What are the numbers behind an exercise program?
Every fitness routine — whether casual walking, marathon training, or strength cycles — eventually gets reduced to a handful of metrics: how hard the body is working (heart rate, METs), how much oxygen it can use (VO₂max), how strong specific muscles are (1RM), how fast it moves over ground (pace), and how far daily activity accumulates (steps and distance). This page is a calculator for each of these. None of them are measured directly on the field — they are estimated from a few inputs (age, weight, time, distance, heart rate) using regression equations fit to small reference populations. The individual error bars are wide (±5–10% is typical), but the equations are useful for setting zones, tracking change over weeks, and comparing activities side by side.
Three vocab distinctions to keep straight: Heart rate (HR) is beats per minute; maximum HR is the highest HR you can sustain; target HR zone is a window of HR (50–90% of max) within which a specific training adaptation happens. MET (metabolic equivalent) is a unit of effort where 1 MET ≈ resting oxygen consumption; 5 METs = 5× resting. 1RM (one-rep max) is the heaviest weight you can lift once with good form; estimated 1RM from a sub-maximal set (say 8 reps at 80 kg) lets you plan training without testing the actual maximum every week.
Max HR — five formulas, five answers
Max HR is hard to measure (you have to exercise until failure, ideally on a treadmill or bike with a graded protocol), so most calculators estimate it from age. The classic Fox formula 220 − age (1971) is the oldest and most-quoted but has a standard error of ±10–12 bpm — quite wide. Tanaka (2001) is a meta-analysis: 208 − 0.7 × age; lower than Fox at most ages and considered more accurate. Gulati (2010) was fit specifically on women: 206 − 0.88 × age, slightly lower than Tanaka in mid-life. With the sample (age 30), the page returns: Fox 190, Tanaka 187, Gulati 180, Gellish 186, Inbar 185 bpm — a 10-bpm spread. None of these account for training state, genetics, or measurement protocol; they are rough population defaults — Tanaka is the best general default, Gulati fits women, and Fox survives on mental-math convenience.
Training zones — Karvonen vs Zoladz
Once you have a max HR (and ideally a resting HR), you can carve it into 5 training zones: Zone 1 (50–60%, recovery/warm-up), Zone 2 (60–70%, endurance/fat burn), Zone 3 (70–80%, aerobic/cardio), Zone 4 (80–90%, threshold/tempo), Zone 5 (90–100%, anaerobic/sprint). The Karvonen method (HRR-based) uses target = resting + % × (max − resting); it accounts for individual aerobic base because a fit person has a low resting HR and so a higher absolute target for the same effort level. The Zoladz method (max-HR-based) is simpler: target = % × max HR, ignoring resting. With Max 190, Rest 65 (Karvonen): Zone 1 = 128–140, Zone 2 = 140–153, Zone 3 = 153–165, Zone 4 = 165–178, Zone 5 = 178–190 bpm. A common training plan spends 80% of weekly minutes in Zones 1–2 and 20% in Zones 3–5 (polarized training).
VO₂max — the body's aerobic ceiling
VO₂max (maximal oxygen uptake) is the volume of oxygen your body can use per kilogram of body weight per minute during whole-body exercise — the gold standard of cardiorespiratory fitness. It is measured in a lab with a mask and gas analyzer; this page estimates it from field tests. Cooper (1968): run/jog as far as you can in 12 minutes, then VO₂max (mL/kg/min) = (distance_m − 504.9) / 44.73. With the sample (2400 m), VO₂max = 42.4 (Fair for an adult male — Poor <32, Fair 38–44, Good 44–51, Excellent 51–57, Superior ≥57). Rockport (1987): walk one mile as fast as you can, record HR at the end, and use a 5-variable regression (weight, age, gender, time, HR). Cooper demands all-out effort; Rockport is suitable for older or less-fit adults.
