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JavaScript
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math_ratio_calculator

Read-onlyIdempotent

Simplify, solve proportion, scale, split, or percentage calculations on ratios. Input numbers and select an operation to get instant results.

Instructions

Ratio Calculator (Simplify, Solve Proportion, Scale, Split, Percentage). Run one of five ratio operations on numbers you supply. The operation field selects the mode: simplify reduces an integer ratio by its GCD; solveProportion solves a is to b as c is to d for the one omitted term; scale multiplies every part so an anchored part hits a target; split distributes a total across parts with largest-remainder rounding; percentage expresses each part as a percent of the whole. Use this for proportions, scaling, and part-whole splits; use math_percentage_calculator for percent-of and percent-change math, or math_statistics_calculator for descriptive statistics on a dataset. Runs locally on the numbers you provide: read-only, non-destructive, contacts no external service, and is rate-limited (60 requests/minute for anonymous callers). Returns a JSON envelope (success, operation, result) whose result shape depends on the chosen operation.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
operationYesMode selector. simplify, scale, split, and percentage read the parts array; solveProportion reads a, b, c, d instead.
partsNoRatio terms for simplify, scale, split, and percentage (ignored by solveProportion). 2 to 8 finite numbers greater than zero; numeric strings are coerced. simplify additionally requires every value to be a positive integer.
aNoFirst proportion term (solveProportion only). Provide exactly three of a, b, c, d, each greater than zero, and omit the one to solve for.
bNoSecond proportion term (solveProportion only). Provide exactly three of a, b, c, d and omit the one to solve for.
cNoThird proportion term (solveProportion only). Provide exactly three of a, b, c, d and omit the one to solve for.
dNoFourth proportion term (solveProportion only). Provide exactly three of a, b, c, d and omit the one to solve for.
anchorNoAnchor for the scale operation (required for scale, ignored otherwise): pin one part to a target value and scale the rest.
totalNoTotal to distribute across parts for the split operation (required for split, ignored otherwise). Each rounded allocation is proportional to its part.

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
successNoTrue when the calculation succeeded.
operationNoThe operation that was executed (echoed from the request).
resultNoOperation-specific output. simplify returns input, simplified, gcd. solveProportion returns a, b, c, d, unknown, equation. scale returns input, scaled, anchor (index, value), factor. split returns total, parts, allocations, rounded, rounding. percentage returns parts, percentages, total.
errorNoPresent only on failure (HTTP 400/500) with the validation message; omitted on success.

