Flat Earth Science

Earth curvature calculator

calculate_curvature

Read-onlyIdempotent

Calculates how much of a distant target the Earth's curvature hides, from the surface distance, the observer's eye height, the target's height and an assumed refraction coefficient. Returns the hidden and visible height, the tangent-plane drop, the horizon distance and dip, the maximum mutual sight-line range and the midpoint bulge on a smooth sphere of radius 6,371.0084 km.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "distance": "<distance>"
    },
    "name": "calculate_curvature"
  }
}

Input Schema

Name	Required	Description
`units`	No	Metric uses kilometres and metres; imperial uses miles and feet. Metric without it.
`distance`	Yes	Surface distance between the observer and the target, along the ground: 0 to 1000 km, or 0 to 621 miles when units is imperial.
`eyeHeight`	No	Height of the observer's eye above the surface: 0 to 1000 m, or feet when units is imperial. Defaults to 2 m (6.56 ft).
`refraction`	No	Assumed refraction coefficient k from -0.3 to 0.3: 0 is straight rays and positive values bend rays toward the surface. Defaults to 0.
`targetHeight`	No	Height of the target's top above the same surface: 0 to 1000 m, or feet when units is imperial. Defaults to 10 m (32.8 ft).

Output Schema

Name	Required	Description	Default
`item`	Yes
`view`	Yes
`request`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedNov 11, 2026

TDQS

A3.5/5.0

Behavior4/5

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

The annotations already establish read-only, idempotent, non-destructive, closed-world behavior, so the description's added value is model context: the smooth-sphere radius, the assumed refraction coefficient, and the computed outputs. It stops short of discussing approximation limits beyond the smooth-sphere assumption, so it is strong but not exceptional.

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 two front-loaded sentences with no filler. The second sentence enumerates return values even though an output schema exists, making part of it redundant.

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

Completeness4/5

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

For a deterministic math tool with full schema coverage, an output schema, and safety annotations, the description provides enough model context to call it correctly. The main remaining gap is routing guidance relative to sibling horizon and visibility tools.

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 units, ranges, defaults, and refraction semantics. The description names the four inputs but adds no syntax or format meaning beyond what the schema provides, which fits the baseline of 3.

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

Purpose4/5

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

The description gives a specific verb and resource: it calculates how much of a distant target Earth curvature hides, and it names the inputs and outputs. It does not explicitly distinguish itself from the sibling get_horizon_distance tool, which also exposes horizon distance, so sibling differentiation is incomplete.

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

Usage Guidelines2/5

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

There is no explicit when-to-use or when-not-to-use guidance, and no alternative tool is named. An agent must infer from the purpose that this is for target visibility calculations rather than the dedicated horizon tool.

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

All Flat Earth Science tools Inspect

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