# Kinematics SUVAT API > Kinematics (SUVAT) maths as an API, computed locally and deterministically. The solve endpoint takes any three of the five constant-acceleration variables — initial velocity u, final velocity v, acceleration a, time t and displacement s — and returns the other two, picking the right equation among v = u + at, s = ut + ½at², s = ½(u+v)t, v² = u² + 2as and s = vt − ½at² automatically. The freefall endpoint computes the fall time, distance and impact velocity for a vertical drop from a height (or over a given time), with an adjustable gravity and optional initial velocity, no air resistance. The stopping endpoint computes reaction, braking and total stopping distance and braking time for a vehicle from its speed and either a deceleration or a road-surface friction coefficient (a = μ·g), with an optional reaction time. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics-education, engineering, simulation, automotive and game-development app developers, motion and braking-distance tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is linear-motion SUVAT; for projectile launch and trajectory use a projectile API and for momentum and collisions a momentum 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/kinematics-api/..." ``` ## Pricing - **Free** (Free) — 3,000 calls/Mo, 2 req/s - **Starter** ($5/Mo) — 40,000 calls/Mo, 5 req/s - **Pro** ($15/Mo) — 250,000 calls/Mo, 15 req/s - **Mega** ($49/Mo) — 2,000,000 calls/Mo, 50 req/s ## Endpoints ### Kinematics #### `GET /v1/freefall` — Free fall **Parameters:** - `height` (query, optional, string) — Drop height (m) Example: `44.1` - `time` (query, optional, string) — Or fall time (s) - `initial_velocity` (query, optional, string) — Initial downward velocity (m/s) Example: `0` - `gravity` (query, optional, string) — Gravity (m/s², default 9.80665) **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/kinematics-api/v1/freefall?height=44.1&initial_velocity=0" ``` **Response:** ```json { "data": { "note": "Free fall, no air resistance: h = u·t + ½g·t², impact velocity = u + g·t. Default g = 9.80665 m/s².", "inputs": { "time_s": null, "height_m": 44.1, "gravity_ms2": 9.80665, "initial_velocity_ms": 0 }, "fall_time_s": 2.998983, "fall_distance_m": 44.1, "impact_velocity_ms": 29.409973, "impact_velocity_kmh": 105.875904 }, "meta": { "timestamp": "2026-06-04T18:38:07.560Z", "request_id": "6e3252b7-4754-4014-b23a-3912abc8a193" }, "status": "ok", "message": "Free fall", "success": true } ``` #### `GET /v1/solve` — SUVAT solver **Parameters:** - `u` (query, optional, string) — Initial velocity (m/s) Example: `0` - `v` (query, optional, string) — Final velocity (m/s) Example: `30` - `a` (query, optional, string) — Acceleration (m/s²) Example: `3` - `t` (query, optional, string) — Time (s) - `s` (query, optional, string) — Displacement (m) **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/kinematics-api/v1/solve?u=0&v=30&a=3" ``` **Response:** ```json { "data": { "a": 3, "s": 150, "t": 10, "u": 0, "v": 30, "note": "SUVAT for constant acceleration. Square-root cases take the positive root; supply a sign in the knowns for the other branch.", "inputs": { "given": [ "u", "v", "a" ] } }, "meta": { "timestamp": "2026-06-04T18:38:07.659Z", "request_id": "51185aee-298a-4bf3-a12d-01be81bc84b0" }, "status": "ok", "message": "SUVAT solve", "success": true } ``` #### `GET /v1/stopping` — Stopping distance **Parameters:** - `speed` (query, optional, string) — Speed (m/s) Example: `30` - `speed_kmh` (query, optional, string) — Or speed (km/h) - `deceleration` (query, optional, string) — Deceleration (m/s²) Example: `6` - `friction` (query, optional, string) — Or friction coefficient μ - `reaction_time` (query, optional, string) — Reaction time (s) Example: `1` **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/kinematics-api/v1/stopping?speed=30&deceleration=6&reaction_time=1" ``` **Response:** ```json { "data": { "note": "Braking: distance = v²/(2a), time = v/a. With a friction coefficient, a = μ·g. Reaction distance = v·reaction_time.", "inputs": { "speed_ms": 30, "reaction_time_s": 1, "deceleration_ms2": 6 }, "braking_time_s": 5, "braking_distance_m": 75, "reaction_distance_m": 30, "total_stopping_distance_m": 105 }, "meta": { "timestamp": "2026-06-04T18:38:07.745Z", "request_id": "384ca825-aced-49c9-aef4-dc96d57b9d36" }, "status": "ok", "message": "Stopping distance", "success": true } ``` ### Meta #### `GET /v1/meta` — Spec **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/kinematics-api/v1/meta" ``` **Response:** ```json { "data": { "notes": "SI units: velocity m/s, acceleration m/s², time s, displacement m. Constant acceleration only. Default gravity 9.80665 m/s².", "service": "kinematics-api", "formulae": { "eq1": "v = u + at", "eq2": "s = ut + ½at²", "eq3": "s = ½(u+v)t", "eq4": "v² = u² + 2as", "eq5": "s = vt − ½at²" }, "endpoints": { "GET /v1/meta": "This document.", "GET /v1/solve": "SUVAT solver — give any three of u, v, a, t, s and get all five.", "GET /v1/freefall": "Free-fall time, distance and impact velocity from a height or time.", "GET /v1/stopping": "Reaction, braking and total stopping distance and braking time." }, "description": "Kinematics (SUVAT) calculator: solve constant-acceleration motion from any three of u, v, a, t, s; vertical free fall from a height; and braking distance/time from a speed and deceleration or friction." }, "meta": { "timestamp": "2026-06-04T18:38:07.844Z", "request_id": "0cd1dc2e-da39-429b-a4c7-6399cc8b8b46" }, "status": "ok", "message": "Meta", "success": true } ``` --- Marketplace page: https://www.oanor.com/api/kinematics-api OpenAPI spec: https://www.oanor.com/api/kinematics-api/openapi.json