Scientific formula reference
Formula library
| Quantity | Formula | Units | Source |
|---|---|---|---|
| Cardiac output | Q̇ = HR × SV | L·min⁻¹ = beats·min⁻¹ × L·beat⁻¹ | Standard physiology |
| Fick principle | V̇O₂ = Q̇ × (a–v̄O₂ difference) | mL·min⁻¹ | Fick (1870); standard physiology |
| Relative VO₂ | V̇O₂ (mL·kg⁻¹·min⁻¹) = V̇O₂ (mL·min⁻¹) ÷ mass (kg) | mL·kg⁻¹·min⁻¹ | Standard |
| MET | 1 MET ≈ 3.5 mL O₂·kg⁻¹·min⁻¹ | — | Convention (Compendium of Physical Activities) |
| HRmax (Tanaka) | HRmax = 208 − 0.7 × age | beats·min⁻¹ | Tanaka et al., 2001 |
| Karvonen target HR | HR = (HRmax − HRrest) × % + HRrest | beats·min⁻¹ | Karvonen et al., 1957 |
| Session-RPE load | Load = CR-10 RPE × duration (min) | arbitrary units | Foster et al., 2001 |
| BMR (Mifflin–St Jeor) | 10m + 6.25h − 5a + 5 (men) / −161 (women) | kcal·day⁻¹ | Mifflin et al., 1990 |
| 1RM (Epley) | 1RM = w × (1 + r/30) | kg | Epley, 1985 |
| 1RM (Brzycki) | 1RM = w × 36/(37 − r) | kg | Brzycki, 1993 |
| BMI | BMI = mass ÷ height² | kg·m⁻² | WHO |
| Waist-to-height ratio | WHtR = waist ÷ height | ratio | Ashwell et al., 2012 |
| Stroke volume | SV = EDV − ESV | mL·beat⁻¹ | Standard physiology |
| PCSA | PCSA = (mass × cos θ) ÷ (ρ × fibre length) | cm² | Lieber & Fridén, 2000 |
| Torque | τ = F × moment arm | N·m | Standard mechanics |
| Impulse–momentum | F × t = m × Δv | N·s | Standard mechanics |
| Arterial O₂ content | CaO₂ = 1.34 × Hb × SaO₂ + 0.003 × PaO₂ | mL O₂·dL⁻¹ | Standard physiology |
| Ejection fraction | EF = SV ÷ EDV | % | Standard physiology |
| Cooper 12-min run | VO₂max = (d − 504.9) ÷ 44.73 | mL·kg⁻¹·min⁻¹ | Cooper, 1968 |
| Rockport walk | 132.853 − 0.0769W − 0.3877A + 6.315S − 3.2649T − 0.1565HR | mL·kg⁻¹·min⁻¹ | Kline et al., 1987 |
| Rate of force development | RFD = ΔF ÷ Δt | N·s⁻¹ | Maffiuletti et al., 2016 |
| Energy availability | EA = (energy intake − exercise energy expenditure) ÷ FFM | kcal·kg FFM⁻¹·day⁻¹ | Loucks; IOC consensus |
Other libraries — roadmap
The fitness assessment, exercise technique, sports-performance testing, rehabilitation protocol and nutrition reference libraries are built in Phase 6 (see the completion tracker and the project ROADMAP).