{"calculator":{"slug":"altitude-adjustment-calculator","math":{"href":"https://www.tracktoolspro.com/api/calculators/altitude-adjustment-calculator","jsonPointer":"/calculator/math","version":"2026-10-21.1","implementationVersion":"b5a8aca7b85361476e0321a08b7fa5f516fc9535","scope":"Canonical HTTP function and documented corresponding mounted-form math. This is public inspectable documentation, not access control or independent empirical validation.","unitNotation":"Input paths use [] and *; output paths are JSON Pointers with * (one segment) and ** (descendants). Empty output path denotes scalar result. Units apply to numeric quantities or explicitly described numeric strings; labels/statuses/booleans are dimensionless. More specific units, including count/index exceptions, override broad patterns.","interfaceNotes":["HTTP input is described by the adjacent inputSchema. The original handlers may accept numeric strings; this metadata adds no validation.","Mounted forms accept displayed clock/unit strings and enforce their own limits. Mounted tools limit strings to 200 characters and numeric parts to magnitude 1000000. Do not assume mounted/API input interchangeability.","Some legacy extreme/invalid tuples can produce null/empty results or nonfinite numbers serialized as null. Those are unavailable answers, not exact numerical predictions. Per-calculator domain describes the intended mathematical inputs."],"kind":"empirical-model","implementationFiles":["lib/formulas/altitude.ts"],"equations":["For altitudeMeters<=750, F=1. Otherwise h=ln(altitudeMeters), d=ln(distanceMeters).","A(h)=0.0194294334323786*h^4-0.58204012227*h^3+6.53099074887773*h^2-32.4795428772407*h+61.3421201263799.","B(h)=-0.285467149404212*h^4+8.55856793339852*h^3-96.1580193931405*h^2+478.077054822298*h-892.151236317125.","F=(ln(altitudeMeters*distanceMeters)*A(h)+B(h))/ln(distanceMeters); convertedSeconds=timeSeconds/F; timeDiff=timeSeconds-convertedSeconds; percentImpact=100*(F-1)."],"inputUnits":{"timeSeconds":"s","altitudeMeters":"m","distanceMeters":"m"},"outputUnits":{"/originalSeconds":"s","/convertedSeconds":"s","/timeDiff":"s","/percentImpact":"%","/adjustmentFactor":"dimensionless"},"domain":["Finite nonnegative altitude/time and positive distance; API rejects nonfinite model outputs, including distance 1m logarithmic singularity above threshold. Zero time/altitude finite identities remain."],"rounding":["Raw IEEE-754 numbers; the mounted page formats clocks separately."],"assumptions":["Uses the entered values and the selected convention; this documentation does not strengthen existing validation."],"limitations":["Product-specific polynomial, not an official altitude qualification adjustment or a published universal physiological law. No independent calibration range established."],"mountedPageNotes":[],"workedExamples":[{"input":{"timeSeconds":1200,"altitudeMeters":1609,"distanceMeters":5000},"expected":{"/convertedSeconds":1186.3668179002848,"/adjustmentFactor":1.0114915403010378},"absoluteTolerance":1e-8,"note":"Illustrative canonical-handler result; not independent validation of an empirical model."}],"constantsAndTables":{"thresholdMeters":750,"polynomialCoefficients":"Full retained coefficients are in the equations and linked implementation; no published calibration is claimed."},"sources":[{"title":"Canonical HTTP binding at the documented implementation revision","url":"https://github.com/wickthumb/track_tools_pro_marketing/blob/b5a8aca7b85361476e0321a08b7fa5f516fc9535/lib/calculator-functions.ts","note":"Existing calculation handler; math metadata is additive."},{"title":"lib/formulas/altitude.ts","url":"https://github.com/wickthumb/track_tools_pro_marketing/blob/b5a8aca7b85361476e0321a08b7fa5f516fc9535/lib/formulas/altitude.ts","note":"Primary implementation source for these equations/tables, not a claim of scientific calibration."}]},"annotations":{"readOnlyHint":true,"consequentialHint":false},"name":"Altitude Adjustment Calculator","description":"Calculate how altitude affects your running performance. Convert times between sea level and high altitude venues. Essential for track and field athletes competing at venues like Albuquerque, Flagstaff, Boulder, or Mexico City.","category":"Conversions & Adjustments","method":"POST","endpoint":"/api/calculators/altitude-adjustment-calculator","page":"/calculators/altitude-adjustment-calculator","inputSchema":{"type":"object","required":["timeSeconds","altitudeMeters","distanceMeters"],"properties":{"timeSeconds":{"type":"number","description":"Race time at altitude in seconds.","minimum":0},"altitudeMeters":{"type":"number","description":"Venue altitude in meters.","minimum":0},"distanceMeters":{"type":"number","description":"Race distance in meters.","minimum":5e-324}}},"example":{"timeSeconds":1200,"altitudeMeters":1609,"distanceMeters":5000}}}