{
  "id": "one-rep-max",
  "version": "d18e4edbd734",
  "status": "published",
  "name": "One Rep Max Calculator",
  "question": "What is my one rep max?",
  "summary": "Estimates the one-repetition maximum (1RM) from a weight lifted for 1 to 10 reps with the Brzycki and Epley equations, or the weight to use for a number of reps.",
  "category": "sports",
  "subcategory": "lifting",
  "url": "https://www.acalculator.org/sports/one-rep-max-calculator",
  "markdown": "https://www.acalculator.org/sports/one-rep-max-calculator.md",
  "kind": "formulas",
  "method": "1RM = weight × 36 ÷ (37 − reps) (Brzycki 1993); Epley (1985): 1RM = weight × (1 + reps ÷ 30).",
  "assumptions": [
    "The set went to failure: you could not have done one more rep with good form.",
    "Reps are from 1 to 10. Both equations lose accuracy with more reps, and they were fit on lifts such as the bench press, squat and deadlift.",
    "Brzycki gives exactly the weight lifted for 1 rep. Epley gives 1/30 more than the weight for 1 rep; that is how the equation is written.",
    "The weight lifted and the one rep max are at most 2,000 lb (907 kg)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "w": {
        "title": "Weight lifted",
        "description": "The weight you lifted for the set, including the bar.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0,
        "maximum": 907.18474
      },
      "r": {
        "title": "Reps",
        "description": "How many full repetitions you did with that weight before you could not do another.",
        "type": "number",
        "minimum": 1,
        "maximum": 10
      },
      "max": {
        "title": "One rep max (Brzycki)",
        "description": "The most you could lift once, estimated with Brzycki’s equation.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0,
        "maximum": 907.18474
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "w",
      "r",
      "max"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "weight": {
      "label": "Weight lifted",
      "description": "The weight you lifted for the set, including the bar.",
      "format": "quantity"
    },
    "reps": {
      "label": "Reps",
      "description": "How many full repetitions you did with that weight before you could not do another.",
      "format": "number"
    },
    "oneRm": {
      "label": "One rep max (Brzycki)",
      "description": "The most you could lift once, estimated with Brzycki’s equation.",
      "format": "quantity",
      "unit": "lb"
    },
    "epley": {
      "label": "One rep max (Epley)",
      "description": "The one rep max from Epley’s equation: weight × (1 + reps ÷ 30).",
      "format": "quantity",
      "unit": "lb"
    },
    "average": {
      "label": "Average of both",
      "description": "The mean of the Brzycki and Epley estimates.",
      "format": "quantity",
      "unit": "lb"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "w": 90.718474,
      "r": 5
    },
    "outputs": {
      "oneRm": 102.05828325,
      "epley": 105.83821966666667,
      "average": 103.94825145833335
    },
    "text": "Lifting 200 lb for 5 reps puts your estimated one rep max at 225 lb."
  },
  "examples": [
    {
      "given": {
        "w": 90.718474,
        "r": 5
      },
      "expect": {
        "max": 102.05828325,
        "epley": 105.83821966666667,
        "average": 103.94825145833335
      },
      "source": "hand calculation in content.mdx: Brzycki (1993) 200 × 36 ÷ 32 = 225 lb = 102.06 kg; Epley (1985) 200 × (1 + 5 ÷ 30) = 233.3 lb = 105.84 kg; mean 229.2 lb",
      "tolerance": 1e-12
    },
    {
      "given": {
        "w": 100,
        "r": 10
      },
      "expect": {
        "max": 133.33333333333334,
        "epley": 133.33333333333331
      },
      "source": "hand calculation in content.mdx: 100 × 36 ÷ 27 = 133.33 kg; 100 × (1 + 10 ÷ 30) = 133.33 kg",
      "tolerance": 1e-12
    },
    {
      "given": {
        "max": 100,
        "r": 8
      },
      "expect": {
        "w": 80.55555555555556
      },
      "source": "hand calculation in content.mdx: weight = 100 × (37 − 8) ÷ 36 = 80.56 kg",
      "tolerance": 1e-12
    },
    {
      "given": {
        "w": 135,
        "max": 150
      },
      "expect": {
        "r": 4.600000000000001
      },
      "source": "hand calculation in content.mdx: reps = 37 − 36 × 135 ÷ 150 = 4.6",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "Brzycki, M. (1993). Strength testing: predicting a one-rep max from reps-to-fatigue. Journal of Physical Education, Recreation and Dance 64(1), 88–90. https://doi.org/10.1080/07303084.1993.10606684",
    "Epley, B. (1985). Poundage chart. In Boyd Epley Workout. Lincoln, NE: Body Enterprises.",
    "LeSuer, D. A., J. H. McCormick, J. L. Mayhew, R. L. Wasserstein, and M. D. Arnold (1997). The accuracy of prediction equations for estimating 1-RM performance in the bench press, squat, and deadlift. Journal of Strength and Conditioning Research 11(4), 211–213.",
    "NIST Special Publication 811 (2008), Appendix B.8: 1 lb = 0.45359237 kg exactly. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "vo2-max",
    "pace"
  ],
  "changelog": []
}