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed15 schema fields changedv0.5.1
    • addedInput schema / additionalProperties
      Added value: +false
    • addedInput schema / properties / a
      Added value: +{
+  "description": "First proportion term (solveProportion only). Provide exactly three of a, b, c, d, each greater than zero, and omit the one to solve for.",
+  "type": "number"
+}
    • addedInput schema / properties / anchor
      Added value: +{
+  "additionalProperties": false,
+  "description": "Anchor for the scale operation (required for scale, ignored otherwise): pin one part to a target value and scale the rest.",
+  "properties": {
+    "index": {
+      "description": "Zero-based index of the part to anchor; must be within the parts array.",
+      "minimum": 0,
+      "type": "integer"
+    },
+    "value": {
+      "description": "Target value the anchored part should become; the scale factor is value divided by the original part.",
+      "type": "number"
+    }
+  },
+  "type": "object"
+}
    • addedInput schema / properties / b
      Added value: +{
+  "description": "Second proportion term (solveProportion only). Provide exactly three of a, b, c, d and omit the one to solve for.",
+  "type": "number"
+}
    • addedInput schema / properties / c
      Added value: +{
+  "description": "Third proportion term (solveProportion only). Provide exactly three of a, b, c, d and omit the one to solve for.",
+  "type": "number"
+}
    • addedInput schema / properties / d
      Added value: +{
+  "description": "Fourth proportion term (solveProportion only). Provide exactly three of a, b, c, d and omit the one to solve for.",
+  "type": "number"
+}
    • addedInput schema / properties / operation / description
      Added value: +"Mode selector. simplify, scale, split, and percentage read the parts array; solveProportion reads a, b, c, d instead."
    • addedInput schema / properties / operation / enum
      Added value: +[
+  "simplify",
+  "solveProportion",
+  "scale",
+  "split",
+  "percentage"
+]
    • addedInput schema / properties / parts / description
      Added value: +"Ratio terms for simplify, scale, split, and percentage (ignored by solveProportion). 2 to 8 finite numbers greater than zero; numeric strings are coerced. simplify additionally requires every value to be a positive integer."
    • changedInput schema / properties / parts / items / type
      Previous value: -"integer"New value: +"number"
    • addedInput schema / properties / parts / maxItems
      Added value: +8
    • addedInput schema / properties / parts / minItems
      Added value: +2
    • addedInput schema / properties / total
      Added value: +{
+  "description": "Total to distribute across parts for the split operation (required for split, ignored otherwise). Each rounded allocation is proportional to its part.",
+  "type": "number"
+}
    • changedInput schema / required
      Previous value: -[
-  "operation",
-  "parts"
-]New value: +[
+  "operation"
+]
    • changedOutput schema / (root)
      Previous value: -nullNew value: +{
+  "properties": {
+    "error": {
+      "description": "Present only on failure (HTTP 400/500) with the validation message; omitted on success.",
+      "type": "string"
+    },
+    "operation": {
+      "description": "The operation that was executed (echoed from the request).",
+      "type": "string"
+    },
+    "result": {
+      "description": "Operation-specific output. simplify returns input, simplified, gcd. solveProportion returns a, b, c, d, unknown, equation. scale returns input, scaled, anchor (index, value), factor. split returns total, parts, allocations, rounded, rounding. percentage returns parts, percentages, total.",
+      "properties": {
+        "a": {
+          "description": "Resolved first proportion term (solveProportion).",
+          "type": "number"
+        },
+        "allocations": {
+          "description": "Exact unrounded proportional allocations of the total (split).",
+          "items": {
+            "type": "number"
+          },
+          "type": "array"
+        },
+        "anchor": {
+          "description": "The anchor that was applied (scale).",
+          "properties": {
+            "index": {
+              "description": "Zero-based index of the anchored part.",
+              "type": "integer"
+            },
+            "value": {
+              "description": "Target value the anchored part was set to.",
+              "type": "number"
+            }
+          },
+          "type": "object"
+        },
+        "b": {
+          "description": "Resolved second proportion term (solveProportion).",
+          "type": "number"
+        },
+        "c": {
+          "description": "Resolved third proportion term (solveProportion).",
+          "type": "number"
+        },
+        "d": {
+          "description": "Resolved fourth proportion term (solveProportion).",
+          "type": "number"
+        },
+        "equation": {
+          "description": "The solved proportion rendered as a over b equals c over d (solveProportion).",
+          "type": "string"
+        },
+        "factor": {
+          "description": "Multiplier applied to every part (scale).",
+          "type": "number"
+        },
+        "gcd": {
+          "description": "Greatest common divisor of the input parts (simplify).",
+          "type": "integer"
+        },
+        "input": {
+          "description": "Validated input parts (simplify and scale).",
+          "items": {
+            "type": "number"
+          },
+          "type": "array"
+        },
+        "parts": {
+          "description": "Validated input parts (split and percentage).",
+          "items": {
+            "type": "number"
+          },
+          "type": "array"
+        },
+        "percentages": {
+          "description": "Each part as a percent of the whole (percentage).",
+          "items": {
+            "type": "number"
+          },
+          "type": "array"
+        },
+        "rounded": {
+          "description": "Integer allocations via largest-remainder rounding (split).",
+          "items": {
+            "type": "integer"
+          },
+          "type": "array"
+        },
+        "rounding": {
+          "description": "Rounding mode applied to the split allocations (always rounded).",
+          "type": "string"
+        },
+        "scaled": {
+          "description": "Parts after applying the scale factor (scale).",
+          "items": {
+            "type": "number"
+          },
+          "type": "array"
+        },
+        "simplified": {
+          "description": "Parts reduced by their GCD (simplify).",
+          "items": {
+            "type": "number"
+          },
+          "type": "array"
+        },
+        "total": {
+          "description": "Echoed total (split) or sum of parts (percentage).",
+          "type": "number"
+        },
+        "unknown": {
+          "description": "Which term was solved for, one of a, b, c, or d (solveProportion).",
+          "type": "string"
+        }
+      },
+      "type": "object"
+    },
+    "success": {
+      "description": "True when the calculation succeeded.",
+      "type": "boolean"
+    }
+  },
+  "type": "object"
+}
  2. First observedv0.1.0

TDQS

A4.8/5.0
Behavior5/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

The description discloses behavioral traits beyond annotations: 'Runs locally on the numbers you provide: read-only, non-destructive, contacts no external service, and is rate-limited (60 requests/minute for anonymous callers).' This adds context about local execution and rate limits, which are not covered by the readOnlyHint and idempotentHint annotations. No contradictions.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is a single paragraph, but each sentence serves a purpose: defining scope, listing modes, usage guidance, and behavioral notes. It front-loads the tool's purpose and operation list. While slightly verbose (e.g., detailed operation descriptions could be shortened), it remains clear and well-organized.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's complexity (5 operations, 8 parameters, nested objects, output schema), the description covers all necessary aspects: operation modes, parameter requirements, constraints (e.g., 'simplify requires positive integers'), usage guidance, and behavioral safety. The presence of an output schema means return values need not be described. Complete for agent selection and invocation.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so baseline is 3. The description adds value by explaining the operation modes in a narrative way (e.g., 'simplify reduces an integer ratio by its GCD; solveProportion solves a is to b as c is to d'), and clarifies conditional usage of parameters like anchor and total. This enhances understanding beyond the schema's property descriptions.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly identifies the tool as a ratio calculator with five specific operations (simplify, solveProportion, scale, split, percentage), and distinguishes it from sibling tools math_percentage_calculator and math_statistics_calculator. The verb 'run' and resource 'ratio operations' provide a specific, actionable purpose.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Explicit usage guidance is provided: 'Use this for proportions, scaling, and part-whole splits; use math_percentage_calculator for percent-of and percent-change math, or math_statistics_calculator for descriptive statistics on a dataset.' This clearly states when to use this tool and when to choose alternatives.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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