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Calculator Methodology

How we calculate your Zone 2 heart rate

The Zone 2 calculator combines four pieces of peer-reviewed research: Karvonen 1957 for the heart rate reserve method, Tanaka 2001 for HRmax, Uth-Sorensen 2004 for VO2max estimation, and the Pandolf 1977 load-carriage equation for the pace back-solve. Looney 2021 and Simpson 2010 explain why HR is more trustworthy than pace under a ruck.

By Joel KellyLast reviewed: May 14, 2026

Answer-first summary

Zone 2 = 60-70% of heart rate reserve via the Karvonen method (Karvonen 1957, PMID 13470504). HRmax defaults to Tanaka's 208 - 0.7 × age regression (Tanaka 2001, PMID 11153730), the modern replacement for the unpublished 220-age rule.

When you add body weight and ruck weight, the tool estimates VO2max from your HRmax/HRrest ratio (Uth 2004, PMID 14624296), converts that to a metabolic rate at Zone 2 intensity, and back-solves the Pandolf equation (PMID 908672) to find the walking pace that should produce that effort. Trust the HR reading first - the pace is a starting point.

1. Karvonen target HR (the primary output)

The Karvonen method anchors the calculator. The equation is simple:

Target HR = ((HRmax - HRrest) × intensity) + HRrest

For Zone 2 we use intensity = 0.60 to 0.70 (60-70% of heart rate reserve). The midpoint (0.65) is the value the calculator suggests as a daily target.

2. Why Tanaka 2001 instead of 220-age

The 220-age formula has no peer-reviewed primary source - Fox, Naughton, and Haskell published it as an observational fit in 1971, not as a research-derived equation. It systematically overestimates HRmax in adults over 40 by 5-10 BPM.

Tanaka, Monahan, and Seals (JACC 2001;37(1):153-156, PMID 11153730) derived HRmax = 208 - 0.7 × age from a meta-analysis of 351 studies (492 groups, 18,712 subjects), then cross-validated it on 514 healthy lab subjects. The formula has a standard deviation of about 10 BPM at any given age, which is why the calculator reports a band and discloses the uncertainty.

Both formulas are available in the UI. Tanaka is the default. Fox is provided for users who prefer the legacy framing or cross-comparing with watches that still use 220-age.

3. The pace back-solve (Pandolf + Uth-Sorensen)

Heart rate is the primary target. Pace is the secondary output - an estimate of the walking speed that should land you inside the HR band on flat pavement.

The chain works like this:

  1. Estimate VO2max from HR ratio using Uth-Sorensen (PMID 14624296): VO2max ≈ 15.3 × (HRmax / HRrest). The formula has limits (it overestimates in trained athletes and underestimates in beta-blocker users), but it gives a defensible per-user value without requiring a lab test.
  2. Convert %HRR to %VO2 reserve. Heart rate reserve fraction approximates VO2 reserve fraction across most of the working range, so 60-70% HRR ≈ 60-70% of the gap between resting VO2 (3.5 mL/kg/min) and VO2max.
  3. Convert VO2 to metabolic rate in watts using the standard 1 L O2 ≈ 5 kcal and 1 kcal/min = 69.78 W conversions.
  4. Solve Pandolf for V. At grade = 0 and terrain coefficient eta = 1.0 (paved), the equation reduces to a quadratic in V that yields the walking speed in m/s. We convert to min/mile or min/km for display.

Every step in this chain has friction with real-world data. We expose that honestly: the pace band is bracketed, comes with the explicit VO2max estimate used, and ships with a "trust the HR" reminder on the result screen.

4. Why HR beats pace under load

The load-HR research is the reason this tool defaults to HR over pace - and the reason we cite it on the result screen.

Looney et al. 2021 (PMID 33652153) studied 15 soldiers carrying 0/22/44/66% body mass with the MOLLE 4000 backpack. They concluded: "the relative work intensity of heavy load carriage may be better described when expressed relative to HRmax versus V̇O2max." In other words, %HRmax tracks perceived effort better than %VO2max under heavy loads - making HR-based zoning methodologically defensible for rucking.

Simpson et al. 2010 (PMID 20962921) measured what happens when you push pace under load. With 18 British Parachute and SAS soldiers carrying a 20 kg pack, raising speed from 6.4 to 7.4 km/h increased mean HR by 20 BPM. That is a Zone-shift just from a small pace change. The right adjustment is to slow down, not to ignore HR drift.

