{"uid":"cap_NoYXtJH0xPLzRj9W-zit4","slug":"map-tile-maths-mercator-projection-lat-lon-epsg-3857-metres-ade008bf","name":"Map Tile Maths – Mercator Projection (lat/lon ↔ EPSG:3857 metres)","description":"Convert latitude/longitude to Web Mercator EPSG:3857 metres, or metres back to degrees, with scale distortion.","url":"https://map-tiles.x402tookit.com/mercator-project?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":{"x":{"type":"number","description":"EPSG:3857 easting in metres (with y), within +/-20037508.34"},"y":{"type":"number","description":"EPSG:3857 northing in metres"},"latitude":{"type":"number","description":"Latitude within +/-85.0511 (with longitude)"},"longitude":{"type":"number","description":"Longitude -180 to 180"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"x":{"type":["null","number"]},"y":{"type":["null","number"]},"asOf":{"type":["null","string"]},"source":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"latitude":{"type":["null","number"]},"longitude":{"type":["null","number"]},"disclaimer":{"type":["null","string"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"scaleFactor":{"type":["null","number"]},"maxExtentMeters":{"type":["null","number"]},"areaInflationFactor":{"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_Drs-FPuYVFfUYhh2_AAci","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":"Converts latitude/longitude coordinates to Web Mercator EPSG:3857 metre coordinates (or vice versa), returning scale distortion factors at the given location.","exampleAgentPrompt":"Convert latitude 51.5074, longitude -0.1278 (central London) to Web Mercator EPSG:3857 metre coordinates, and tell me the scale distortion factor at that location.","exampleUseCases":[{"title":"GIS pipeline coordinate transformation","prompt":"I need to transform the coordinates lat 40.7128, lon -74.0060 (New York City) into Web Mercator EPSG:3857 metres for a GIS pipeline — what are the x and y values and what's the scale distortion there?"},{"title":"Reverse-project map tile origin point","prompt":"I have a Web Mercator coordinate of x = -11131949.08, y = 4865942.27 and I need to convert it back to latitude and longitude — can you do that for me?"},{"title":"Assess Mercator distortion at high latitude","prompt":"What's the Mercator scale factor and area inflation for Oslo at latitude 59.9139, longitude 10.7522? I'm trying to understand how much the map distorts at that latitude."}],"resultDescription":"Returns the converted coordinates in both directions (EPSG:3857 x/y metres and/or latitude/longitude degrees), a scale factor indicating linear distortion at that latitude, an area inflation factor showing how much areas are exaggerated, and the maximum valid extent in metres for the projection.","failureModes":["Latitude outside ±85.0511 degrees — Web Mercator is undefined at the poles beyond this bound","Longitude outside ±180 degrees — invalid input rejected","EPSG:3857 x or y outside ±20037508.34 metres — exceeds valid projection extent","Missing required coordinate pair (must supply either lat+lon or x+y, not a mix)","Payment failure or insufficient USDC balance — 402 response returned"],"whenToPreferThis":"Choose this endpoint when you need a precise, mathematically correct conversion between WGS84 geographic coordinates and Web Mercator EPSG:3857 metre coordinates, especially when you also need scale distortion metadata. It is ideal for GIS pipelines, map rendering calculations, and any workflow where understanding Mercator projection distortion at a specific latitude is important. Prefer it over client-side libraries when you need a reliable, stateless server-side conversion with distortion factors included.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-30T00:35:01.473Z","isFirstParty":false,"canonicalSlug":"map-tile-maths-mercator-projection-lat-lon-epsg-3857-metres-ade008bf"}