1. Karvonen target HR (the primary output)
The Karvonen method anchors the calculator. The equation is simple:
Target HR = ((HRmax - HRrest) × intensity) + HRrestFor 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 et al. (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 remains available for comparison with watches that still use 220-age.
3. How the pace estimate is calculated
Heart rate is the primary target. When you enter body weight and ruck weight, the tool also estimates a flat-pavement pace that may correspond to the heart rate band.
The calculation has four steps:
- 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). It provides an estimate when no lab measurement is available.
- 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.
- Convert VO2 to metabolic rate in watts using the standard 1 L O2 ≈ 5 kcal and 1 kcal/min = 69.78 W conversions.
- 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.
These conversions add uncertainty. The result shows a pace range and the VO2max estimate used. Adjust the pace using your measured heart rate.
4. Why heart rate comes before pace under load
Research on loaded walking supports using heart rate to adjust pace.
Looney et al. 2021 (PMID 33652153) studied 15 soldiers carrying 0/22/44/66% body mass with the MOLLE 4000 backpack. The study reported that relative work intensity under heavy loads may be better described as a percentage of HRmax than as a percentage of VO2max.
Simpson et al. 2010 (PMID 20962921) studied 18 British Parachute and SAS soldiers carrying a fixed 20 kg pack. Raising speed from 6.4 to 7.4 km/h increased mean heart rate by 20 BPM. A pace change can move heart rate outside the selected band, so the tool treats pace as an estimate.
Where the estimate can miss
- Beta-blockers and AFib change the HR response. Pregnancy and recent cardiac events can also change it. 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 and soft surfaces shift the pace that produces the target HR. Heat and altitude do too, as can dehydration or short sleep.
- The calculator stops its optional pace estimate above 25% of body weight. The cited military studies included heavier loads, but they do not validate this combined estimate for higher-load training or sessions over two hours.
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 may pick up the pace a little if that fits the day's goal. Do not add weight simply to raise your heart rate.
For race pace, interval work, or GORUCK event prep, this is the wrong tool. Those sit in higher zones and need different targets.