Where this calculator gets wrong

  • Beta-blockers, AFib, pregnancy, and recent cardiac events change the HR response. Use RPE ("conversational pace") and check with a clinician.
  • Marathon runners and high-VO2max athletes commonly exceed Tanaka HRmax by 5-10 BPM. The reported band is a starting point, not a hard cap.
  • Resting HR drops 5-10 BPM in the first 3 months of regular cardio training. Recalculate every 4-6 weeks for accuracy.
  • The pace back-solve assumes flat pavement. Hills, soft surfaces, heat, altitude, dehydration, and short sleep all shift the actual pace that produces the target HR.
  • Loads above 50% body mass or sessions over 2 hours are outside the validated load-HR envelope.

How to use the band

Take the middle of the HR band as your default target for slow, conversational rucks. If your watch shows HR climbing toward the top of the band, slow your pace rather than push through. If it sits below the bottom of the band and you feel like you could talk easily, you have room to either add weight or pick up the pace a little - whichever fits the day's goal.

For race pace, interval work, or GORUCK event prep, this is the wrong tool. Those sit in higher zones and need different targets.

Methodology review cadence

This page is reviewed at least quarterly. The Looney lab at USARIEM is actively publishing on heavy-load cardiorespiratory response - if a new equation supersedes the Karvonen + Tanaka + Pandolf combination used here, we update this page within 60 days and bump the last-reviewed date.

Source block

  • Karvonen, 1957

    The effects of training on heart rate; a longitudinal study

    Karvonen MJ, Kentala E, Mustala O. Annales Medicinae Experimentalis et Biologiae Fenniae 35(3):307-315. PMID: 13470504.

    Origin of the heart rate reserve (HRR) method used in the calculator. Target HR = ((HRmax - HRrest) * intensity) + HRrest.

  • Tanaka et al., 2001

    Age-predicted maximal heart rate revisited

    Tanaka H, Monahan KD, Seals DR. Journal of the American College of Cardiology 37(1):153-156. PMID: 11153730. DOI: 10.1016/S0735-1097(00)01054-8.

    The regression equation HRmax = 208 - 0.7 * age, derived from a meta-analysis of 351 studies (492 groups, 18,712 subjects) and cross-validated in 514 lab subjects. Default HRmax formula in this tool.

  • Uth et al., 2004

    Estimation of VO2max from the ratio between HRmax and HRrest - the Heart Rate Ratio Method

    Uth N, Sorensen H, Overgaard K, Pedersen PK. European Journal of Applied Physiology 91(1-2):111-115. PMID: 14624296. DOI: 10.1007/s00421-003-0988-y.

    VO2max approx 15.3 * (HRmax / HRrest), in mL/kg/min. Used to back-solve the Pandolf equation when the user provides body weight and ruck weight.

  • Pandolf et al., 1977

    Predicting energy expenditure with loads while standing or walking very slowly

    Pandolf KB, Givoni B, Goldman RF. Journal of Applied Physiology 43(4):577-581. PMID: 908672. DOI: 10.1152/jappl.1977.43.4.577.

    The load-carriage equation we invert to estimate the walking pace that produces the target metabolic rate at the user's body weight and ruck weight.

  • Simpson et al., 2010

    Effect of load mass on heart rate and oxygen uptake during walking with backpack loads

    Simpson KM, Munro BJ, Steele JR. Applied Physiology, Nutrition, and Metabolism 35(5):650-656. PMID: 20962921. DOI: 10.1139/H10-053.

    Measured a 20 BPM mean HR increase when British Parachute and SAS soldiers raised pace from 6.4 to 7.4 km/h carrying a 20 kg backpack. Anchors the HR-load guidance in the calculator output.

  • Looney et al., 2021

    Cardiorespiratory responses to heavy military load carriage over complex terrain

    Looney DP, Hennessy ER, Potter AW, Pryor JL, Roberts BM, Friedl KE. Applied Ergonomics. PMID: 33652153. DOI: 10.1016/j.apergo.2021.103401.

    Found that under heavy loads (0/22/44/66% body mass with the MOLLE 4000), relative work intensity is better described relative to HRmax than VO2max - validating HR-driven pacing for loaded walking.

Run the calculator

Enter your age, resting heart rate, and (optionally) body weight and ruck weight to see your Zone 2 band and the corresponding walking pace estimate.

Open the Zone 2 calculator