# Bragg Diffraction API > X-ray crystallography maths as an API, computed locally and deterministically. The angle endpoint applies Bragg’s law, n·λ = 2·d·sinθ, to give the diffraction angle θ and the experimentally plotted 2θ from a crystal’s inter-planar spacing and the X-ray wavelength, defaulting to the common Cu Kα source at 0.15406 nm and reporting the highest observable order ⌊2d/λ⌋ — a 0.2 nm plane spacing diffracts Cu Kα to θ ≈ 22.65°, a 2θ peak near 45.3°. The spacing endpoint inverts the law, d = n·λ/(2·sinθ), reading the lattice spacing straight off a measured XRD peak — the everyday job of indexing a diffraction pattern, so a 2θ of 31.77° for table salt gives the 0.2814 nm (200) spacing. The wavelength endpoint solves λ = 2·d·sinθ/n to identify or calibrate the source. Lengths are entered in nanometres or ångström and angles in degrees, and any diffraction order n is supported. Everything is computed locally and deterministically, so it is instant and private. Ideal for materials-science, crystallography, mineralogy, XRD, semiconductor and solid-state-physics app developers, lattice-spacing and pattern-indexing tools, and laboratory software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is reflection-geometry Bragg diffraction with the 2d factor; for optical double-slit and grating diffraction use a wave-optics diffraction API. ## Authentication All requests require your oanor API key in the `x-oanor-key` header. Get one at https://www.oanor.com/developer/keys. ```bash curl -H "x-oanor-key: oanor_live_…" "https://api.oanor.com/bragg-api/..." ``` ## Pricing - **Free** (Free) — 3,500 calls/Mo, 2 req/s - **Starter** ($6/Mo) — 33,000 calls/Mo, 6 req/s - **Pro** ($19/Mo) — 168,000 calls/Mo, 15 req/s - **Mega** ($59/Mo) — 1,020,000 calls/Mo, 40 req/s ## Endpoints ### Bragg #### `GET /v1/angle` — Bragg angle from spacing **Parameters:** - `spacing_nm` (query, optional, string) — Inter-planar spacing d (nm) Example: `0.2` - `spacing_angstrom` (query, optional, string) — d-spacing (ångström) - `wavelength_nm` (query, optional, string) — Wavelength (nm, default Cu Kα 0.15406) - `order` (query, optional, string) — Diffraction order n Example: `1` **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/bragg-api/v1/angle?spacing_nm=0.2&order=1" ``` **Response:** ```json { "data": { "note": "Bragg's law n·λ = 2·d·sinθ. θ is the glancing angle from the planes; XRD patterns are plotted against 2θ. Default wavelength is Cu Kα = 0.15406 nm.", "inputs": { "order": 1, "spacing_nm": 0.2, "wavelength_nm": 0.15406 }, "max_order": 2, "theta_deg": 22.653053, "two_theta_deg": 45.306106 }, "meta": { "timestamp": "2026-06-05T19:50:23.738Z", "request_id": "4c0f0c3e-e224-4083-97e6-35875f0ef856" }, "status": "ok", "message": "Bragg angle", "success": true } ``` #### `GET /v1/spacing` — d-spacing from angle **Parameters:** - `two_theta` (query, optional, string) — Measured 2θ (deg) Example: `45.31` - `theta` (query, optional, string) — Or θ (deg) - `wavelength_nm` (query, optional, string) — Wavelength (nm, default Cu Kα) - `order` (query, optional, string) — Diffraction order n Example: `1` **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/bragg-api/v1/spacing?two_theta=45.31&order=1" ``` **Response:** ```json { "data": { "note": "Inter-planar spacing d = n·λ/(2·sinθ). This is how a crystal's lattice spacing is read off an XRD peak.", "inputs": { "order": 1, "theta_deg": 22.655, "wavelength_nm": 0.15406 }, "spacing_nm": 0.19998371, "spacing_angstrom": 1.999837 }, "meta": { "timestamp": "2026-06-05T19:50:23.819Z", "request_id": "36c08afd-efaf-4aef-8304-2ec7eef4eef5" }, "status": "ok", "message": "d-spacing", "success": true } ``` #### `GET /v1/wavelength` — Wavelength from spacing & angle **Parameters:** - `spacing_nm` (query, optional, string) — d-spacing (nm) Example: `0.2` - `spacing_angstrom` (query, optional, string) — d-spacing (ångström) - `two_theta` (query, optional, string) — 2θ (deg) Example: `45.31` - `theta` (query, optional, string) — Or θ (deg) - `order` (query, optional, string) — Order n Example: `1` **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/bragg-api/v1/wavelength?spacing_nm=0.2&two_theta=45.31&order=1" ``` **Response:** ```json { "data": { "note": "Wavelength λ = 2·d·sinθ/n — used to calibrate or identify the X-ray source from a known reflection.", "inputs": { "order": 1, "theta_deg": 22.655, "spacing_nm": 0.2 }, "wavelength_nm": 0.15407255, "wavelength_angstrom": 1.540725 }, "meta": { "timestamp": "2026-06-05T19:50:23.900Z", "request_id": "61d2dadc-7021-4c5e-9e3a-2f501f36f036" }, "status": "ok", "message": "Wavelength", "success": true } ``` ### Meta #### `GET /v1/meta` — Spec **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/bragg-api/v1/meta" ``` **Response:** ```json { "data": { "notes": "Lengths in nm or ångström, angles in degrees. Reflection (Bragg) geometry with the 2d factor; for optical double-slit/grating diffraction use a wave-optics diffraction API.", "service": "bragg-api", "constants": { "cu_k_alpha_nm": 0.15406 }, "endpoints": { "GET /v1/meta": "This document.", "GET /v1/angle": "Bragg angle θ and 2θ from d-spacing and wavelength.", "GET /v1/spacing": "Inter-planar spacing from the Bragg angle.", "GET /v1/wavelength": "Wavelength from spacing and angle." }, "description": "Bragg's law for X-ray crystallography: diffraction angle, inter-planar d-spacing and wavelength from n·λ = 2·d·sinθ." }, "meta": { "timestamp": "2026-06-05T19:50:23.973Z", "request_id": "b6ed4da5-044e-46d4-b43a-c553f33c0581" }, "status": "ok", "message": "Meta", "success": true } ``` --- Marketplace page: https://www.oanor.com/api/bragg-api OpenAPI spec: https://www.oanor.com/api/bragg-api/openapi.json