> ## Documentation Index
> Fetch the complete documentation index at: https://docs.iotools.cloud/llms.txt
> Use this file to discover all available pages before exploring further.
# Center of Gravity Calculator
> Calculate the weighted center of gravity (centroid) of a set of point masses. Enter each point as X, Y, Mass (label optional, negative mass for a cutout) — get the total mass, the CG coordinates, a per-point contribution breakdown, and a plotted diagram.
[Try Center of Gravity Calculator in your browser →](https://iotools.cloud/tool/center-of-gravity-calculator/)
## OpenAPI
````yaml https://api.iotools.cloud/v1/openapi post /v1/tool/center-of-gravity-calculator
openapi: 3.1.0
info:
title: iotools.cloud API
version: 1.0.0
description: >-
Run any iotools.cloud tool over HTTP.
Authenticate with `Authorization: Bearer iot_live_…`.
**Only `POST /v1/tool/{slug}` costs credits.** Every GET here — the catalog,
a tool's schema, your balance — is free. A tool call is charged its own
weight or your plan's per-call minimum, whichever is larger;
`x-iotools-credit-cost` on each operation is quoted at the free-tier
minimum, and `GET /v1/tools/list` returns the exact figure for your key.
`GET /v1/me/credits` reports what you have left, and `GET /v1/me/usage`
reports what it went on.
Failures are RFC 9457 problem documents — branch on `code`.
servers:
- url: https://api.iotools.cloud
description: Production
security:
- bearerAuth: []
tags:
- name: Catalog
description: Find a tool and read its contract. Free.
- name: Converters
description: >-
Convert between formats, encodings, and units — Base64, CSV and JSON,
timestamps, and more. Fast, free, and processed right in your browser.
- name: Formatters
description: >-
Format, beautify, minify, and validate code and data — JSON, HTML, CSS,
SQL, and regex. Clean up messy input in one click, with nothing to upload.
- name: Generators
description: >-
Generate exactly what you need and on demand — passwords, UUIDs, QR codes,
hashes, random numbers, and more. Secure, instant, and free.
- name: Calculators
description: >-
Crunch the numbers fast — from everyday math to specialized conversions
and unit work. Free online calculators that run entirely in your browser.
- name: Editors
description: >-
Edit and transform text, code, and images with quick, focused editors that
run entirely in your browser — nothing to install, and no sign-up needed.
- name: Utilities
description: >-
Everyday developer and web utilities — DNS and IP lookups, redirect and
certificate checkers, and other quick diagnostics. Free and
privacy-friendly.
- name: Account
description: Your key's allowance, limits and usage history.
paths:
/v1/tool/center-of-gravity-calculator:
post:
tags:
- Calculators
summary: Center of Gravity Calculator
description: >-
Calculate the weighted center of gravity (centroid) of a set of point
masses. Enter each point as X, Y, Mass (label optional, negative mass
for a cutout) — get the total mass, the CG coordinates, a per-point
contribution breakdown, and a plotted diagram.
[Try Center of Gravity Calculator in your browser
→](https://iotools.cloud/tool/center-of-gravity-calculator/)
operationId: run_center_of_gravity_calculator
requestBody:
required: false
content:
application/json:
schema:
type: object
properties:
points:
type: string
description: Points (Label, X, Y, Mass)
required: []
examples:
four_point_bracket_assembly:
summary: Four-point bracket assembly
value:
points: |-
Bracket, 0, 0, 1
Flange, 1.2, 0.8, 8
Boss, 2.4, 0.2, 10
Washer, 1.1, 1.7, 6
plate_with_a_cutout_negative_mass:
summary: Plate with a cutout (negative mass)
value:
points: |-
Plate, 0, 0, 100
Hole, 3, 2, -20
responses:
'200':
description: Tool output
content:
application/json:
examples:
four_point_bracket_assembly:
summary: Four-point bracket assembly
value:
tool: center-of-gravity-calculator
tool_version: 1.0.1
outputs:
summary:
- metric: Point Count
value: '4'
- metric: Total Mass
value: '25'
- metric: Center of Gravity X
value: '1.608'
- metric: Center of Gravity Y
value: '0.744'
breakdown:
- point: Bracket
x: '0'
'y': '0'
mass: '1'
of-total-mass: 4%
distance-from-cg: '1.77178'
- point: Flange
x: '1.2'
'y': '0.8'
mass: '8'
of-total-mass: 32%
distance-from-cg: '0.411825'
- point: Boss
x: '2.4'
'y': '0.2'
mass: '10'
of-total-mass: 40%
distance-from-cg: '0.960833'
- point: Washer
x: '1.1'
'y': '1.7'
mass: '6'
of-total-mass: 24%
distance-from-cg: '1.08259'
svg: >-
credits_used: 3
credits_remaining: null
plate_with_a_cutout_negative_mass:
summary: Plate with a cutout (negative mass)
value:
tool: center-of-gravity-calculator
tool_version: 1.0.1
outputs:
summary:
- metric: Point Count
value: '2'
- metric: Total Mass
value: '80'
- metric: Center of Gravity X
value: '-0.75'
- metric: Center of Gravity Y
value: '-0.5'
breakdown:
- point: Plate
x: '0'
'y': '0'
mass: '100'
of-total-mass: 125%
distance-from-cg: '0.901388'
- point: Hole
x: '3'
'y': '2'
mass: '-20'
of-total-mass: '-25%'
distance-from-cg: '4.50694'
svg: >-
credits_used: 3
