staffing-math

FTE needed for a workload

required_fte

Read-onlyIdempotent

Calculate full-time equivalents and headcount for a steady workload using weekly volume, minutes per case, shrinkage, target occupancy, and weekly hours.

Instructions

How many people a steady workload needs. Give weekly volume and minutes per case; shrinkage, target occupancy and hours per week fall back to stated defaults. Returns FTE, people to staff (rounded up), every input marked given or assumed, and the arithmetic with numbers filled in. Use hiring_plan when volume changes over time or the question is about hiring, and erlang_staffing for live queues with an answer-time target.

Input Schema

Name	Required	Description
`shrinkage`	No	Share of paid time not available for the work: PTO, sick time, training, meetings. 0.30 means 30%. Default 0.3.
`weekly_volume`	Yes	Cases, tickets or items arriving per week.
`minutes_per_case`	Yes	Average handling time per case, in minutes.
`target_occupancy`	No	Share of available time you plan to keep people busy with the work. Default 0.85.
`hours_per_fte_week`	No	Paid hours per full-time person per week. Default 40.

Output Schema

Name	Required	Description	Default
`fte`	Yes
`notes`	Yes
`steps`	Yes
`answer`	Yes
`engine`	Yes
`inputs`	Yes
`people`	Yes
`weekly_work_hours`	Yes
`fte_per_extra_minute`	Yes
`planned_hours_per_fte_week`	Yes
`productive_hours_per_fte_week`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.3.0Nov 5, 2026

TDQS

A4.3/5.0

Behavior3/5

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

Annotations already declare readOnlyHint, idempotentHint, non-destructive, and closed-world behavior. The description adds useful context about defaults and the returned arithmetic, but it does not go much beyond what the annotations and output schema already establish.

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

Conciseness5/5

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

The description is front-loaded with the purpose, then inputs/defaults, then return values, then alternatives. Every sentence is useful and there is no redundant wording.

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 output schema and annotations, the description is complete enough for an agent to select and invoke the tool correctly. It covers purpose, required inputs, defaults, return shape, and sibling alternatives.

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

Parameters3/5

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

Schema description coverage is 100%, so the schema already documents all five parameters, including defaults and ranges. The description reinforces which inputs are required and which fall back to defaults, but adds little semantic detail beyond the schema.

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 states a specific computation: how many people a steady workload needs from weekly volume and minutes per case. It clearly scopes the tool to steady workloads, which distinguishes it from the sibling tools.

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?

It explicitly names when to use the alternatives: hiring_plan for changing volume or hiring questions, and erlang_staffing for live queues with an answer-time target. It also tells the caller which inputs to provide.

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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