{"uid":"cap_zdQ72hKys0NytU2T0q0mx","slug":"special-relativity-calculator-a110c3b9","name":"Special Relativity Calculator","description":"Special relativity: Lorentz factor, time dilation, length contraction, total and kinetic energy and momentum at a given speed.","url":"https://physics-calc.x402tookit.com/relativity?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"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"]},"momentumKgMS":{"type":["null","number"]},"totalEnergyJ":{"type":["null","number"]},"lorentzFactor":{"type":["null","number"]},"restEnergyMeV":{"type":["null","number"]},"kineticEnergyJ":{"type":["null","number"]},"totalEnergyMeV":{"type":["null","number"]},"timeDifferenceS":{"type":["null","number"]},"contractedLengthM":{"type":["null","number"]},"lengthContractionFactor":{"type":["null","number"]},"relativisticKineticMinusClassical":{"type":["null","number"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_0neBhhzzKEqLyAKuRsJP9","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes Lorentz factor, time dilation, length contraction, relativistic energy, and momentum for a given speed","exampleAgentPrompt":"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?","exampleUseCases":[{"title":"Twin paradox time dilation check","prompt":"If a twin travels at 0.99c and 5 years pass on their clock, how much time passes on Earth? Give me the Lorentz factor and the time difference."},{"title":"Particle accelerator energy calculation","prompt":"Calculate the total relativistic energy and momentum in both joules and MeV for a proton with rest mass 1.67e-27 kg traveling at 0.999c."},{"title":"Spaceship length contraction","prompt":"A spaceship is 500 metres long at rest. How long does it appear to an observer when it flies past at 270,000,000 m/s? Also give me the Lorentz factor."}],"resultDescription":"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. 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Prefer this over classical mechanics endpoints when velocities exceed ~10% of the speed of light where relativistic effects become non-negligible.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-30T00:35:31.976Z","isFirstParty":false,"canonicalSlug":"special-relativity-calculator-a110c3b9"}