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.
Endpoint tested and returned HTTP 200 on 21 Aug 2026
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 21 Aug 2026, 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 'https://newton.vercel.app/api/v2/derive/x%5E2'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);import requests
res = requests.get("https://newton.vercel.app/api/v2/derive/x%5E2", timeout=20)
res.raise_for_status()
print(res.json()){
"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.
Alternatives to Newton Math API
If Newton Math API does not fit, these science & space apis cover similar ground. Every one was called before publishing, and each links to its own reference page with a working curl command and the response it returned.
| API | What it does | Auth | CORS | Last verified |
|---|---|---|---|---|
| NASA APOD | Free NASA Astronomy Picture of the Day API. Daily space images with expert explanations, HD URLs and archive access back to 1995. Tested curl example. | Key | Yes | 19 Aug 2026 |
| Open Notify ISS | Free API returning the International Space Station's live latitude and longitude. No key, updates in real time. Tested curl example and live JSON response. | No key | Yes | 19 Aug 2026 |
| USGS Earthquake | Free USGS earthquake API with no key: live global seismic events as GeoJSON, filterable by magnitude, time and location. Tested curl example and live response. | No key | Yes | 19 Aug 2026 |
| Launch Library 2 | Free rocket launch API with no key: upcoming and past launches from every space agency, with rockets, missions, pads and live stream links. Tested example. | No key | Yes | 19 Aug 2026 |
| NIH RePORTER | Free NIH RePORTER API with no key: search every NIH-funded research project by year, institution, investigator, funding amount and topic. POST-based query API. Tested example included. | No key | No | 21 Aug 2026 |
| NOAA Space Weather Prediction Center | Free NOAA Space Weather Prediction Center API with no key: geomagnetic storm alerts, solar flare warnings, Kp index, solar wind and aurora forecasts as JSON products. | No key | Yes | 21 Aug 2026 |
Newton Math API is an independent third-party service and is not affiliated with ByteTools or ByteVancer. Details on this page were verified on 21 Aug 2026; always check the official documentation before relying on this API in production, as terms and limits can change.