Newton Math API

Free Newton maths API with no key: differentiate, integrate, simplify, factor, find zeroes and more from a plain URL. No account, tiny JSON responses, CORS enabled.

No API key requiredCORS enabledHTTPSFree tier

Endpoint tested and returned HTTP 200 on 2026-08-21

What is the Newton Math API?

The Newton API is a free, key-free service that performs symbolic and numeric mathematics from a URL. Operations include differentiation, integration, simplification, factorisation, finding zeroes and roots, and trigonometric evaluation, each returning a small JSON object with the result as a string.

Newton exists to make symbolic maths available to a front-end with one fetch. The URL is the expression: `/api/v2/derive/x%5E2` returns `2 x`. There is no key, no body and no session, which makes it a natural fit for teaching tools, calculator widgets and anything where shipping a computer algebra system to the browser would be absurd overkill.

The constraints follow from that simplicity. Expressions go in the URL path, so `^` must be encoded as `%5E` and `/` becomes a problem — division needs the alternative parenthesised forms the docs describe. Results come back as display strings like `2 x`, not as parse trees, so you get something to show a user rather than something to compute with. And this is a small community-run project on free hosting: it handles ordinary school and undergraduate expressions well, has no service level, and will not stand in for SymPy or Mathematica on anything demanding.

Quick facts

Base URL: https://newton.vercel.app/api/v2
Authentication: No API key or account. Newton is an open-source community project deployed on free serverless hosting, with no uptime guarantee.
Rate limit: None published. Responses are tiny; cache repeated expressions rather than re-requesting them.
Pricing: Free, with no registration.
CORS: Enabled — callable directly from browser JavaScript
Official docs: Read the docs

How to use the Newton Math API

Every request below was executed against the live API on 2026-08-21, and the response shown is the real body it returned — not an illustration.

1. Differentiate x squared

GET https://newton.vercel.app/api/v2/derive/x%5E2

curl

curl 'https://newton.vercel.app/api/v2/derive/x%5E2'

JavaScript (fetch)

const res = await fetch("https://newton.vercel.app/api/v2/derive/x%5E2");
if (!res.ok) throw new Error(`Request failed: ${res.status}`);
const data = await res.json();
console.log(data);

Python (requests)

import requests

res = requests.get("https://newton.vercel.app/api/v2/derive/x%5E2", timeout=20)
res.raise_for_status()
print(res.json())

Response — HTTP 200

{
  "operation": "derive",
  "expression": "x^2",
  "result": "2 x"
}

Parameters

Parameter	Type	Required	Description
`operation`	path segment	Required	The operation: `derive`, `integrate`, `simplify`, `factor`, `zeroes`, `tangent`, `area`, `cos`, `sin`, `tan`, `log` and others. `derive`
`expression`	path segment	Required	The mathematical expression, URL-encoded. `^` becomes `%5E`, spaces `%20`. `x%5E2`
`(operation) zeroes`	path	Optional	Find the roots of an expression. `zeroes/x%5E2-4`
`(operation) tangent`	path	Optional	Tangent line at a point, expressed as `point\|expression`. `tangent/2%7Cx%5E3`
`(operation) area`	path	Optional	Definite integral between bounds, expressed as `lower:upper\|expression`. `area/2:4%7Cx%5E3`

Response fields

operationstring: Echoes the operation performed, useful for logging.
expressionstring: The expression as the server parsed it. Compare it against what you sent to catch encoding mistakes.
resultstring: The answer as a display string, for example `2 x`. It is formatted for humans, not for re-parsing.

What you can build with the Newton Math API

Add a derivative or integral step to an educational web app
Check homework answers in a study tool
Show a worked simplification in a maths tutorial site
Compute roots for a graphing widget without a client-side CAS
Prototype a maths feature before committing to a heavier library

Common errors and how to fix them

Wrong result or a parse failure

The expression was not URL-encoded.

Fix: `^` must be `%5E`, `|` must be `%7C` and spaces `%20`. Always compare the returned `expression` against what you intended.

Division breaks the path

A forward slash in the expression is read as a path separator.

Fix: Use the parenthesised division forms documented in the project README rather than a literal `/`.

Unsupported expression

Newton handles a limited grammar.

Fix: It is aimed at school and early-undergraduate expressions. Multivariable calculus, matrices and special functions are out of scope.

Service unavailable

Free serverless hosting with cold starts.

Fix: Retry once after a short pause, cache results, and have a fallback for anything user-facing.

Newton Math API — frequently asked questions

Is the Newton API free?

Yes, free with no key, no account and no published rate limit. It is an open-source community project rather than a commercial service, so treat availability as best-effort.

How do I encode an expression in the URL?

Percent-encode everything: `^` as `%5E`, `|` as `%7C`, spaces as `%20`. Division is the awkward case because a literal slash is read as a path separator — use the parenthesised forms from the documentation instead.

Can it handle calculus beyond single-variable?

No. Newton covers derivatives, integrals, simplification, factorisation and roots for single-variable expressions. Multivariable calculus, linear algebra and special functions need a real computer algebra system.

Is the result machine-readable?

Only loosely. `result` is a display string like `2 x`, formatted for a human reader rather than as a parse tree. If you need to compute with the answer you will have to parse that string yourself.

Tools that pair with this API

Derivative Calculator

Differentiate any function of x symbolically. Get f′(x) and f″(x) in simplified form, their value at a point, and a numerical check of the result.

Definite Integral Calculator

Evaluate a definite integral numerically with adaptive Simpson's rule. See the value, the error estimate and a shaded plot of the area under the curve.

Online Graphing Calculator

Plot up to three y = f(x) functions on one graph. Supports sin, cos, tan, log, sqrt, powers and more, with adjustable window and PNG export.

Newton Math API is an independent third-party service and is not affiliated with ByteTools or ByteVancer. Details on this page were verified on 2026-08-21; always check the official documentation before relying on this API in production, as terms and limits can change.