{
  "id": "rpe",
  "version": "2b3f1ce57810",
  "status": "published",
  "name": "RPE Calculator",
  "question": "What should I lift at my target RPE?",
  "summary": "Estimates your one-rep max from a set’s weight, reps and RPE (reps in reserve), and the weight to load for a target number of reps at a target RPE.",
  "category": "sports",
  "subcategory": "lifting",
  "url": "https://www.acalculator.org/sports/rpe-calculator",
  "markdown": "https://www.acalculator.org/sports/rpe-calculator.md",
  "kind": "function",
  "method": "Reps in reserve = 10 − RPE; reps to failure n = reps + reps in reserve; 1RM = weight × 36 ÷ (37 − n); target weight = 1RM × (37 − n₂) ÷ 36, with n₂ = target reps + (10 − target RPE).",
  "assumptions": [
    "The RPE scale is the repetitions-in-reserve scale: RPE 10 = no reps left, 9 = 1, 8 = 2, 7 = 3, 6 = 4, and half points in between.",
    "Brzycki’s equation links a weight to the reps you could do to failure; it is meant for 10 reps or fewer, so reps plus reps in reserve must be 10 or fewer."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "w": {
        "title": "Weight lifted",
        "description": "The weight of the set you did, bar included.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0,
        "maximum": 907.18474
      },
      "r": {
        "title": "Reps done",
        "description": "How many reps you did in that set, from 1 to 10.",
        "type": "integer",
        "minimum": 1,
        "maximum": 10
      },
      "rpe": {
        "title": "RPE of that set",
        "description": "How hard the set was on the 6 to 10 RPE scale.",
        "type": "string",
        "enum": [
          "10",
          "9.5",
          "9",
          "8.5",
          "8",
          "7.5",
          "7",
          "6.5",
          "6"
        ]
      },
      "tr": {
        "title": "Target reps",
        "description": "The reps you plan for the next set, from 1 to 10.",
        "type": "integer",
        "minimum": 1,
        "maximum": 10
      },
      "trpe": {
        "title": "Target RPE",
        "description": "How hard the planned set should be, from 6 to 10.",
        "type": "string",
        "enum": [
          "10",
          "9.5",
          "9",
          "8.5",
          "8",
          "7.5",
          "7",
          "6.5",
          "6"
        ]
      }
    }
  },
  "outputs": {
    "target": {
      "label": "Weight for the target set",
      "description": "Estimated 1RM × (37 − target reps to failure) ÷ 36.",
      "format": "quantity",
      "unit": "lb"
    },
    "oneRm": {
      "label": "Estimated one rep max",
      "description": "Weight × 36 ÷ (37 − reps to failure) (Brzycki).",
      "format": "quantity",
      "unit": "lb"
    },
    "rir": {
      "label": "Reps in reserve",
      "description": "10 − RPE: reps you could still have done.",
      "format": "number"
    },
    "targetRir": {
      "label": "Target reps in reserve",
      "description": "10 − target RPE.",
      "format": "number"
    },
    "percent": {
      "label": "Target as % of 1RM",
      "description": "(37 − target reps to failure) ÷ 36 × 100.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "w": 102.05828325,
      "r": 5,
      "rpe": "8",
      "tr": 3,
      "trpe": "9"
    },
    "outputs": {
      "target": 112.26411157500002,
      "oneRm": 122.46993990000001,
      "rir": 2,
      "targetRir": 1,
      "percent": 91.66666666666667
    },
    "text": "From 225 lb × 5 at RPE 8: 2 reps left, load 247.5 lb for 3 reps at RPE 9: 1 rep left."
  },
  "examples": [
    {
      "given": {
        "w": 102.05828325,
        "r": 5,
        "rpe": "8",
        "tr": 3,
        "trpe": "9"
      },
      "expect": {
        "oneRm": 122.4699399,
        "target": 112.264111575,
        "rir": 2,
        "percent": 91.66666666666667
      },
      "source": "Helms et al., Application of the Repetitions in Reserve-Based Rating of Perceived Exertion Scale for Resistance Training, Strength and Conditioning Journal 38(4), 2016, https://doi.org/10.1519/SSC.0000000000000218 (RPE 8 = 2 reps in reserve, RPE 9 = 1); Brzycki, 1993, Strength testing: predicting a one-rep max from reps-to-fatigue, https://doi.org/10.1080/07303084.1993.10606684; hand calculation in content.mdx: 225 × 36 ÷ 30 = 270; 270 × 33 ÷ 36 = 247.5",
      "tolerance": 1e-12
    },
    {
      "given": {
        "w": 100,
        "r": 1,
        "rpe": "10",
        "tr": 5,
        "trpe": "10"
      },
      "expect": {
        "oneRm": 100,
        "target": 88.88888888888889,
        "percent": 88.88888888888889
      },
      "source": "Helms et al., Application of the Repetitions in Reserve-Based Rating of Perceived Exertion Scale for Resistance Training, Strength and Conditioning Journal 38(4), 2016, https://doi.org/10.1519/SSC.0000000000000218 (RPE 10 = maximum effort); Brzycki, 1993, Strength testing: predicting a one-rep max from reps-to-fatigue, https://doi.org/10.1080/07303084.1993.10606684; hand calculation in content.mdx: 100 × 36 ÷ 36 = 100; 100 × (37 − 5) ÷ 36 = 88.89",
      "tolerance": 1e-12
    },
    {
      "given": {
        "w": 140,
        "r": 6,
        "rpe": "7.5",
        "tr": 8,
        "trpe": "8"
      },
      "expect": {
        "rir": 2.5,
        "oneRm": 176.8421052631579
      },
      "source": "Helms et al., Application of the Repetitions in Reserve-Based Rating of Perceived Exertion Scale for Resistance Training, Strength and Conditioning Journal 38(4), 2016, https://doi.org/10.1519/SSC.0000000000000218; Brzycki, 1993, Strength testing: predicting a one-rep max from reps-to-fatigue, https://doi.org/10.1080/07303084.1993.10606684; hand calculation in content.mdx: n = 6 + 2.5 = 8.5; 140 × 36 ÷ 28.5 = 176.84 kg; the target set (8 + 2 = 10 to failure) needs 10 or fewer, so it is allowed",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "Helms, E. R., J. Cronin, A. Storey, and M. C. Zourdos (2016). Application of the Repetitions in Reserve-Based Rating of Perceived Exertion Scale for Resistance Training. Strength and Conditioning Journal 38(4), 42–49. https://doi.org/10.1519/SSC.0000000000000218 (retrieved 2026-10-01)",
    "Helms, E. R. and others (2018). RPE vs. Percentage 1RM Loading in Periodized Programs Matched for Sets and Repetitions. Frontiers in Physiology 9:247 (the RIR scale: 10 = maximal, 9.5 = no more reps but slightly more load, 9 = 1 RIR, 8.5 = 1–2 RIR, 8 = 2 RIR). https://www.frontiersin.org/journals/physiology/articles/10.3389/fphys.2018.00247/full (retrieved 2026-10-01)",
    "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 (retrieved 2026-10-01)"
  ],
  "related": [
    "one-rep-max"
  ],
  "changelog": []
}