape, limits, and errors
POST a JSON object with one required field, expression — also accepted as text or expr. Empty strings, omitted fields, non-string junk, unexpected characters, unmatched parentheses, and leftover tokens after a complete parse fail with invalid_input naming expression. Pair the number with your own step list if you need a classroom walkthrough; this endpoint evaluates the expression and does not emit a line-by-line rewrite beyond the formula field. Successful API calls use the published $0.002 base price.
Where a modulo order of operations calculator earns its keep
Data-cleaning scripts that compute bucket indexes, wrap-around clocks, or stride remainders mixed with offsets can call a tiny parse API instead of pulling a full computer-algebra system.
Technical questions
What does the modulo order of operations calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.