{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"race-time-predictor"},"result":{"entity_type":"calculator","id":"race-time-predictor","calculator_id":"race-time-predictor","canonical_url":"https://tttkmbb.com/fitness/race-time-predictor","name":"Race Time Predictor","title":"Race Time Predictor – 5K, 10K, Half Marathon and Marathon Times with Riegel's Formula","category":"fitness","category_name":"Sports & Fitness","tool_name":"predict_race_time","featured_mcp_tool":false,"description":"Predicts finish times for 5 km, 10 km, half marathon and marathon from one known race result using Riegel's endurance formula T2 = T1 × (D2/D1)^1.06, with the corresponding paces.","use_when":"You have a recent race time (or time trial) and want equivalent-effort predictions for other standard distances, e.g. to set a marathon goal from a half-marathon result.","do_not_use_when":"You only need the pace or constant-pace splits of a run (use running-pace), the known effort was a trail or very hilly race, or it was shorter than about 1.5 km or longer than a marathon.","inputs":[{"name":"distance","label":"Known race distance","type":"number","required":true,"max":500,"exclusive_min":0,"description":"Distance of the race you already ran, in distance_unit.","example":10},{"name":"distance_unit","label":"Distance unit","type":"enum","required":false,"default":"km","values":[{"value":"km","label":"Kilometres","aliases":["kilometers","kilometres","k"]},{"value":"mi","label":"Miles","aliases":["mile","miles"]}],"description":"Unit of the distance input.","example":"km"},{"name":"time","label":"Known race time","type":"string","required":true,"description":"Finish time of the known race as h:mm:ss, mm:ss or minutes.","example":"50:00"},{"name":"exponent","label":"Fatigue exponent","type":"number","required":false,"default":1.06,"min":1,"max":1.3,"description":"Riegel's exponent; 1.06 fits elite and well-trained runners, 1.07–1.10 is often more realistic for recreational marathoners.","example":1.06}],"outputs":[{"name":"predicted_5k","label":"Predicted 5 km","type":"string","unit":"h:mm:ss","decimals":4,"description":"Predicted 5 km time."},{"name":"predicted_10k","label":"Predicted 10 km","type":"string","unit":"h:mm:ss","decimals":4,"description":"Predicted 10 km time."},{"name":"predicted_half_marathon","label":"Predicted half marathon","type":"string","unit":"h:mm:ss","decimals":4,"description":"Predicted time for 21.0975 km."},{"name":"predicted_marathon","label":"Predicted marathon","type":"string","unit":"h:mm:ss","decimals":4,"description":"Predicted time for 42.195 km."},{"name":"predictions","label":"All predictions","type":"list","decimals":4,"description":"Per race: distance_km, time (h:mm:ss), pace_min_per_km and pace_min_per_mile."}],"input_schema":{"type":"object","properties":{"distance":{"description":"Distance of the race you already ran, in distance_unit.","type":"number","maximum":500,"exclusiveMinimum":0,"examples":[10]},"distance_unit":{"description":"Unit of the distance input.","type":"string","enum":["km","mi"],"default":"km","examples":["km"]},"time":{"description":"Finish time of the known race as h:mm:ss, mm:ss or minutes.","type":"string","examples":["50:00"]},"exponent":{"description":"Riegel's exponent; 1.06 fits elite and well-trained runners, 1.07–1.10 is often more realistic for recreational marathoners.","type":"number","minimum":1,"maximum":1.3,"default":1.06,"examples":[1.06]}},"additionalProperties":false,"required":["distance","time"]},"output_schema":{"type":"object","properties":{"predicted_5k":{"description":"Predicted 5 km time. Unit: h:mm:ss.","type":"string","x-unit":"h:mm:ss"},"predicted_10k":{"description":"Predicted 10 km time. Unit: h:mm:ss.","type":"string","x-unit":"h:mm:ss"},"predicted_half_marathon":{"description":"Predicted time for 21.0975 km. Unit: h:mm:ss.","type":"string","x-unit":"h:mm:ss"},"predicted_marathon":{"description":"Predicted time for 42.195 km. Unit: h:mm:ss.","type":"string","x-unit":"h:mm:ss"},"predictions":{"description":"Per race: distance_km, time (h:mm:ss), pace_min_per_km and pace_min_per_mile.","type":"array"}}},"formula":"T2 = T1 × (D2 / D1)^exponent, exponent = 1.06 (Riegel 1981); pace = T2 / D2","method":"Riegel's power law was fitted to world-record performances from about 3.5 minutes to 4 hours and assumes comparable training for the target distance. Predictions from short races to the marathon are usually optimistic for non-elite runners.","sources":[{"name":"Riegel PS (1981) Athletic records and human endurance, American Scientist 69:285-290","url":"https://pubmed.ncbi.nlm.nih.gov/7235349/","type":"peer_reviewed","retrieved_at":"2026-09-23"},{"name":"World Athletics – Book of Rules (Technical Rules: road race distances 5 km, 10 km, half marathon 21.0975 km, marathon 42.195 km)","url":"https://worldathletics.org/about-iaaf/documents/book-of-rules","type":"standard","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"10 km in 50:00","inputs":{"distance":10,"distance_unit":"km","time":"50:00"},"expected":{"predicted_5k":"0:23:59","predicted_10k":"0:50:00","predicted_half_marathon":"1:50:19","predicted_marathon":"3:50:01"},"url":"https://tttkmbb.com/api/v1/calculate/race-time-predictor?distance=10&distance_unit=km&time=50%3A00"},{"name":"Half marathon in 1:45:00","inputs":{"distance":21.0975,"distance_unit":"km","time":"1:45:00"},"expected":{"predicted_5k":"0:22:50","predicted_10k":"0:47:35","predicted_marathon":"3:38:55"},"url":"https://tttkmbb.com/api/v1/calculate/race-time-predictor?distance=21.0975&distance_unit=km&time=1%3A45%3A00"}],"faq":[{"q":"Why 1.06?","a":"Riegel found that record times scale with distance to the power 1.06 for running (the 'fatigue factor'): doubling the distance takes about 2.085 times as long, i.e. pace slows by roughly 4 % per doubling."},{"q":"How accurate is the prediction?","a":"Typically within a few percent between neighbouring distances (10 km ↔ half marathon). Marathon predictions from a 5 km are often 5–10 % too fast unless mileage is high; raising the exponent to 1.07–1.10 compensates."}],"tags":["race time predictor","riegel formula","marathon prediction","half marathon time","equivalent performance"],"related":[{"calculator_id":"running-pace","reason":"Constant-pace splits and speed for a given distance and time."},{"calculator_id":"vo2-max","reason":"Estimate aerobic capacity from a 12-minute run."}],"links":{"html":"https://tttkmbb.com/fitness/race-time-predictor","markdown":"https://tttkmbb.com/fitness/race-time-predictor.md","json":"https://tttkmbb.com/fitness/race-time-predictor.json","api":"https://tttkmbb.com/api/v1/calculate/race-time-predictor","schema":"https://tttkmbb.com/api/v1/calculators/race-time-predictor","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:31:45Z","next_actions":[{"tool":"run_calculator","calculator_id":"race-time-predictor","reason":"Run Race Time Predictor with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/fitness/race-time-predictor.md"}}