Force–velocity profiling
Three calculators, one place: build an athlete’s profile from sprint splits, loaded vertical jumps, or a load–velocity test. Sprint and jump give you F0, V0 and peak power; load–velocity gives L0, V0 and slope. Computed instantly on the published Samozino & Morin methods. Your inputs never leave the browser.
Start timing at first movement
Model fit R² = 0.9999 · air density 1.205 kg/m³ · frontal area 0.541 m². Vmax 7.52 m/s, τ 1.211 s.
What this says (and doesn’t)
For context, well-trained sprinters typically sit around F0 7–10 N/kg and V0 7.5–11 m/s (men), or F0 6–9 N/kg and V0 6–9.5 m/s (women) (Haugen et al., 2019). Reading this athlete’s F0 and V0 against the range for their sex shows the balance between force and velocity that coaches call a “force-oriented” or “velocity-oriented” profile. We show the numbers, not a verdict.
- F0 — the theoretical maximum horizontal force the athlete applies at the very start, per kg of body mass.
- V0 — the theoretical top running velocity where no further horizontal force can be applied.
- Pmax — the peak horizontal power, produced at roughly half of V0.
This is a descriptive snapshot — not an “optimal” target or a training prescription. What an ideal sprint profile looks like is genuinely debated in the research, so we don’t claim one.
Push-off distance = your extended lower-limb length minus your crouch (starting) hip height — the range the legs extend through. Typically 0.25–0.40 m.
Use a controlled squat jump
Model fit R² = 0.9963. The method's optimal slope for this power output is -16.75 (per kg).
What this says (and doesn’t)
This athlete's force–velocity slope is shallower than the method's optimal for their power output — a relatively more velocity-oriented profile.
- F0 — the theoretical maximum force the legs apply at zero velocity, per kg of body mass.
- V0 — the theoretical maximum extension velocity at which no further force can be applied.
- vs optimal — the athlete’s F–v slope as a fraction of the slope the method computes as optimal for maximising jump height at their current power output.
The optimal figure is the jump method’s own construct, shown for description. It is not our recommendation of what to train, and it holds power output fixed — a real training block changes power too.
Only used to express the max load as a percentage of body weight.
Same effort, same measurement
The load × velocity product peaks at half of L0 and half of V0. We report that peak in kg·m/s and deliberately don’t call it “Pmax” or convert it to Watts, because the entered load is a mass and the true resistance force depends on the sled or device.
What this says (and doesn’t)
- V0 — extrapolated velocity with no added load.
- L0 — extrapolated load at which velocity would reach zero.
- Peak L·V — the peak of the load × velocity relationship (kg·m/s), at roughly half of each intercept. Not a power in Watts.
This is a descriptive profile. We deliberately don’t map it onto training-load “zones” or tell you which load to train — that prescription is contested and out of scope here.
How it works
Sprint — a mono-exponential velocity model, v(t) = Vmax·(1 − e^(−t/τ)), is fitted to your split-time positions; from the modelled acceleration we compute horizontal force (with an air-drag correction from temperature, pressure, stature and mass) and regress force against velocity for F0, V0, the slope, Pmax = F0·V0/4, and the ratio-of-force terms.
Vertical jump — each loaded squat jump gives one mean force (m·g·(h/hPO + 1)) and one mean velocity (√(g·h/2)); a linear regression across loads yields F0, V0, Sfv and Pmax. Because the jump method also defines an optimal profile for a given power output, we show it as a dashed line and a “% of optimal” figure.
Load–velocity — a straight line through your (load, velocity) points gives the velocity intercept V0, the load intercept L0, the slope, and the peak of the load × velocity relationship (kg·m/s, which we deliberately do not call a Watts “Pmax”).
Every result is descriptive. None of these tools tells you an athlete’s ideal profile or what to train — the jump “optimal” is the method’s own construct at a fixed power output, shown for context, and we deliberately omit the load–velocity training-zone spectrum. What an ideal profile looks like is actively debated, and we don’t make claims we can’t stand behind.
Method & credit
These calculators are our own implementations of published, peer-reviewed methods. We gratefully acknowledge J-B Morin’s freely shared reference spreadsheets, which we used only to validate our numbers — we do not host, redistribute, or copy those files.
- Sprint: Samozino P., Rabita G., Dorel S., et al. (2016). A simple method for measuring power, force, velocity properties, and mechanical effectiveness in sprint running. Scand J Med Sci Sports 26(6):648–658. PMID 25996964 · Morin J-B. & Samozino P. (2016). Interpreting Power-Force-Velocity Profiles for Individualized and Specific Training. Int J Sports Physiol Perform 11(2):267–272. PMID 26694658
- Reference ranges: the sprint F0 / V0 comparison values shown are the elite-athlete ranges reported by Haugen T., Breitschädel F. & Seiler S. (2019). Sprint mechanical variables in elite athletes: are force-velocity profiles sport specific or individual? PLOS ONE 14(7):e0215551. DOI 10.1371/journal.pone.0215551
- Vertical jump: Samozino P. et al. (2008) A simple method for measuring force, velocity and power output during squat jump; Samozino P. et al. (2012) Optimal Force-Velocity Profile in Ballistic Movements—Altius; Samozino P. et al. (2014) Force-Velocity Profile: Imbalance Determination and Effect on Lower Limb Ballistic Performance.
- Load–velocity: the standard linear load–velocity relationship (Jiménez-Reyes, García-Ramos et al.). We compute L0, V0 and the slope only; we do not reproduce the training-zone spectrum the reference sheet renders.
- Reference spreadsheets & interpretation resources: jbmorin.net
Coach a squad of sprinters?
Sprinting is periodization software for sprint & track coaches — plan training blocks, prescribe against Training Max, and keep every athlete’s data in one place. Saving these tests against an athlete is on our roadmap.