{
  "slug": "one-rep-max-brzycki",
  "title": "One-Rep Max Calculator (Brzycki Formula)",
  "category": "Strength Training",
  "category_slug": "strength-training",
  "tier": 1,
  "summary": "Estimate your one-rep max from sub-maximal lifts using the Brzycki (1993) formula.",
  "description": "This calculator estimates your one-repetition maximum (1RM) using the Brzycki formula, a linear regression model published in 1993 and widely applied in strength training. It requires the weight lifted and the number of repetitions performed (up to 36 reps) and outputs an estimated maximum weight that could be lifted for a single repetition. The formula was derived from barbell-exercise data in trained lifters and is most accurate when reps are kept below 10, as prediction error tends to increase with higher repetition ranges.",
  "page_url": "https://fitmetriclab.com/en/tools/strength-training/one-rep-max-brzycki/",
  "api_url": "https://fitmetriclab.com/api/tools/one-rep-max-brzycki.json",
  "formula": {
    "id": "one_rep_max_brzycki",
    "expression": "\\text{1RM} = w \\times \\frac{36}{37 - 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": "84.4 kg"
  },
  "result_summary_template": "Lifting {weight_kg} for {reps} repetitions, the Brzycki formula estimates a one-rep max of {result}.",
  "methodology": "Applies the Brzycki (1993) formula: 1RM = weight × 36 / (37 - reps). This linear regression model estimates maximal strength from sub-maximal repetitions, using fixed coefficients derived from barbell-exercise data in trained lifters.",
  "sources": [
    {
      "label": "Brzycki M. Strength testing—predicting a one-rep max from reps-to-fatigue. Journal of Physical Education, Recreation & Dance. 1993;64(1):88–90.",
      "url": "https://doi.org/10.1080/07303084.1993.10606684"
    },
    {
      "label": "LeSuer DA, McCormick JH, Mayhew JL, 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):211–213.",
      "url": "https://pubmed.ncbi.nlm.nih.gov/27995264/"
    },
    {
      "label": "Reynolds JM, Gordon TJ, Robergs RA. Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry. J Strength Cond Res. 2006;20(3):584–592.",
      "url": "https://pubmed.ncbi.nlm.nih.gov/16937972/"
    }
  ],
  "faqs": [
    {
      "question": "What is the Brzycki formula and who developed it?",
      "answer": "Matt Brzycki published this linear regression equation in 1993 to estimate one-rep max from sub-maximal lifts. It uses the constants 36 and 37, derived from observed strength data, to extrapolate maximal capacity without requiring a true 1RM test."
    },
    {
      "question": "Why does accuracy drop above 10 reps?",
      "answer": "As repetitions increase beyond 10, muscular endurance and lactate tolerance become limiting factors rather than pure maximal strength. The Brzycki formula assumes a consistent strength-to-endurance relationship that holds best in the 2–10 rep range."
    },
    {
      "question": "Can I use this for Olympic lifts or explosive movements?",
      "answer": "The Brzycki formula was developed using slow-tempo barbell exercises like bench press and squat. Olympic lifts involve technical skill and bar speed that are not captured by rep-based regression, so prediction error may be higher."
    },
    {
      "question": "How does Brzycki compare to other 1RM formulas?",
      "answer": "Brzycki tends to produce slightly higher estimates than Epley or Lander formulas in the mid-rep range. Research shows no single equation is universally superior; individual variation and exercise type both influence which model tracks closest to measured 1RM."
    },
    {
      "question": "Should I test my actual 1RM or rely on the estimate?",
      "answer": "Estimated 1RM values serve as planning benchmarks and training-load references. Direct 1RM testing offers precise data but introduces fatigue and injury risk; many programs use sub-maximal estimates to inform percentage-based programming while reserving true max tests for competition or periodic assessment."
    }
  ],
  "related_tools": [
    {
      "slug": "dots-score",
      "title": "DOTS Score Calculator",
      "api_url": "https://fitmetriclab.com/api/tools/dots-score.json",
      "page_url": "https://fitmetriclab.com/en/tools/strength-training/dots-score/"
    },
    {
      "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."
}