Performance
Equivalency

Enter a performance

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Purdy points
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VO₂ max ml/kg/min
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Effort % VO₂ max
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400m split avg pace
Distance Purdy VO₂ Cameron Riegel Average

Equivalent times across four formulas. The Average column is the unweighted mean; the spread between Riegel and Cameron is your honest uncertainty band.

How each number is computed

Purdy Gardner and Purdy running curve 1970, revised 1981
A log-log fit to the world-record envelope returns a standard time at every distance; the score is 1000 · Tstd(D) / T. Equivalents come from inverting the same envelope. Equal-score runs are equally close to the all-time fastest performance ever recorded at their distance.
VO₂ Daniels and Gilbert oxygen model Oxygen Power, 1979
From the race pace, compute the oxygen cost of running at that velocity (a polynomial in m/min). Divide by the fraction-of-VO₂-max that race duration can sustain (a sum of two exponentials in race duration). The result is implied VO₂ max, a physiological constant. Equivalent times at other distances are the times whose implied VO₂ max equals it, solved by bisection.
Cameron Pete Cameron's distance-aware fade 1998
Generalises Riegel: pace multiplied by a per-distance correction a(D) = 13.49681 − 0.048865·D + 2.438936·D−0.7905 (D in miles) is the invariant. The correction is steeper at sprint distances and gentler past the half marathon, matching observed fade more closely than a single exponent.
Riegel Peter Riegel's exponent RW magazine, 1977
The classic: T₂ = T₁ · (D₂/D₁)1.06. One exponent, every distance. Tends to overpredict marathon time from a 5k and underpredict mile time from a 10k, but it remains the field's most-cited starting point.
Average Unweighted mean
The four formulas disagree by design. Their average is a reasonable single estimate; their spread is a reasonable uncertainty bound. If Cameron and Riegel disagree by more than about 3%, treat the answer with caution.