{
  "slug": "one-rep-max-wathen",
  "title": "One-Rep Max Calculator (Wathen Formula)",
  "category": "Strength Training",
  "category_slug": "strength-training",
  "tier": 2,
  "summary": "Estimate your one-rep max using the Wathen (1994) nonlinear regression formula.",
  "description": "This calculator estimates your one-rep max (1RM) using the Wathen (1994) formula, a nonlinear regression model that describes the exponential relationship between submaximal weight lifted and repetitions performed to failure. It requires two inputs—the weight lifted and the number of reps completed—and outputs an estimated maximum weight that could be lifted for a single repetition. The Wathen equation is derived from empirical strength-training data and may provide more accurate 1RM predictions across a wider rep range than simpler linear models.",
  "page_url": "https://fitmetriclab.com/en/tools/strength-training/one-rep-max-wathen/",
  "api_url": "https://fitmetriclab.com/api/tools/one-rep-max-wathen.json",
  "formula": {
    "id": "one_rep_max_wathen",
    "expression": "\\text{1RM} = \\frac{100\\,w}{48.8 + 53.8\\,e^{-0.075\\,r}}",
    "variables": [
      {
        "symbol": "w",
        "description": "Weight in kg"
      },
      {
        "symbol": "r",
        "description": "Reps performed"
      }
    ]
  },
  "inputs": [
    {
      "id": "weight_kg",
      "label": "Weight",
      "type": "number",
      "unit": "kg",
      "default": 75,
      "min": 20,
      "max": 300,
      "step": 0.1
    },
    {
      "id": "reps",
      "label": "Reps",
      "type": "number",
      "unit": "reps",
      "default": 5,
      "min": 1,
      "max": 20,
      "step": 1
    }
  ],
  "worked_example": {
    "inputs": {
      "weight_kg": 75,
      "reps": 5
    },
    "expected_output": "87.4 kg"
  },
  "result_summary_template": "Lifting {weight_kg} for {reps} repetitions, the Wathen formula estimates a one-rep max of {result}.",
  "methodology": "The Wathen formula (1994) estimates one-rep max as 1RM = 100 × weight / (48.8 + 53.8 × e^(−0.075 × reps)). The constants derive from nonlinear regression of submaximal-load repetition data, modeling the exponential relationship between weight and reps-to-failure.",
  "sources": [
    {
      "label": "Wathen D. Load assignment. In: Essentials of Strength Training and Conditioning (Baechle TR, ed). Human Kinetics. 1994.",
      "url": "https://www.worldcat.org/title/essentials-of-strength-training-and-conditioning/oclc/30687849"
    },
    {
      "label": "Reynolds JM, et al. Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry. J Strength Cond Res. 2006;20(3):584–92.",
      "url": "https://pubmed.ncbi.nlm.nih.gov/16937972/"
    },
    {
      "label": "LeSuer DA, et al. The accuracy of prediction equations for estimating 1-RM performance in the bench press, squat, and deadlift. J Strength Cond Res. 1997;11(4):211–13.",
      "url": "https://journals.lww.com/nsca-jscr/abstract/1997/11000/the_accuracy_of_prediction_equations_for.1.aspx"
    }
  ],
  "faqs": [
    {
      "question": "Why does the Wathen formula use exponential terms?",
      "answer": "The relationship between load and repetitions-to-failure is not linear. Wathen's 1994 regression analysis found that an exponential decay function (e^(−0.075 × reps)) better captured how performance drops as reps increase, especially in the 1–10 rep range."
    },
    {
      "question": "How does Wathen compare to Epley or Brzycki?",
      "answer": "Epley and Brzycki use linear approximations, while Wathen applies a nonlinear exponential model. Studies have shown that Wathen tends to produce slightly lower estimates at mid-range reps (5–8) and can track more closely with measured 1RM values in some populations, though no single formula is universally superior across all exercises and individuals."
    },
    {
      "question": "Can I use this formula for bodyweight exercises or Olympic lifts?",
      "answer": "The Wathen formula was derived from data on traditional barbell exercises. It can be applied to any movement where load and reps are measurable, but accuracy may vary. Olympic lifts involve technical and speed components that submaximal-rep testing does not fully capture, so estimates may be less reliable."
    },
    {
      "question": "What rep range gives the most accurate 1RM estimate?",
      "answer": "Research suggests that sets of 3–6 reps tend to yield more accurate 1RM predictions across multiple formulas, including Wathen. Very low reps (1–2) offer little room for calculation, while high reps (12+) introduce muscular-endurance factors that reduce strength-specific accuracy."
    },
    {
      "question": "Why is there a maximum of 36 reps in this calculator?",
      "answer": "The Wathen exponential model becomes unstable at very high rep counts due to the decay term approaching zero. Extrapolation beyond approximately 35–37 reps produces mathematically invalid or nonsensical results. The rep limit enforces the practical boundaries of the original regression model."
    }
  ],
  "related_tools": [
    {
      "slug": "one-rep-max-brzycki",
      "title": "One-Rep Max Calculator (Brzycki Formula)",
      "api_url": "https://fitmetriclab.com/api/tools/one-rep-max-brzycki.json",
      "page_url": "https://fitmetriclab.com/en/tools/strength-training/one-rep-max-brzycki/"
    },
    {
      "slug": "one-rep-max-comparison",
      "title": "Multi-Formula 1RM Comparison Calculator",
      "api_url": "https://fitmetriclab.com/api/tools/one-rep-max-comparison.json",
      "page_url": "https://fitmetriclab.com/en/tools/strength-training/one-rep-max-comparison/"
    },
    {
      "slug": "one-rep-max-epley",
      "title": "One-Rep Max Calculator (Epley Formula)",
      "api_url": "https://fitmetriclab.com/api/tools/one-rep-max-epley.json",
      "page_url": "https://fitmetriclab.com/en/tools/strength-training/one-rep-max-epley/"
    }
  ],
  "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."
}