credits_remaining: null
schema:
type: object
required:
- tool
- tool_version
- outputs
- credits_used
- credits_remaining
properties:
outputs:
type: object
properties:
summary:
type: array
items:
type: object
properties:
metric:
type: string
description: Metric
value:
type: string
description: Value
x-iotools-columns:
- metric
- value
svg:
type: string
description: Diagram (SVG source)
breakdown:
type: array
items:
type: object
properties:
point:
type: string
description: Point
x:
type: string
description: X
'y':
type: string
description: 'Y'
mass:
type: string
description: Mass
of-total-mass:
type: string
description: '% of Total Mass'
distance-from-cg:
type: string
description: Distance from CG
x-iotools-columns:
- point
- x
- 'y'
- mass
- of-total-mass
- distance-from-cg
tool:
type: string
description: The tool's slug, echoing the {slug} in the request path.
tool_version:
type: string
description: Output-contract version for this tool.
credits_used:
type: integer
description: >-
Credits this call consumed, after any settlement refund. 0
when metering is disabled.
credits_remaining:
type:
- integer
- 'null'
description: >-
Credits left in the current monthly allowance, or null
when metering is disabled.
request_id:
type: string
description: Correlation id, also sent as x-request-id.
'400':
$ref: '#/components/responses/ValidationError'
'401':
$ref: '#/components/responses/Unauthorized'
'402':
$ref: '#/components/responses/InsufficientCredits'
'403':
$ref: '#/components/responses/ToolNotAllowed'
'404':
$ref: '#/components/responses/ToolNotFound'
'413':
$ref: '#/components/responses/PayloadTooLarge'
'429':
$ref: '#/components/responses/RateLimited'
'500':
$ref: '#/components/responses/ToolFailed'
'503':
$ref: '#/components/responses/ToolDisabled'
security:
- bearerAuth: []
components:
responses:
ValidationError:
description: Invalid request.
content:
application/problem+json:
schema:
type: object
description: >-
RFC 9457 problem document, served as application/problem+json.
Branch on `code`; `title` is human prose and may be reworded
without notice. Some failures add extension members — `fields` on
validation errors, `retry_after` on 429s,
`credits_used`/`credits_remaining` on billing-adjacent failures —
documented on the responses that carry them.
required:
- type
- title
- status
- code
properties:
type:
type: string
format: uri
description: Stable documentation URI for this failure.
examples:
- https://iotools.cloud/docs/errors/validation_error
title:
type: string
description: Short human-readable summary of the failure.
examples:
- Invalid request
status:
type: integer
description: HTTP status code, matching the response's own status.
code:
type: string
description: >-
Stable machine-readable error code — branch on this, not
`title`.
enum:
- validation_error
detail:
type: string
description: Human explanation of this occurrence.
request_id:
type: string
description: Correlation id, also sent as x-request-id.
fields:
type:
- object
- string
additionalProperties:
type: string
description: >-
What failed: a map of field name → message. Absent when the
body itself is malformed; a single string when the failure
isn't tied to one field.
example:
type: https://iotools.cloud/docs/errors/validation_error
title: Invalid request
status: 400
code: validation_error
detail: One or more inputs are invalid — see `fields`.
request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
fields:
inputString: Required
Unauthorized:
description: Missing or invalid API key.
content:
application/problem+json:
schema:
type: object
description: >-
RFC 9457 problem document, served as application/problem+json.
Branch on `code`; `title` is human prose and may be reworded
without notice. Some failures add extension members — `fields` on
validation errors, `retry_after` on 429s,
`credits_used`/`credits_remaining` on billing-adjacent failures —
documented on the responses that carry them.
required:
- type
- title
- status
- code
properties:
type:
type: string
format: uri
description: Stable documentation URI for this failure.
examples:
- https://iotools.cloud/docs/errors/invalid_api_key
title:
type: string
description: Short human-readable summary of the failure.
examples:
- Invalid API key
status:
type: integer
description: HTTP status code, matching the response's own status.
code:
type: string
description: >-
Stable machine-readable error code — branch on this, not
`title`.
enum:
- invalid_api_key
detail:
type: string
description: Human explanation of this occurrence.
request_id:
type: string
description: Correlation id, also sent as x-request-id.
example:
type: https://iotools.cloud/docs/errors/invalid_api_key
title: Invalid API key
status: 401
code: invalid_api_key
detail: 'Provide ''Authorization: Bearer ''.'
request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
InsufficientCredits:
description: Monthly credit allowance exhausted.
content:
application/problem+json:
schema:
type: object
description: >-
RFC 9457 problem document, served as application/problem+json.
