{
  "slug": "race-time-predictor",
  "title": "Race Time Predictor (Riegel Formula)",
  "category": "Running",
  "category_slug": "running",
  "tier": 1,
  "summary": "Estimate race finish time at a new distance using the Riegel formula and a known performance.",
  "description": "This calculator estimates race finish time at a new distance using the Riegel formula, a widely used endurance prediction model published by Peter Riegel in 1977. It requires a known race distance and finish time, plus a target race distance, and applies the equation T₂ = T₁ × (D₂/D₁)^1.06 to predict performance at the new distance, outputting an estimated finish time and corresponding pace. The formula assumes similar training status and race conditions between performances and is most reliable for distances within the same general event category (e.g., 5K to half-marathon).",
  "page_url": "https://fitmetriclab.com/en/tools/running/race-time-predictor/",
  "api_url": "https://fitmetriclab.com/api/tools/race-time-predictor.json",
  "formula": {
    "id": "race_time_predictor",
    "expression": "T_2 = T_1 \\times \\left(\\frac{D_2}{D_1}\\right)^{1.06}",
    "variables": [
      {
        "symbol": "D_1",
        "description": "Known distance in km"
      },
      {
        "symbol": "T_1",
        "description": "Known time in minutes"
      },
      {
        "symbol": "D_2",
        "description": "Target distance in km"
      }
    ]
  },
  "inputs": [
    {
      "id": "known_distance_km",
      "label": "Known Distance",
      "type": "number",
      "unit": "km",
      "default": 5,
      "min": 0.1,
      "max": 200,
      "step": 0.1
    },
    {
      "id": "known_time_min",
      "label": "Known Time",
      "type": "number",
      "unit": "min",
      "default": 25,
      "min": 0.5,
      "max": 500,
      "step": 0.1
    },
    {
      "id": "target_distance_km",
      "label": "Target Distance",
      "type": "number",
      "unit": "km",
      "default": 10,
      "min": 0.1,
      "max": 200,
      "step": 0.1
    }
  ],
  "worked_example": {
    "inputs": {
      "known_distance_km": 5,
      "known_time_min": 25,
      "target_distance_km": 10
    },
    "expected_output": "52:07"
  },
  "result_summary_template": "For a known race of {known_distance_km} at {known_time_min}, the Riegel formula predicts a race time of {result} for {target_distance_km}.",
  "methodology": "Applies the Riegel formula: T₂ = T₁ × (D₂/D₁)^1.06, where T₁ is known race time, D₁ is known distance, D₂ is target distance, and 1.06 is the empirically derived fatigue exponent. Originally published by Peter Riegel in Runner's World (1977).",
  "sources": [
    {
      "label": "Riegel PS. Athletic records and human endurance. American Scientist. 1981;69(3):285-290.",
      "url": "https://www.jstor.org/stable/27850427"
    },
    {
      "label": "Vickers AJ, Vertosick EA. An empirical study of race times in recreational endurance runners. BMC Sports Sci Med Rehabil. 2016;8:26.",
      "url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5020511/"
    },
    {
      "label": "Daniels J. Daniels' Running Formula. 3rd ed. Human Kinetics; 2013.",
      "url": "https://us.humankinetics.com/products/daniels-running-formula-3rd-edition"
    }
  ],
  "faqs": [
    {
      "question": "What is the Riegel formula?",
      "answer": "The Riegel formula is a mathematical model that predicts race time at one distance based on performance at another. It uses the equation T₂ = T₁ × (D₂/D₁)^1.06, where the exponent 1.06 represents the fatigue effect as distance increases. Peter Riegel published this relationship in 1977 after analyzing race results across multiple distances."
    },
    {
      "question": "Why is the exponent 1.06 instead of 1.0?",
      "answer": "An exponent of 1.0 would imply that performance scales linearly with distance—that doubling distance exactly doubles time. The 1.06 exponent reflects empirical observation that endurance deteriorates slightly with longer distances. This means a runner who completes 5K in 20 minutes will typically take more than 40 minutes for 10K, because the body fatigues nonlinearly."
    },
    {
      "question": "How accurate are these predictions?",
      "answer": "Accuracy depends on how similar the known and target distances are, and whether conditions remain consistent. The formula tends to perform well within one step of common race distances (5K to 10K, 10K to half-marathon). Predictions become less reliable when extrapolating across very different distances or when training status, terrain, or weather conditions change significantly."
    },
    {
      "question": "Can this formula predict marathon time from a 5K?",
      "answer": "The calculator will generate a result, but large distance ratios reduce reliability. Predicting marathon performance from a 5K involves extrapolating across a 8.4× distance increase, where differences in aerobic capacity, fuel utilization, and training specificity become significant. More accurate marathon predictions typically use a half-marathon or other long-distance result as the baseline."
    },
    {
      "question": "Does the calculator adjust for hills or weather?",
      "answer": "No. The Riegel formula is purely mathematical and does not account for course elevation, temperature, humidity, wind, or surface conditions. The prediction assumes equivalent race environments. Adjustments for these factors require separate correction models or empirical data from similar courses."
    }
  ],
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    {
      "slug": "marathon-predictor",
      "title": "Marathon Time Predictor",
      "api_url": "https://fitmetriclab.com/api/tools/marathon-predictor.json",
      "page_url": "https://fitmetriclab.com/en/tools/running/marathon-predictor/"
    },
    {
      "slug": "vdot-calculator",
      "title": "VDOT Calculator (Jack Daniels)",
      "api_url": "https://fitmetriclab.com/api/tools/vdot-calculator.json",
      "page_url": "https://fitmetriclab.com/en/tools/running/vdot-calculator/"
    },
    {
      "slug": "age-graded-performance",
      "title": "Age-Graded Running Performance Calculator",
      "api_url": "https://fitmetriclab.com/api/tools/age-graded-performance.json",
      "page_url": "https://fitmetriclab.com/en/tools/running/age-graded-performance/"
    }
  ],
  "last_updated": "2026-04-22",
  "price": {
    "value": 0,
    "currency": "USD"
  },
  "runs_in_browser": true,
  "disclaimer": "Educational estimate produced from a published formula. Not medical, nutritional, or training advice. Calculations are deterministic — apply the formula to the inputs to reproduce the result."
}