1RM — strength from a sub-maximal set
One-rep max (1RM) is the heaviest weight you can lift once with proper form. Testing it directly is fatiguing and risky; the page uses regression equations fit on sub-maximal sets of 1–10 reps: Epley w × (1 + reps/30) (the simplest), Brzycki w × 36 / (37 − reps), Lander w / (1.013 − 0.0267 × reps), Lombardi w × reps^0.10, O'Conner w × (1 + reps/40). With the sample (80 kg × 8 reps), the formulas return 101.3, 99.3, 100.1, 98.5, 96.0 kg — a 5-kg spread. The formulas assume linear fatigue, which breaks down above 10 reps (true 1RM becomes less predictable).
Pace — speed across distance
Running pace is time per unit distance — typically min/km or min/mile. With the sample (5 km in 25:00), pace = 5:00 /km = 8:03 /mi, speed = 12.0 km/h (7.5 mph). The page also reports splits for 400 m, 800 m, 1000 m, and the mile — useful for interval sessions (e.g. "10 × 400 m at 2:00 with 90 sec rest"). Pace is the inverse of speed; the formulas are: pace (s/km) = time (s) / distance (km), speed (km/h) = distance / time × 3600.
Calories — METs × weight × time
Activity calories are estimated by kcal = METs × weight (kg) × time (h). The MET (metabolic equivalent) is a unit where 1 MET = resting energy expenditure (~3.5 mL O₂/kg/min, ~1 kcal/kg/h). The Compendium of Physical Activities catalogs METs for hundreds of activities: walking 3 METs, brisk walking 5, jogging 7, running 10 km/h 9.8, running 12 km/h 12, running 14 km/h 14, cycling moderate 6, swimming 8, strength training 5. With the sample (Running 10 km/h, 9.8 METs, 70 kg, 30 min), calories = 9.8 × 70 × 0.5 = 343 kcal. The equation also ignores EPOC (excess post-exercise oxygen consumption) — the small afterburn that adds 6–15% over the next 24 hours for very hard sessions.
Steps — distance and calories from a count
A pedometer counts steps; turning that into distance requires the user's stride length. The page estimates stride from height: ~0.414 × height in cm (a population average that ignores gender and walking speed). With the sample (10000 steps, height 170 cm), autoStride returns 170 × 0.414 = 70.4 cm, distance = 7040 m = 7.04 km (4.37 mi). Calories: 10000 × 0.04 ≈ 400 kcal (very rough — assumes ~0.04 kcal/step for a typical adult; actual varies by weight and pace). The "10,000 steps a day" target is a Japanese marketing number from the 1960s (万歩計, manpo-kei), not a clinical threshold — modern literature suggests 7,000–8,000 steps is already associated with substantial mortality benefit, with diminishing returns above 10,000.
Common misconceptions
- Max HR formulas are not personal. Even the best formula has ±10 bpm standard error. If training zones feel wrong, measure max HR with a graded exercise test or use a 30-minute time trial as a proxy (avg HR over the last 20 minutes ≈ 95–100% of max for trained athletes).
- VO₂max from a field test is not lab VO₂max. Real lab measurement uses breath-by-breath gas analysis and a graded protocol to volitional exhaustion; field tests stop when motivation runs out. Real lab values run 5–15% higher than the same person tested with Cooper or Rockport.
- 1RM estimates are most reliable for low reps. Below 5 reps the formulas are very accurate (within 2–3%); above 10 reps they drift and can over-estimate by 10% or more. Use direct 1RM testing for the most accurate numbers.
- MET-based calorie burn ignores afterburn, body composition, and efficiency. A 70 kg cyclist and 70 kg runner burn similar kcal/h by MET, but a trained cyclist is mechanically more efficient (more watts per kcal burned) and may actually burn less. Fitness watches use individual calibration to reduce this gap.
Related tools: Body Metrics for the BMI, body-fat, and BSA context that determines weight × METs calorie burn, Nutrition & Diet for the energy-balance side (calories in vs calories out), and Clinical Medicine for the cardiovascular-risk side of elevated resting HR or poor recovery.
