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, 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:
- 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.
- 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.
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.