The short version
You measured a sprint split — maybe a 10–20, a 10–40, or a flying 10 — and you want a 40-yard dash time without making the athlete run another full sprint. The naive approach (multiplying a split by some constant) gets the answer wrong, especially for fast athletes. Tru40 uses a peer-reviewed sprint model to do it properly.
Why simple multipliers fail
Sprint speed is not constant over a 40-yard dash. The first 10 yards is dominated by acceleration; the last 20 by maximum velocity. So a "split × multiplier" approach throws information away — it assumes every athlete distributes effort the same way.
A concrete example: two athletes both run a 1.60-second 10-yard split. Athlete A accelerates more aggressively and tops out earlier; athlete B builds speed more gradually but reaches a higher peak. By the 40-yard mark, athlete B has caught up and passed. A multiplier-based estimator gives both the same 40 time, which is wrong by 0.1–0.2 seconds in either direction.
The error compounds at the extremes. Faster athletes plateau differently than slower ones — they reach maximum velocity sooner and spend more of the 40 at top speed. Any single multiplier you pick will work for one band of athletes and break for the rest.
The mono-exponential sprint model
A better model treats sprinting as exponential acceleration toward a maximum sprint speed (MSS), with a time constant (TAU) that captures how quickly the athlete approaches that ceiling. The model was first proposed by Furusawa, Hill and Parkinson in 1927 — yes, 1927 — and re-validated for modern sprint testing by Samozino, Morin and colleagues between 2015 and 2016.
From a single split, you can't solve for MSS and TAU independently — you need two equations and have one. So Tru40 uses a TAU/MSS ratio (≈ 0.081) derived from the published NFL Combine population data in Clark, Rieger and Bruno (2017), Journal of Strength and Conditioning Research. That gives realistic 40 times across the 4.2–5.2 s range without overfitting.
With the ratio fixed, finding MSS is a one-dimensional search: pick an MSS, compute the split time the model predicts, compare to the measured split, adjust, repeat. The calculator below does this in milliseconds using a bisection method.
A worked example
A college soccer winger runs a flying-10 in 0.95 seconds. What's the equivalent 40-yard dash?
- Convert the flying 10 to metres: 10 yd = 9.144 m, covered in 0.95 s → average velocity ≈ 9.62 m/s during the flying segment.
- Because the athlete is already at near-maximum speed during a flying segment, the model fits an MSS close to 9.7 m/s with TAU ≈ 0.78 s.
- Solving the distance equation for d = 36.576 m (40 yd) gives t ≈ 4.57 seconds.
You can verify this with the calculator below. Pick "Flying 10 yards" in the split type, type 0.95, and you'll get the same answer.
Tru40 calculator
Where the model breaks down
Three caveats worth keeping in mind:
- Hand timing reads fast. A handheld stopwatch typically gets started late, so hand-timed splits read 0.20–0.30 seconds faster than electronic ones. The calculator can't know which method you used — feed it a hand-timed split and the Tru40 result will be biased low by roughly the same amount. Pick a timing method and stick to it across athletes for fair comparisons.
- Start technique matters. The model assumes a standing or three-point start at rest. A rolling start, a track-style block start, or a flying start with extra runway will produce splits that don't fit the population profile, and the Tru40 will read accordingly off.
- Very slow or very young athletes drift outside calibration. The TAU/MSS ratio was fit to NFL Combine population data. For 40 times above 5.5 seconds or for pre-pubertal athletes, the population assumption gets shaky. Use the model qualitatively in that range; don't read individual hundredths.
How Performance House uses Tru40
Inside the platform, every sprint test stores both the raw split and the Tru40 estimate alongside it. The Performance Index uses the Tru40 (so a flying 10 and a full 40 contribute to the speed sub-score on the same scale), but the raw split is preserved so you can still look at acceleration vs. top speed separately.
Practically, that means:
- An athlete who can only run a flying 10 (e.g. limited gym space) still has a comparable speed score.
- An athlete with multiple splits in the same session gets a more confident MSS/TAU fit, and the calculator uses both.
- Trend charts plot the Tru40 estimate so progress is measured on a consistent scale across sessions and across athletes.
The same convertToTru40() function that runs in the platform powers the calculator above — same math, same answer. If you want it built into your test workflow, with the radar, the trend, and the Performance Index already wired up, Performance House is the place. Free for up to 5 athletes.
Frequently asked questions
Why not just multiply a 10-yard split by 4 to get a 40?
Because athletes don't run at the same speed for the whole 40. The first 10 yards is dominated by acceleration; the last 20 by maximum velocity. A 1.6-second 10-yard time × 4 gives a 6.4-second 40, which is unrealistic — actual 40 times for a 1.6 ten are closer to 4.5 s. The error gets worse the faster the athlete.
Can I use Tru40 with a hand-timed split?
Yes, but be aware that hand timing typically reads 0.20–0.30 seconds faster than electronic timing because the timer reacts late on the start. If you input a hand-timed split, the Tru40 estimate will be biased low by roughly the same amount. For comparison across athletes, stick to one timing method.
Does Tru40 work for women, kids, or non-football athletes?
The underlying physics is identical for any athlete. The population calibration uses NFL Combine data, which biases the TAU/MSS ratio toward elite male sprinters. For most field-sport athletes the ratio holds; for very slow runs (>6 seconds for a 40) or very young athletes the estimate gets less reliable.
Can I get an even more accurate estimate with two splits instead of one?
Yes. With two splits you can fit MSS (maximum sprint speed) and TAU (acceleration time constant) independently instead of relying on a population-average ratio. Performance House lets you log multiple splits in a single sprint test and uses both when fitting the curve.
What's a 'flying 10' and why is it useful?
A flying 10 is a 10-yard sprint measured after the athlete has already accelerated — typically from a running start over 10–20 yards into the gate. It isolates maximum velocity from acceleration, which is useful for tracking top-speed development separately from start mechanics. A flying 10 of 1.05 seconds corresponds to roughly 9.7 m/s of max speed.