Branch on `code`; `title` is human prose and may be reworded
without notice. Some failures add extension members — `fields` on
validation errors, `retry_after` on 429s,
`credits_used`/`credits_remaining` on billing-adjacent failures —
documented on the responses that carry them.
required:
- type
- title
- status
- code
properties:
type:
type: string
format: uri
description: Stable documentation URI for this failure.
examples:
- https://iotools.cloud/docs/errors/insufficient_credits
title:
type: string
description: Short human-readable summary of the failure.
examples:
- Insufficient credits
status:
type: integer
description: HTTP status code, matching the response's own status.
code:
type: string
description: >-
Stable machine-readable error code — branch on this, not
`title`.
enum:
- insufficient_credits
detail:
type: string
description: Human explanation of this occurrence.
request_id:
type: string
description: Correlation id, also sent as x-request-id.
credits_used:
type: integer
description: Always 0 — a refused call charges nothing.
credits_remaining:
type: integer
description: Credits left in the allowance — fewer than this call costs.
example:
type: https://iotools.cloud/docs/errors/insufficient_credits
title: Insufficient credits
status: 402
code: insufficient_credits
detail: This call costs 1 credit and 0 remain in this month's allowance.
request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
credits_used: 0
credits_remaining: 0
ToolNotAllowed:
description: Tool exists but has no API surface.
content:
application/problem+json:
schema:
type: object
description: >-
RFC 9457 problem document, served as application/problem+json.
Branch on `code`; `title` is human prose and may be reworded
without notice. Some failures add extension members — `fields` on
validation errors, `retry_after` on 429s,
`credits_used`/`credits_remaining` on billing-adjacent failures —
documented on the responses that carry them.
required:
- type
- title
- status
- code
properties:
type:
type: string
format: uri
description: Stable documentation URI for this failure.
examples:
- https://iotools.cloud/docs/errors/tool_not_allowed
title:
type: string
description: Short human-readable summary of the failure.
examples:
- Tool not available over the API
status:
type: integer
description: HTTP status code, matching the response's own status.
code:
type: string
description: >-
Stable machine-readable error code — branch on this, not
`title`.
enum:
- tool_not_allowed
detail:
type: string
description: Human explanation of this occurrence.
request_id:
type: string
description: Correlation id, also sent as x-request-id.
example:
type: https://iotools.cloud/docs/errors/tool_not_allowed
title: Tool not available over the API
status: 403
code: tool_not_allowed
detail: >-
"Background Remover" is available on iotools.cloud but has no API
endpoint.
request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
ToolNotFound:
description: No such tool.
content:
application/problem+json:
schema:
type: object
description: >-
RFC 9457 problem document, served as application/problem+json.
Branch on `code`; `title` is human prose and may be reworded
without notice. Some failures add extension members — `fields` on
validation errors, `retry_after` on 429s,
`credits_used`/`credits_remaining` on billing-adjacent failures —
documented on the responses that carry them.
required:
- type
- title
- status
- code
properties:
type:
type: string
format: uri
description: Stable documentation URI for this failure.
examples:
- https://iotools.cloud/docs/errors/tool_not_found
title:
type: string
description: Short human-readable summary of the failure.
examples:
- Tool not found
status:
type: integer
description: HTTP status code, matching the response's own status.
code:
type: string
description: >-
Stable machine-readable error code — branch on this, not
`title`.
enum:
- tool_not_found
detail:
type: string
description: Human explanation of this occurrence.
request_id:
type: string
description: Correlation id, also sent as x-request-id.
example:
type: https://iotools.cloud/docs/errors/tool_not_found
title: Tool not found
status: 404
code: tool_not_found
detail: No tool with that slug. See GET /v1/tools/list.
request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
PayloadTooLarge:
description: Body too large.
content:
application/problem+json:
schema:
type: object
description: >-
RFC 9457 problem document, served as application/problem+json.
