To estimate your maximal oxygen uptake (VO₂ max) from routine runs, you’ll need to:
- Estimate the oxygen cost (VO₂) of your running pace,
- Determine your maximum heart rate (HRₘₐₓ) (or measure it directly in a truly maximal effort), and
- Extrapolate your VO₂ max from the submaximal data.
Below is a step‑by‑step recipe using the three runs you logged.
1. Convert pace to speed in m/min
| date | km/h | → m/min |
|---|---|---|
| 2019-01‑28 | 9.141 km/h | 9.141 × 1000 ÷ 60 ≈ 152.35 m/min |
| 2019-01‑29 | 8.132 km/h | 8.132 × 1000 ÷ 60 ≈ 135.53 m/min |
| 2019-02‑07 | 8.602 km/h | 8.602 × 1000 ÷ 60 ≈ 143.37 m/min |
2. Estimate the oxygen cost (VO₂) at that pace
For level ground, the ACSM running‐economy equation applies:
$$
\dot V O_{2,\text{ex}} ;(\mathrm{ml/kg/min})
= 0.2 \times \text{speed (m/min)} + 3.5
$$
| date | speed (m/min) | VO₂_ex (ml/kg/min) |
|---|---|---|
| 2019-01‑28 | 152.35 | 0.2·152.35 + 3.5 ≈ 33.0 |
| 2019-01‑29 | 135.53 | 0.2·135.53 + 3.5 ≈ 30.6 |
| 2019-02‑07 | 143.37 | 0.2·143.37 + 3.5 ≈ 32.2 |
3. Estimate your HRₘₐₓ
If you haven’t performed an all‐out test, use one of the age‑based formulas as an approximation.
A common one is Tanaka et al.:
$$
\text{HR}_{\max} \approx 208 - 0.7 \times \text{age}
$$
(If you know your true maximal heart rate from a field or laboratory test, use that.)
4. Extrapolate VO₂ max from submaximal effort
Under the linear assumption between heart rate and VO₂:
$$
\dot V O_{2,\max}
;=;
\dot V O_{2,\text{ex}}
\times
\frac{\text{HR}{\max}}{\text{HR}{\text{ex}}}
$$
Where:
- $\dot V O_{2,\text{ex}}$ is from step 2,
- $\text{HR}_{\text{ex}}$ is the average heart rate you recorded,
- $\text{HR}_{\max}$ is from step 3.
Example calculation
Let’s say you’re 30 years old. Then
$$
\text{HR}{\max} \approx 208 - 0.7\times30 = 187\ \text{bpm}.
$$
For your 2019-01‑28 run (VO₂_ex ≈ 33.0 ml/kg/min, HR_ex ≈ 167.9 bpm):
$$
\dot V O{2,\max}
= 33.0 \times \frac{187}{167.9}
\approx 33.0 \times 1.114
\approx \mathbf{36.8\ ml/kg/min}.
$$
You would repeat that for each run:
| date | VO₂_ex | HR_ex (bpm) | HRₘₐₓ (187) | VO₂_max (ml/kg/min) |
|---|---|---|---|---|
| 2019-01‑28 | 33.0 | 167.9 | 187 | 33.0 × 187/167.9 ≈ 36.8 |
| 2019-01‑29 | 30.6 | 157.1 | 187 | 30.6 × 187/157.1 ≈ 36.4 |
| 2019-02‑07 | 32.2 | 161.6 | 187 | 32.2 × 187/161.6 ≈ 37.3 |
Averaging these gives you a VO₂ max in the neighborhood of 36–37 ml/kg/min.
5. Alternative: Uth–Sørensen submaximal test
If you also know your resting heart rate (HR_rest), you can use the simpler Uth formula:
$$
\dot V O_{2,\max}
;=;
15.3 \times \frac{\text{HR}{\max}}{\text{HR}{\text{rest}}}
$$
This bypasses the need to estimate VO₂_ex from pace, but does require an accurate resting heart rate (measured in supine rest, ideally first thing in the morning).
Caveats & Tips
- Accuracy hinges on**:
- HRₘₐₓ** being close to your true maximum.
- The linear HR–VO₂ relationship (valid ~50–85% of VO₂ max).
- A perfectly level course (no hills).
- Field vs. lab: A maximal graded exercise test in a lab remains the gold standard; these submaximal estimates usually carry an error of ±5–10%.
- Practical use: Track your estimates over weeks; a rising VO₂ max suggests improving fitness (even if the absolute number is slightly off).
Bottom line:
- Compute your running VO₂ at submax pace using the ACSM equation.
- Estimate or measure your HRₘₐₓ (and maybe HR_rest).
- Extrapolate to VO₂ max via the HR ratio (or Uth formula).
That workflow will yield a reasonable VO₂ max estimate from routine GPS + HR runs.