# Special Relativity Calculator

> Special Relativity Calculator is a paid API for AI agents from physics-calc.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).

Computes Lorentz factor, time dilation, length contraction, relativistic energy, and momentum for a given speed

## Facts

- Endpoint: GET https://physics-calc.x402tookit.com/relativity?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-30
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/special-relativity-calculator-a110c3b9
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_zdQ72hKys0NytU2T0q0mx

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability special-relativity-calculator-a110c3b9
```

Example prompt: What is the Lorentz factor, time dilation, and relativistic kinetic energy for a 2 kg object moving at 0.85 times the speed of light, given that 60 seconds pass on the moving clock?

## When to prefer this

Use this endpoint when you need precise relativistic physics calculations — Lorentz factor, time dilation, length contraction, or relativistic energy/momentum — especially for education, science homework, particle physics, or astrophysics scenarios. It accepts either beta (fraction of c) or speed in m/s, making it flexible for both physics-native and engineering inputs. Prefer this over classical mechanics endpoints when velocities exceed ~10% of the speed of light where relativistic effects become non-negligible.

## Known failure modes

- beta >= 1 or < 0 causes an error (speed must be 0 to 0.999999999 as fraction of c)
- speedMS exceeding or equal to speed of light returns an error
- Neither beta nor speedMS provided results in missing lorentzFactor and dependent fields
- restMassKg not provided means energy and momentum fields return null
- Very high beta values (e.g. 0.9999999999) may hit floating-point precision limits

## How this service works

Special relativity: Lorentz factor, time dilation, length contraction, total and kinetic energy and momentum at a given speed.

## Output

Returns a JSON object with: lorentzFactor, speedMS, beta, dilatedTimeS, timeDifferenceS, contractedLengthM, lengthContractionFactor, restEnergyJ, restEnergyMeV, kineticEnergyJ, totalEnergyJ, totalEnergyMeV, momentumKgMS, relativisticKineticMinusClassical, plus a summary string and disclaimer. Fields are null when their required input was not supplied.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [],
     "properties": {
      "beta": {
       "type": "number",
       "description": "Speed as a fraction of the speed of light, 0 to 0.999999999 (give this or speedMS)"
      },
      "speedMS": {
       "type": "number",
       "description": "Speed in m/s (alternative to beta)"
      },
      "restMassKg": {
       "type": "number",
       "description": "Rest mass in kg, for energy and momentum"
      },
      "properTimeS": {
       "type": "number",
       "description": "Time elapsed on the moving clock, seconds"
      },
      "properLengthM": {
       "type": "number",
       "description": "Length of the object at rest, metres"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "beta": {
       "type": [
        "null",
        "number"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "speedMS": {
       "type": [
        "null",
        "number"
       ]
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "disclaimer": {
       "type": [
        "null",
        "string"
       ]
      },
      "notChecked": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "restEnergyJ": {
       "type": [
        "null",
        "number"
       ]
      },
      "dilatedTimeS": {
       "type": [
        "null",
        "number"
       ]
      },
  
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/special-relativity-calculator-a110c3b9/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from physics-calc.x402tookit.com](https://www.zero.xyz/host/physics-calc.x402tookit.com/llms.txt)