> ## 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.
# Triangle Calculator
> Solve a triangle from any three known values (with at least one side): SSS, SAS, ASA, AAS, or the ambiguous SSA case. Computes the missing sides and angles, area, perimeter, heights, inradius, circumradius, and classifies the triangle by sides and angles.
[Try Triangle Calculator in your browser →](https://iotools.cloud/tool/triangle-calculator/)
## OpenAPI
````yaml https://api.iotools.cloud/v1/openapi post /v1/tool/triangle-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/triangle-calculator:
post:
tags:
- Calculators
summary: Triangle Calculator
description: >-
Solve a triangle from any three known values (with at least one side):
SSS, SAS, ASA, AAS, or the ambiguous SSA case. Computes the missing
sides and angles, area, perimeter, heights, inradius, circumradius, and
classifies the triangle by sides and angles.
[Try Triangle Calculator in your browser
→](https://iotools.cloud/tool/triangle-calculator/)
operationId: run_triangle_calculator
requestBody:
required: false
content:
application/json:
schema:
type: object
properties:
sideA:
type: number
description: Side a
minimum: 0
sideB:
type: number
description: Side b
minimum: 0
sideC:
type: number
description: Side c
minimum: 0
angleA:
type: number
description: Angle A (opposite a)
minimum: 0
angleB:
type: number
description: Angle B (opposite b)
minimum: 0
angleC:
type: number
description: Angle C (opposite c)
minimum: 0
angleUnit:
enum:
- degrees
- radians
description: Angle unit
required: []
examples:
sss_3_4_5_right_triangle:
summary: SSS (3-4-5 right triangle)
value:
sideA: '3'
sideB: '4'
sideC: '5'
angleUnit: degrees
sas_two_sides_included_angle_c:
summary: SAS (two sides + included angle C)
value:
sideA: '4'
sideB: '5'
angleC: '60'
angleUnit: degrees
asa_two_angles_included_side_c:
summary: ASA (two angles + included side c)
value:
angleA: '50'
angleB: '60'
sideC: '10'
angleUnit: degrees
responses:
'200':
description: Tool output
content:
application/json:
examples:
sss_3_4_5_right_triangle:
summary: SSS (3-4-5 right triangle)
value:
tool: triangle-calculator
tool_version: 1.0.1
outputs:
result: |-
Configuration: SSS (three sides)
Sides
a = 3
b = 4
c = 5
Angles
A = 36.869898°
B = 53.130102°
C = 90°
Properties
Area = 6
Perimeter = 12
Type (sides) = Scalene
Type (angles) = Right
Heights
h_a = 4
h_b = 3
h_c = 2.4
Radii
Inradius (r) = 1
Circumradius (R) = 2.5
svg: >-
credits_used: 3
credits_remaining: null
sas_two_sides_included_angle_c:
summary: SAS (two sides + included angle C)
value:
tool: triangle-calculator
tool_version: 1.0.1
outputs:
result: |-
Configuration: SAS (two sides and included angle C)
Sides
a = 4
b = 5
c = 4.5825757
Angles
A = 49.106605°
B = 70.893395°
C = 60°
Properties
Area = 8.660254
Perimeter = 13.582576
Type (sides) = Scalene
Type (angles) = Acute
Heights
h_a = 4.330127
h_b = 3.4641016
h_c = 3.7796447
Radii
Inradius (r) = 1.2752006
Circumradius (R) = 2.6457513
svg: >-
credits_used: 3
credits_remaining: null
asa_two_angles_included_side_c:
summary: ASA (two angles + included side c)
value:
tool: triangle-calculator
tool_version: 1.0.1
outputs:
result: |-
Configuration: ASA/AAS (two angles and a side)
Sides
a = 8.1520747
b = 9.2160499
c = 10
Angles
A = 50°
B = 60°
C = 70°
Properties
Area = 35.299519
Perimeter = 27.368125
Type (sides) = Scalene
Type (angles) = Acute
Heights
h_a = 8.660254
h_b = 7.6604444
h_c = 7.0599038
Radii
Inradius (r) = 2.5796082
Circumradius (R) = 5.3208889
svg: >-
credits_used: 3
credits_remaining: null
schema:
type: object
required:
- tool
- tool_version
- outputs
- credits_used
- credits_remaining
properties:
outputs:
type: object
properties:
result:
type: string
description: Solution
svg:
type: string
description: Diagram (SVG source)
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_…
````