Branch on `code`; `title` is human prose and may be reworded
without notice. Some failures add extension members — `fields` on
validation errors, `retry_after` on 429s,
`credits_used`/`credits_remaining` on billing-adjacent failures —
documented on the responses that carry them.
required:
- type
- title
- status
- code
properties:
type:
type: string
format: uri
description: Stable documentation URI for this failure.
examples:
- https://iotools.cloud/docs/errors/payload_too_large
title:
type: string
description: Short human-readable summary of the failure.
examples:
- Payload too large
status:
type: integer
description: HTTP status code, matching the response's own status.
code:
type: string
description: >-
Stable machine-readable error code — branch on this, not
`title`.
enum:
- payload_too_large
detail:
type: string
description: Human explanation of this occurrence.
request_id:
type: string
description: Correlation id, also sent as x-request-id.
example:
type: https://iotools.cloud/docs/errors/payload_too_large
title: Payload too large
status: 413
code: payload_too_large
detail: Request body exceeds this tool's size limit.
request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
RateLimited:
description: Per-minute rate limit exceeded.
headers:
Retry-After:
description: Seconds to wait before retrying (RFC 9110 delta-seconds).
schema:
type: integer
content:
application/problem+json:
schema:
type: object
description: >-
RFC 9457 problem document, served as application/problem+json.
Branch on `code`; `title` is human prose and may be reworded
without notice. Some failures add extension members — `fields` on
validation errors, `retry_after` on 429s,
`credits_used`/`credits_remaining` on billing-adjacent failures —
documented on the responses that carry them.
required:
- type
- title
- status
- code
properties:
type:
type: string
format: uri
description: Stable documentation URI for this failure.
examples:
- https://iotools.cloud/docs/errors/rate_limited
title:
type: string
description: Short human-readable summary of the failure.
examples:
- Rate limit exceeded
status:
type: integer
description: HTTP status code, matching the response's own status.
code:
type: string
description: >-
Stable machine-readable error code — branch on this, not
`title`.
enum:
- rate_limited
detail:
type: string
description: Human explanation of this occurrence.
request_id:
type: string
description: Correlation id, also sent as x-request-id.
retry_after:
type: integer
description: >-
Seconds until the window resets — the same value as the
`Retry-After` header.
example:
type: https://iotools.cloud/docs/errors/rate_limited
title: Rate limit exceeded
status: 429
code: rate_limited
detail: Too many requests. Retry in 30s.
request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
retry_after: 30
ToolFailed:
description: Tool failed to run.
content:
application/problem+json:
schema:
type: object
description: >-
RFC 9457 problem document, served as application/problem+json.
Branch on `code`; `title` is human prose and may be reworded
without notice. Some failures add extension members — `fields` on
validation errors, `retry_after` on 429s,
`credits_used`/`credits_remaining` on billing-adjacent failures —
documented on the responses that carry them.
required:
- type
- title
- status
- code
properties:
type:
type: string
format: uri
description: Stable documentation URI for this failure.
examples:
- https://iotools.cloud/docs/errors/processing_error
- https://iotools.cloud/docs/errors/internal_error
title:
type: string
description: Short human-readable summary of the failure.
examples:
- Tool failed to run
- Internal error
status:
type: integer
description: HTTP status code, matching the response's own status.
code:
type: string
description: >-
Stable machine-readable error code — branch on this, not
`title`.
enum:
- processing_error
- internal_error
detail:
type: string
description: Human explanation of this occurrence.
request_id:
type: string
description: Correlation id, also sent as x-request-id.
credits_used:
type: integer
description: >-
Always 0 on `processing_error` — a failed run is refunded,
floor included.
credits_remaining:
type: integer
description: >-
Credits left after the refund. Absent when metering is
disabled.
example:
type: https://iotools.cloud/docs/errors/processing_error
title: Tool failed to run
status: 500
code: processing_error
detail: The tool failed to run. Please try again.
request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
credits_used: 0
ToolDisabled:
description: Tool temporarily disabled.
content:
application/problem+json:
schema:
type: object
description: >-
RFC 9457 problem document, served as application/problem+json.
Branch on `code`; `title` is human prose and may be reworded
without notice. Some failures add extension members — `fields` on
validation errors, `retry_after` on 429s,
`credits_used`/`credits_remaining` on billing-adjacent failures —
documented on the responses that carry them.
required:
- type
- title
- status
- code
properties:
type:
type: string
format: uri
description: Stable documentation URI for this failure.
examples:
- https://iotools.cloud/docs/errors/tool_disabled
- https://iotools.cloud/docs/errors/api_unconfigured
title:
type: string
description: Short human-readable summary of the failure.
examples:
- Tool temporarily disabled
- API not configured
status:
type: integer
description: HTTP status code, matching the response's own status.
code:
type: string
description: >-
Stable machine-readable error code — branch on this, not
`title`.
enum:
- tool_disabled
- api_unconfigured
detail:
type: string
description: Human explanation of this occurrence.
request_id:
type: string
description: Correlation id, also sent as x-request-id.
example:
type: https://iotools.cloud/docs/errors/tool_disabled
title: Tool temporarily disabled
status: 503
code: tool_disabled
detail: This tool is temporarily unavailable. Try again shortly.
request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
securitySchemes:
bearerAuth:
type: http
scheme: bearer
bearerFormat: iot_live_…
````