Matrix transpose calculator
Flip a matrix over its main diagonal in one step: rows 1 2 3 and 4 5 6 become columns, giving a 3×2 result with rows 1 4, 2 5 and 3 6. Handy for symmetry checks and data tables. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Runs in your browser. Free, unlimited — your data never leaves this page.
The matrix transpose is one of the simplest and most useful operations in linear algebra: turn every row into a column and every column into a row so that an m-by-n array becomes n-by-m. Students meet A transpose when proving (AB) transpose equals B transpose times A transpose, when writing least-squares normal equations, and when checking that a matrix is symmetric. Engineers use the same swap for covariance layouts, image channel reordering, and adapting data that arrived row-major into column-major consumers. This capability takes one rectangular numeric matrix, validates that every row has the same length, and returns the transposed grid with both original and result dimensions.
What the matrix transpose means and why shape matters
Write a matrix A with m rows and n columns. Its transpose A^T is the n-by-m matrix defined by the rule that the entry in row j and column i of A^T equals the entry in row i and column j of A. In plain language, you flip the array over its main diagonal: the first row of A becomes the first column of A^T, the second row becomes the second column, and so on.
Square matrices stay square; a two-by-three matrix becomes three-by-two. Symmetric matrices satisfy A^T equals A, so the tool is also a quick sanity check when you expect symmetry. The definition only makes sense for rectangular arrays: every row must have exactly n entries.
If row zero has three numbers and row one has two, there is no agreed elementary transpose, because column counts disagree and you cannot place a consistent n-by-m result without guessing missing cells. The operation is linear in the number of entries: one read and one write per cell, no multiplications and no iterative solvers. Understanding transpose early pays off later for adjoints, covariance forms, and the fact that left-multiplying by A^T is the dual of right-multiplying by A in many least-squares setups.
Practical use, pricing, limits, and delivery
Use the browser tool when you want an immediate transpose while checking homework, preparing a lecture slide, flipping a small data table, or verifying that a covariance-style layout matches a column-vector convention without installing a computer-algebra system. There is no language model, no external linear-algebra 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 matrix always yields the same transpose grid.
Prefer this tool for pure shape swap; for matrix products, determinants, inverses, or entrywise addition, use a different capability. Keep entries within ordinary floating-range magnitudes so intermediate overflow is not a concern; for classroom integers and typical engineering scales the solver is exact within double precision. 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 A^T for rectangular matrices, including clear failures when rows have unequal length, without a local CAS install.
Data layout and pipeline reshape
Scripts that need row-major data as column-major (or the reverse) call a deterministic transpose oracle instead of reimplementing index swaps in every language.
Teaching transpose before products
Lesson pages can show 2×3 becoming 3×2 so learners connect the definition to later identities such as (AB)^T = B^T A^T.
FAQ
What happens if the matrix rows have unequal length?
The error message states that rows have unequal length and names the column counts that disagree.
Does transpose work for non-square matrices?
Yes. An m×n matrix becomes n×m. Square matrices stay square; a 2×3 input becomes 3×2.
Is the matrix transpose calculator free?
The browser tool runs free on your device.
Does this multiply or invert matrices?
No. This capacity only returns the transpose by swapping rows and columns. Products, inverses, and determinants need different capabilities.
How do I transpose a 2×3 matrix?
Turn each row into a column. The matrix with rows 1 2 3 and 4 5 6 becomes a 3×2 matrix with rows 1 4, 2 5 and 3 6; the first row of the original is now the first column.
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/matrix-transpose \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"matrix":[[1,2,3],[4,5,6]]}'const res = await fetch("https://api.kit.forhosting.com/algebra/matrix-transpose", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"matrix": [
[
1,
2,
3
],
[
4,
5,
6
]
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/algebra/matrix-transpose",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"matrix": [
[
1,
2,
3
],
[
4,
5,
6
]
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/algebra/matrix-transpose", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"matrix":[[1,2,3],[4,5,6]]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"matrix":[[1,2,3],[4,5,6]]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/algebra/matrix-transpose", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"matrix": [
[
1,
2,
3
],
[
4,
5,
6
]
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "algebra.matrix_transpose",
"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
Jagged inputs, empty matrices, and non-numeric cells fail with invalid_input instead of inventing padding.
What the matrix transpose means and why shape matters
This calculator refuses that case with invalid_input and a message that names the unequal lengths, so homework checkers and API clients never silently accept a jagged matrix.
How to call the transpose calculator and read the response
Near-zero float dust is cleaned so goldens and demos stay stable while ordinary non-integer reals keep full double precision. Send a JSON body with the required field matrix: a non-empty array of rows, each row a non-empty array of finite numbers, all rows sharing the same length. You may also use aliases a, A, input, or m, and you may pass the matrix as a JSON string of the same nested structure when a form field only accepts text. The engine rejects missing fields, empty matrices, jagged rows, NaN or Infinity cells, and non-numeric strings with invalid_input, and those failures are not charged. On success the response includes result (the n-by-m transpose), rows and cols for the result dimensions, original_rows and original_cols for the input shape, and matrix as the parsed numeric copy of the input. Wire the endpoint into scripts that already speak JSON and need a stable contract rather than reimplementing shape checks and index swaps in every language you support across homework platforms, notebooks, and light production helpers.
Practical use, pricing, limits, and delivery
Each successful request is one billable item at $0.002; failed validation and unequal-length rows do not consume balance.
Technical questions
How do I transpose a matrix with this API?
Send JSON with matrix as an array of equal-length numeric rows. The response returns result (A^T), rows, cols, original_rows, and original_cols.